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TheAlgorithms/Python

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TheAlgorithms/Python

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## Audio Filters * [Butterworth Filter](audio_filters/butterworth_filter.py) * [Iir Filter](audio_filters/iir_filter.py) * [Show Response](audio_filters/show_response.py) ## Backtracking * [All Combinations](backtracking/all_combinations.py) * [All Permutations](backtracking/all_permutations.py) * [All Subsequences](backtracking/all_subsequences.py) * [Coloring](backtracking/coloring.py) * [Combination Sum](backtracking/combination_sum.py) * [Crossword Puzzle Solver](backtracking/crossword_puzzle_solver.py) * [Generate Parentheses](backtracking/generate_parentheses.py) * [Hamiltonian Cycle](backtracking/hamiltonian_cycle.py) * [Knight Tour](backtracking/knight_tour.py) * [Match Word Pattern](backtracking/match_word_pattern.py) * [Minimax](backtracking/minimax.py) * [N Queens](backtracking/n_queens.py) * [N Queens Math](backtracking/n_queens_math.py) * [Power Sum](backtracking/power_sum.py) * [Rat In Maze](backtracking/rat_in_maze.py) * [Sudoku](backtracking/sudoku.py) * [Sum Of Subsets](backtracking/sum_of_subsets.py) * [Word Search](backtracking/word_search.py) ## Bit Manipulation * [Binary And Operator](bit_manipulation/binary_and_operator.py) * [Binary Coded Decimal](bit_manipulation/binary_coded_decimal.py) * [Binary Count Setbits](bit_manipulation/binary_count_setbits.py) * [Binary Count Trailing Zeros](bit_manipulation/binary_count_trailing_zeros.py) * [Binary Or Operator](bit_manipulation/binary_or_operator.py) * [Binary Shifts](bit_manipulation/binary_shifts.py) * [Binary Twos Complement](bit_manipulation/binary_twos_complement.py) * [Binary Xor Operator](bit_manipulation/binary_xor_operator.py) * [Bitwise Addition Recursive](bit_manipulation/bitwise_addition_recursive.py) * [Count 1S Brian Kernighan Method](bit_manipulation/count_1s_brian_kernighan_method.py) * [Count Number Of One Bits](bit_manipulation/count_number_of_one_bits.py) * [Excess 3 Code](bit_manipulation/excess_3_code.py) * [Find Previous Power Of Two](bit_manipulation/find_previous_power_of_two.py) * [Gray Code Sequence](bit_manipulation/gray_code_sequence.py) * [Highest Set Bit](bit_manipulation/highest_set_bit.py) * [Index Of Rightmost Set Bit](bit_manipulation/index_of_rightmost_set_bit.py) * [Is Even](bit_manipulation/is_even.py) * [Is Power Of Two](bit_manipulation/is_power_of_two.py) * [Largest Pow Of Two Le Num](bit_manipulation/largest_pow_of_two_le_num.py) * [Missing Number](bit_manipulation/missing_number.py) * [Numbers Different Signs](bit_manipulation/numbers_different_signs.py) * [Power Of 4](bit_manipulation/power_of_4.py) * [Reverse Bits](bit_manipulation/reverse_bits.py) * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py) * [Swap All Odd And Even Bits](bit_manipulation/swap_all_odd_and_even_bits.py) ## Blockchain * [Diophantine Equation](blockchain/diophantine_equation.py) ## Boolean Algebra * [And Gate](boolean_algebra/and_gate.py) * [Imply Gate](boolean_algebra/imply_gate.py) * [Karnaugh Map Simplification](boolean_algebra/karnaugh_map_simplification.py) * [Multiplexer](boolean_algebra/multiplexer.py) * [Nand Gate](boolean_algebra/nand_gate.py) * [Nimply Gate](boolean_algebra/nimply_gate.py) * [Nor Gate](boolean_algebra/nor_gate.py) * [Not Gate](boolean_algebra/not_gate.py) * [Or Gate](boolean_algebra/or_gate.py) * [Quine Mc Cluskey](boolean_algebra/quine_mc_cluskey.py) * [Xnor Gate](boolean_algebra/xnor_gate.py) * [Xor Gate](boolean_algebra/xor_gate.py) ## Cellular Automata * [Conways Game Of Life](cellular_automata/conways_game_of_life.py) * [Game Of Life](cellular_automata/game_of_life.py) * [Langtons Ant](cellular_automata/langtons_ant.py) * [Nagel Schrekenberg](cellular_automata/nagel_schrekenberg.py) * [One Dimensional](cellular_automata/one_dimensional.py) * [Wa Tor](cellular_automata/wa_tor.py) ## Ciphers * [A1Z26](ciphers/a1z26.py) * [Affine Cipher](ciphers/affine_cipher.py) * [Atbash](ciphers/atbash.py) * [Autokey](ciphers/autokey.py) * [Baconian Cipher](ciphers/baconian_cipher.py) * [Base16](ciphers/base16.py) * [Base32](ciphers/base32.py) * [Base64](ciphers/base64.py) * [Base85](ciphers/base85.py) * [Beaufort Cipher](ciphers/beaufort_cipher.py) * [Bifid](ciphers/bifid.py) * [Brute Force Caesar Cipher](ciphers/brute_force_caesar_cipher.py) * [Caesar Cipher](ciphers/caesar_cipher.py) * [Cryptomath Module](ciphers/cryptomath_module.py) * [Decrypt Caesar With Chi Squared](ciphers/decrypt_caesar_with_chi_squared.py) * [Deterministic Miller Rabin](ciphers/deterministic_miller_rabin.py) * [Diffie](ciphers/diffie.py) * [Diffie Hellman](ciphers/diffie_hellman.py) * [Elgamal Key Generator](ciphers/elgamal_key_generator.py) * [Enigma Machine2](ciphers/enigma_machine2.py) * [Fractionated Morse Cipher](ciphers/fractionated_morse_cipher.py) * [Hill Cipher](ciphers/hill_cipher.py) * [Mixed Keyword Cypher](ciphers/mixed_keyword_cypher.py) * [Mono Alphabetic Ciphers](ciphers/mono_alphabetic_ciphers.py) * [Morse Code](ciphers/morse_code.py) * [Onepad Cipher](ciphers/onepad_cipher.py) * [Permutation Cipher](ciphers/permutation_cipher.py) * [Playfair Cipher](ciphers/playfair_cipher.py) * [Polybius](ciphers/polybius.py) * [Porta Cipher](ciphers/porta_cipher.py) * [Rabin Miller](ciphers/rabin_miller.py) * [Rail Fence Cipher](ciphers/rail_fence_cipher.py) * [Rot13](ciphers/rot13.py) * [Rsa Cipher](ciphers/rsa_cipher.py) * [Rsa Factorization](ciphers/rsa_factorization.py) * [Rsa Key Generator](ciphers/rsa_key_generator.py) * [Running Key Cipher](ciphers/running_key_cipher.py) * [Shuffled Shift Cipher](ciphers/shuffled_shift_cipher.py) * [Simple Keyword Cypher](ciphers/simple_keyword_cypher.py) * [Simple Substitution Cipher](ciphers/simple_substitution_cipher.py) * [Transposition Cipher](ciphers/transposition_cipher.py) * [Transposition Cipher Encrypt Decrypt File](ciphers/transposition_cipher_encrypt_decrypt_file.py) * [Trifid Cipher](ciphers/trifid_cipher.py) * [Vernam Cipher](ciphers/vernam_cipher.py) * [Vigenere Cipher](ciphers/vigenere_cipher.py) * [Xor Cipher](ciphers/xor_cipher.py) ## Compression * [Burrows Wheeler](compression/burrows_wheeler.py) * [Huffman](compression/huffman.py) * [Lempel Ziv](compression/lempel_ziv.py) * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py) * [Lz77](compression/lz77.py) * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py) * [Run Length Encoding](compression/run_length_encoding.py) ## Computer Vision * [Flip Augmentation](computer_vision/flip_augmentation.py) * [Haralick Descriptors](computer_vision/haralick_descriptors.py) * [Harris Corner](computer_vision/harris_corner.py) * [Horn Schunck](computer_vision/horn_schunck.py) * [Mean Threshold](computer_vision/mean_threshold.py) * [Mosaic Augmentation](computer_vision/mosaic_augmentation.py) * [Pooling Functions](computer_vision/pooling_functions.py) ## Conversions * [Astronomical Length Scale Conversion](conversions/astronomical_length_scale_conversion.py) * [Binary To Decimal](conversions/binary_to_decimal.py) * [Binary To Hexadecimal](conversions/binary_to_hexadecimal.py) * [Binary To Octal](conversions/binary_to_octal.py) * [Convert Number To Words](conversions/convert_number_to_words.py) * [Decimal To Any](conversions/decimal_to_any.py) * [Decimal To Binary](conversions/decimal_to_binary.py) * [Decimal To Hexadecimal](conversions/decimal_to_hexadecimal.py) * [Decimal To Octal](conversions/decimal_to_octal.py) * [Energy Conversions](conversions/energy_conversions.py) * [Excel Title To Column](conversions/excel_title_to_column.py) * [Hex To Bin](conversions/hex_to_bin.py) * [Hexadecimal To Decimal](conversions/hexadecimal_to_decimal.py) * [Ipv4 Conversion](conversions/ipv4_conversion.py) * [Length Conversion](conversions/length_conversion.py) * [Molecular Chemistry](conversions/molecular_chemistry.py) * [Octal To Binary](conversions/octal_to_binary.py) * [Octal To Decimal](conversions/octal_to_decimal.py) * [Octal To Hexadecimal](conversions/octal_to_hexadecimal.py) * [Prefix Conversions](conversions/prefix_conversions.py) * [Prefix Conversions String](conversions/prefix_conversions_string.py) * [Pressure Conversions](conversions/pressure_conversions.py) * [Rgb Cmyk Conversion](conversions/rgb_cmyk_conversion.py) * [Rgb Hsv Conversion](conversions/rgb_hsv_conversion.py) * [Roman Numerals](conversions/roman_numerals.py) * [Speed Conversions](conversions/speed_conversions.py) * [Temperature Conversions](conversions/temperature_conversions.py) * [Time Conversions](conversions/time_conversions.py) * [Volume Conversions](conversions/volume_conversions.py) * [Weight Conversion](conversions/weight_conversion.py) ## Data Structures * Arrays * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py) * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py) * [Index 2D Array In 1D](data_structures/arrays/index_2d_array_in_1d.py) * [Kth Largest Element](data_structures/arrays/kth_largest_element.py) * [Median Two Array](data_structures/arrays/median_two_array.py) * [Monotonic Array](data_structures/arrays/monotonic_array.py) * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py) * [Permutations](data_structures/arrays/permutations.py) * [Prefix Sum](data_structures/arrays/prefix_sum.py) * [Product Sum](data_structures/arrays/product_sum.py) * [Sparse Table](data_structures/arrays/sparse_table.py) * [Sudoku Solver](data_structures/arrays/sudoku_solver.py) * Binary Tree * [Avl Tree](data_structures/binary_tree/avl_tree.py) * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py) * [Binary Search Tree](data_structures/binary_tree/binary_search_tree.py) * [Binary Search Tree Recursive](data_structures/binary_tree/binary_search_tree_recursive.py) * [Binary Tree Mirror](data_structures/binary_tree/binary_tree_mirror.py) * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py) * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py) * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py) * [Diameter Of Binary Tree](data_structures/binary_tree/diameter_of_binary_tree.py) * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py) * [Distribute Coins](data_structures/binary_tree/distribute_coins.py) * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py) * [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py) * [Floor And Ceiling](data_structures/binary_tree/floor_and_ceiling.py) * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py) * [Is Sorted](data_structures/binary_tree/is_sorted.py) * [Is Sum Tree](data_structures/binary_tree/is_sum_tree.py) * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py) * [Lowest Common Ancestor](data_structures/binary_tree/lowest_common_ancestor.py) * [Maximum Fenwick Tree](data_structures/binary_tree/maximum_fenwick_tree.py) * [Merge Two Binary Trees](data_structures/binary_tree/merge_two_binary_trees.py) * [Mirror Binary Tree](data_structures/binary_tree/mirror_binary_tree.py) * [Non Recursive Segment Tree](data_structures/binary_tree/non_recursive_segment_tree.py) * [Number Of Possible Binary Trees](data_structures/binary_tree/number_of_possible_binary_trees.py) * [Red Black Tree](data_structures/binary_tree/red_black_tree.py) * [Segment Tree](data_structures/binary_tree/segment_tree.py) * [Segment Tree Other](data_structures/binary_tree/segment_tree_other.py) * [Serialize Deserialize Binary Tree](data_structures/binary_tree/serialize_deserialize_binary_tree.py) * [Symmetric Tree](data_structures/binary_tree/symmetric_tree.py) * [Treap](data_structures/binary_tree/treap.py) * [Wavelet Tree](data_structures/binary_tree/wavelet_tree.py) * Disjoint Set * [Alternate Disjoint Set](data_structures/disjoint_set/alternate_disjoint_set.py) * [Disjoint Set](data_structures/disjoint_set/disjoint_set.py) * Hashing * [Bloom Filter](data_structures/hashing/bloom_filter.py) * [Double Hash](data_structures/hashing/double_hash.py) * [Hash Map](data_structures/hashing/hash_map.py) * [Hash Table](data_structures/hashing/hash_table.py) * [Hash Table With Linked List](data_structures/hashing/hash_table_with_linked_list.py) * Number Theory * [Prime Numbers](data_structures/hashing/number_theory/prime_numbers.py) * [Quadratic Probing](data_structures/hashing/quadratic_probing.py) * Tests * [Test Hash Map](data_structures/hashing/tests/test_hash_map.py) * Heap * [Binomial Heap](data_structures/heap/binomial_heap.py) * [Heap](data_structures/heap/heap.py) * [Heap Generic](data_structures/heap/heap_generic.py) * [Max Heap](data_structures/heap/max_heap.py) * [Min Heap](data_structures/heap/min_heap.py) * [Randomized Heap](data_structures/heap/randomized_heap.py) * [Skew Heap](data_structures/heap/skew_heap.py) * Linked List * [Circular Linked List](data_structures/linked_list/circular_linked_list.py) * [Deque Doubly](data_structures/linked_list/deque_doubly.py) * [Doubly Linked List](data_structures/linked_list/doubly_linked_list.py) * [Doubly Linked List Two](data_structures/linked_list/doubly_linked_list_two.py) * [Floyds Cycle Detection](data_structures/linked_list/floyds_cycle_detection.py) * [From Sequence](data_structures/linked_list/from_sequence.py) * [Has Loop](data_structures/linked_list/has_loop.py) * [Is Palindrome](data_structures/linked_list/is_palindrome.py) * [Merge Two Lists](data_structures/linked_list/merge_two_lists.py) * [Middle Element Of Linked List](data_structures/linked_list/middle_element_of_linked_list.py) * [Print Reverse](data_structures/linked_list/print_reverse.py) * [Reverse K Group](data_structures/linked_list/reverse_k_group.py) * [Rotate To The Right](data_structures/linked_list/rotate_to_the_right.py) * [Singly Linked List](data_structures/linked_list/singly_linked_list.py) * [Skip List](data_structures/linked_list/skip_list.py) * [Swap Nodes](data_structures/linked_list/swap_nodes.py) * Queue * [Circular Queue](data_structures/queue/circular_queue.py) * [Circular Queue Linked List](data_structures/queue/circular_queue_linked_list.py) * [Double Ended Queue](data_structures/queue/double_ended_queue.py) * [Linked Queue](data_structures/queue/linked_queue.py) * [Priority Queue Using List](data_structures/queue/priority_queue_using_list.py) * [Queue By List](data_structures/queue/queue_by_list.py) * [Queue By Two Stacks](data_structures/queue/queue_by_two_stacks.py) * [Queue On Pseudo Stack](data_structures/queue/queue_on_pseudo_stack.py) * Stacks * [Balanced Parentheses](data_structures/stacks/balanced_parentheses.py) * [Dijkstras Two Stack Algorithm](data_structures/stacks/dijkstras_two_stack_algorithm.py) * [Infix To Postfix Conversion](data_structures/stacks/infix_to_postfix_conversion.py) * [Infix To Prefix Conversion](data_structures/stacks/infix_to_prefix_conversion.py) * [Next Greater Element](data_structures/stacks/next_greater_element.py) * [Postfix Evaluation](data_structures/stacks/postfix_evaluation.py) * [Prefix Evaluation](data_structures/stacks/prefix_evaluation.py) * [Stack](data_structures/stacks/stack.py) * [Stack Using Two Queues](data_structures/stacks/stack_using_two_queues.py) * [Stack With Doubly Linked List](data_structures/stacks/stack_with_doubly_linked_list.py) * [Stack With Singly Linked List](data_structures/stacks/stack_with_singly_linked_list.py) * [Stock Span Problem](data_structures/stacks/stock_span_problem.py) * Trie * [Radix Tree](data_structures/trie/radix_tree.py) * [Trie](data_structures/trie/trie.py) ## Digital Image Processing * [Change Brightness](digital_image_processing/change_brightness.py) * [Change Contrast](digital_image_processing/change_contrast.py) * [Convert To Negative](digital_image_processing/convert_to_negative.py) * Dithering * [Burkes](digital_image_processing/dithering/burkes.py) * Edge Detection * [Canny](digital_image_processing/edge_detection/canny.py) * Filters * [Bilateral Filter](digital_image_processing/filters/bilateral_filter.py) * [Convolve](digital_image_processing/filters/convolve.py) * [Gabor Filter](digital_image_processing/filters/gabor_filter.py) * [Gaussian Filter](digital_image_processing/filters/gaussian_filter.py) * [Laplacian Filter](digital_image_processing/filters/laplacian_filter.py) * [Local Binary Pattern](digital_image_processing/filters/local_binary_pattern.py) * [Median Filter](digital_image_processing/filters/median_filter.py) * [Sobel Filter](digital_image_processing/filters/sobel_filter.py) * Histogram Equalization * [Histogram Stretch](digital_image_processing/histogram_equalization/histogram_stretch.py) * [Index Calculation](digital_image_processing/index_calculation.py) * Morphological Operations * [Dilation Operation](digital_image_processing/morphological_operations/dilation_operation.py) * [Erosion Operation](digital_image_processing/morphological_operations/erosion_operation.py) * Resize * [Resize](digital_image_processing/resize/resize.py) * Rotation * [Rotation](digital_image_processing/rotation/rotation.py) * [Sepia](digital_image_processing/sepia.py) * [Test Digital Image Processing](digital_image_processing/test_digital_image_processing.py) ## Divide And Conquer * [Closest Pair Of Points](divide_and_conquer/closest_pair_of_points.py) * [Convex Hull](divide_and_conquer/convex_hull.py) * [Heaps Algorithm](divide_and_conquer/heaps_algorithm.py) * [Heaps Algorithm Iterative](divide_and_conquer/heaps_algorithm_iterative.py) * [Inversions](divide_and_conquer/inversions.py) * [Kth Order Statistic](divide_and_conquer/kth_order_statistic.py) * [Max Difference Pair](divide_and_conquer/max_difference_pair.py) * [Max Subarray](divide_and_conquer/max_subarray.py) * [Mergesort](divide_and_conquer/mergesort.py) * [Peak](divide_and_conquer/peak.py) * [Power](divide_and_conquer/power.py) * [Strassen Matrix Multiplication](divide_and_conquer/strassen_matrix_multiplication.py) ## Dynamic Programming * [Abbreviation](dynamic_programming/abbreviation.py) * [All Construct](dynamic_programming/all_construct.py) * [Bitmask](dynamic_programming/bitmask.py) * [Catalan Numbers](dynamic_programming/catalan_numbers.py) * [Climbing Stairs](dynamic_programming/climbing_stairs.py) * [Combination Sum Iv](dynamic_programming/combination_sum_iv.py) * [Edit Distance](dynamic_programming/edit_distance.py) * [Factorial](dynamic_programming/factorial.py) * [Fast Fibonacci](dynamic_programming/fast_fibonacci.py) * [Fibonacci](dynamic_programming/fibonacci.py) * [Fizz Buzz](dynamic_programming/fizz_buzz.py) * [Floyd Warshall](dynamic_programming/floyd_warshall.py) * [Integer Partition](dynamic_programming/integer_partition.py) * [Iterating Through Submasks](dynamic_programming/iterating_through_submasks.py) * [Knapsack](dynamic_programming/knapsack.py) * [Largest Divisible Subset](dynamic_programming/largest_divisible_subset.py) * [Longest Common Subsequence](dynamic_programming/longest_common_subsequence.py) * [Longest Common Substring](dynamic_programming/longest_common_substring.py) * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py) * [Longest Increasing Subsequence O(Nlogn)](dynamic_programming/longest_increasing_subsequence_o(nlogn).py) * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py) * [Matrix Chain Multiplication](dynamic_programming/matrix_chain_multiplication.py) * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py) * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py) * [Max Product Subarray](dynamic_programming/max_product_subarray.py) * [Max Subarray Sum](dynamic_programming/max_subarray_sum.py) * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py) * [Minimum Coin Change](dynamic_programming/minimum_coin_change.py) * [Minimum Cost Path](dynamic_programming/minimum_cost_path.py) * [Minimum Partition](dynamic_programming/minimum_partition.py) * [Minimum Size Subarray Sum](dynamic_programming/minimum_size_subarray_sum.py) * [Minimum Squares To Represent A Number](dynamic_programming/minimum_squares_to_represent_a_number.py) * [Minimum Steps To One](dynamic_programming/minimum_steps_to_one.py) * [Minimum Tickets Cost](dynamic_programming/minimum_tickets_cost.py) * [Optimal Binary Search Tree](dynamic_programming/optimal_binary_search_tree.py) * [Palindrome Partitioning](dynamic_programming/palindrome_partitioning.py) * [Regex Match](dynamic_programming/regex_match.py) * [Rod Cutting](dynamic_programming/rod_cutting.py) * [Smith Waterman](dynamic_programming/smith_waterman.py) * [Subset Generation](dynamic_programming/subset_generation.py) * [Sum Of Subset](dynamic_programming/sum_of_subset.py) * [Trapped Water](dynamic_programming/trapped_water.py) * [Tribonacci](dynamic_programming/tribonacci.py) * [Viterbi](dynamic_programming/viterbi.py) * [Wildcard Matching](dynamic_programming/wildcard_matching.py) * [Word Break](dynamic_programming/word_break.py) ## Electronics * [Apparent Power](electronics/apparent_power.py) * [Builtin Voltage](electronics/builtin_voltage.py) * [Capacitor Equivalence](electronics/capacitor_equivalence.py) * [Carrier Concentration](electronics/carrier_concentration.py) * [Charging Capacitor](electronics/charging_capacitor.py) * [Charging Inductor](electronics/charging_inductor.py) * [Circular Convolution](electronics/circular_convolution.py) * [Coulombs Law](electronics/coulombs_law.py) * [Electric Conductivity](electronics/electric_conductivity.py) * [Electric Power](electronics/electric_power.py) * [Electrical Impedance](electronics/electrical_impedance.py) * [Ic 555 Timer](electronics/ic_555_timer.py) * [Ind Reactance](electronics/ind_reactance.py) * [Ohms Law](electronics/ohms_law.py) * [Real And Reactive Power](electronics/real_and_reactive_power.py) * [Resistor Color Code](electronics/resistor_color_code.py) * [Resistor Equivalence](electronics/resistor_equivalence.py) * [Resonant Frequency](electronics/resonant_frequency.py) * [Wheatstone Bridge](electronics/wheatstone_bridge.py) ## File Transfer * [Receive File](file_transfer/receive_file.py) * [Send File](file_transfer/send_file.py) * Tests * [Test Send File](file_transfer/tests/test_send_file.py) ## Financial * [Equated Monthly Installments](financial/equated_monthly_installments.py) * [Exponential Moving Average](financial/exponential_moving_average.py) * [Interest](financial/interest.py) * [Present Value](financial/present_value.py) * [Price Plus Tax](financial/price_plus_tax.py) * [Simple Moving Average](financial/simple_moving_average.py) ## Fractals * [Julia Sets](fractals/julia_sets.py) * [Koch Snowflake](fractals/koch_snowflake.py) * [Mandelbrot](fractals/mandelbrot.py) * [Sierpinski Triangle](fractals/sierpinski_triangle.py) ## Fuzzy Logic * [Fuzzy Operations](fuzzy_logic/fuzzy_operations.py) ## Genetic Algorithm * [Basic String](genetic_algorithm/basic_string.py) ## Geodesy * [Haversine Distance](geodesy/haversine_distance.py) * [Lamberts Ellipsoidal Distance](geodesy/lamberts_ellipsoidal_distance.py) ## Graphics * [Bezier Curve](graphics/bezier_curve.py) * [Vector3 For 2D Rendering](graphics/vector3_for_2d_rendering.py) ## Graphs * [A Star](graphs/a_star.py) * [Articulation Points](graphs/articulation_points.py) * [Basic Graphs](graphs/basic_graphs.py) * [Bellman Ford](graphs/bellman_ford.py) * [Bi Directional Dijkstra](graphs/bi_directional_dijkstra.py) * [Bidirectional A Star](graphs/bidirectional_a_star.py) * [Bidirectional Breadth First Search](graphs/bidirectional_breadth_first_search.py) * [Boruvka](graphs/boruvka.py) * [Breadth First Search](graphs/breadth_first_search.py) * [Breadth First Search 2](graphs/breadth_first_search_2.py) * [Breadth First Search Shortest Path](graphs/breadth_first_search_shortest_path.py) * [Breadth First Search Shortest Path 2](graphs/breadth_first_search_shortest_path_2.py) * [Breadth First Search Zero One Shortest Path](graphs/breadth_first_search_zero_one_shortest_path.py) * [Check Bipatrite](graphs/check_bipatrite.py) * [Check Cycle](graphs/check_cycle.py) * [Connected Components](graphs/connected_components.py) * [Deep Clone Graph](graphs/deep_clone_graph.py) * [Depth First Search](graphs/depth_first_search.py) * [Depth First Search 2](graphs/depth_first_search_2.py) * [Dijkstra](graphs/dijkstra.py) * [Dijkstra 2](graphs/dijkstra_2.py) * [Dijkstra Algorithm](graphs/dijkstra_algorithm.py) * [Dijkstra Alternate](graphs/dijkstra_alternate.py) * [Dijkstra Binary Grid](graphs/dijkstra_binary_grid.py) * [Dinic](graphs/dinic.py) * [Directed And Undirected (Weighted) Graph](graphs/directed_and_undirected_(weighted)_graph.py) * [Edmonds Karp Multiple Source And Sink](graphs/edmonds_karp_multiple_source_and_sink.py) * [Eulerian Path And Circuit For Undirected Graph](graphs/eulerian_path_and_circuit_for_undirected_graph.py) * [Even Tree](graphs/even_tree.py) * [Finding Bridges](graphs/finding_bridges.py) * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py) * [G Topological Sort](graphs/g_topological_sort.py) * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py) * [Graph Adjacency List](graphs/graph_adjacency_list.py) * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py) * [Graph List](graphs/graph_list.py) * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py) * [Greedy Best First](graphs/greedy_best_first.py) * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py) * [Kahns Algorithm Long](graphs/kahns_algorithm_long.py) * [Kahns Algorithm Topo](graphs/kahns_algorithm_topo.py) * [Karger](graphs/karger.py) * [Markov Chain](graphs/markov_chain.py) * [Matching Min Vertex Cover](graphs/matching_min_vertex_cover.py) * [Minimum Path Sum](graphs/minimum_path_sum.py) * [Minimum Spanning Tree Boruvka](graphs/minimum_spanning_tree_boruvka.py) * [Minimum Spanning Tree Kruskal](graphs/minimum_spanning_tree_kruskal.py) * [Minimum Spanning Tree Kruskal2](graphs/minimum_spanning_tree_kruskal2.py) * [Minimum Spanning Tree Prims](graphs/minimum_spanning_tree_prims.py) * [Minimum Spanning Tree Prims2](graphs/minimum_spanning_tree_prims2.py) * [Multi Heuristic Astar](graphs/multi_heuristic_astar.py) * [Page Rank](graphs/page_rank.py) * [Prim](graphs/prim.py) * [Random Graph Generator](graphs/random_graph_generator.py) * [Scc Kosaraju](graphs/scc_kosaraju.py) * [Strongly Connected Components](graphs/strongly_connected_components.py) * [Tarjans Scc](graphs/tarjans_scc.py) * Tests * [Test Min Spanning Tree Kruskal](graphs/tests/test_min_spanning_tree_kruskal.py) * [Test Min Spanning Tree Prim](graphs/tests/test_min_spanning_tree_prim.py) ## Greedy Methods * [Best Time To Buy And Sell Stock](greedy_methods/best_time_to_buy_and_sell_stock.py) * [Fractional Cover Problem](greedy_methods/fractional_cover_problem.py) * [Fractional Knapsack](greedy_methods/fractional_knapsack.py) * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py) * [Gas Station](greedy_methods/gas_station.py) * [Minimum Coin Change](greedy_methods/minimum_coin_change.py) * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py) * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py) ## Hashes * [Adler32](hashes/adler32.py) * [Chaos Machine](hashes/chaos_machine.py) * [Djb2](hashes/djb2.py) * [Elf](hashes/elf.py) * [Enigma Machine](hashes/enigma_machine.py) * [Fletcher16](hashes/fletcher16.py) * [Hamming Code](hashes/hamming_code.py) * [Luhn](hashes/luhn.py) * [Md5](hashes/md5.py) * [Sdbm](hashes/sdbm.py) * [Sha1](hashes/sha1.py) * [Sha256](hashes/sha256.py) ## Knapsack * [Greedy Knapsack](knapsack/greedy_knapsack.py) * [Knapsack](knapsack/knapsack.py) * [Recursive Approach Knapsack](knapsack/recursive_approach_knapsack.py) * Tests * [Test Greedy Knapsack](knapsack/tests/test_greedy_knapsack.py) * [Test Knapsack](knapsack/tests/test_knapsack.py) ## Linear Algebra * [Gaussian Elimination](linear_algebra/gaussian_elimination.py) * [Jacobi Iteration Method](linear_algebra/jacobi_iteration_method.py) * [Lu Decomposition](linear_algebra/lu_decomposition.py) * Src * [Conjugate Gradient](linear_algebra/src/conjugate_gradient.py) * Gaussian Elimination Pivoting * [Gaussian Elimination Pivoting](linear_algebra/src/gaussian_elimination_pivoting/gaussian_elimination_pivoting.py) * [Lib](linear_algebra/src/lib.py) * [Polynom For Points](linear_algebra/src/polynom_for_points.py) * [Power Iteration](linear_algebra/src/power_iteration.py) * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py) * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py) * [Schur Complement](linear_algebra/src/schur_complement.py) * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py) * [Transformations 2D](linear_algebra/src/transformations_2d.py) ## Linear Programming * [Simplex](linear_programming/simplex.py) ## Machine Learning * [Apriori Algorithm](machine_learning/apriori_algorithm.py) * [Astar](machine_learning/astar.py) * [Automatic Differentiation](machine_learning/automatic_differentiation.py) * [Data Transformations](machine_learning/data_transformations.py) * [Decision Tree](machine_learning/decision_tree.py) * [Dimensionality Reduction](machine_learning/dimensionality_reduction.py) * Forecasting * [Run](machine_learning/forecasting/run.py) * [Frequent Pattern Growth](machine_learning/frequent_pattern_growth.py) * [Gradient Boosting Classifier](machine_learning/gradient_boosting_classifier.py) * [Gradient Descent](machine_learning/gradient_descent.py) * [K Means Clust](machine_learning/k_means_clust.py) * [K Nearest Neighbours](machine_learning/k_nearest_neighbours.py) * [Linear Discriminant Analysis](machine_learning/linear_discriminant_analysis.py) * [Linear Regression](machine_learning/linear_regression.py) * Local Weighted Learning * [Local Weighted Learning](machine_learning/local_weighted_learning/local_weighted_learning.py) * [Logistic Regression](machine_learning/logistic_regression.py) * [Loss Functions](machine_learning/loss_functions.py) * [Mfcc](machine_learning/mfcc.py) * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py) * [Polynomial Regression](machine_learning/polynomial_regression.py) * [Scoring Functions](machine_learning/scoring_functions.py) * [Self Organizing Map](machine_learning/self_organizing_map.py) * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py) * [Similarity Search](machine_learning/similarity_search.py) * [Support Vector Machines](machine_learning/support_vector_machines.py) * [Word Frequency Functions](machine_learning/word_frequency_functions.py) * [Xgboost Classifier](machine_learning/xgboost_classifier.py) * [Xgboost Regressor](machine_learning/xgboost_regressor.py) ## Maths * [Abs](maths/abs.py) * [Addition Without Arithmetic](maths/addition_without_arithmetic.py) * [Aliquot Sum](maths/aliquot_sum.py) * [Allocation Number](maths/allocation_number.py) * [Arc Length](maths/arc_length.py) * [Area](maths/area.py) * [Area Under Curve](maths/area_under_curve.py) * [Average Absolute Deviation](maths/average_absolute_deviation.py) * [Average Mean](maths/average_mean.py) * [Average Median](maths/average_median.py) * [Average Mode](maths/average_mode.py) * [Bailey Borwein Plouffe](maths/bailey_borwein_plouffe.py) * [Base Neg2 Conversion](maths/base_neg2_conversion.py) * [Basic Maths](maths/basic_maths.py) * [Binary Exponentiation](maths/binary_exponentiation.py) * [Binary Multiplication](maths/binary_multiplication.py) * [Binomial Coefficient](maths/binomial_coefficient.py) * [Binomial Distribution](maths/binomial_distribution.py) * [Ceil](maths/ceil.py) * [Chebyshev Distance](maths/chebyshev_distance.py) * [Check Polygon](maths/check_polygon.py) * [Chinese Remainder Theorem](maths/chinese_remainder_theorem.py) * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py) * [Collatz Sequence](maths/collatz_sequence.py) * [Combinations](maths/combinations.py) * [Continued Fraction](maths/continued_fraction.py) * [Decimal Isolate](maths/decimal_isolate.py) * [Decimal To Fraction](maths/decimal_to_fraction.py) * [Dodecahedron](maths/dodecahedron.py) * [Double Factorial](maths/double_factorial.py) * [Dual Number Automatic Differentiation](maths/dual_number_automatic_differentiation.py) * [Entropy](maths/entropy.py) * [Euclidean Distance](maths/euclidean_distance.py) * [Euler Method](maths/euler_method.py) * [Euler Modified](maths/euler_modified.py) * [Eulers Totient](maths/eulers_totient.py) * [Extended Euclidean Algorithm](maths/extended_euclidean_algorithm.py) * [Factorial](maths/factorial.py) * [Factors](maths/factors.py) * [Fast Inverse Sqrt](maths/fast_inverse_sqrt.py) * [Fermat Little Theorem](maths/fermat_little_theorem.py) * [Fibonacci](maths/fibonacci.py) * [Find Max](maths/find_max.py) * [Find Min](maths/find_min.py) * [Floor](maths/floor.py) * [Gamma](maths/gamma.py) * [Gaussian](maths/gaussian.py) * [Gaussian Error Linear Unit](maths/gaussian_error_linear_unit.py) * [Gcd Of N Numbers](maths/gcd_of_n_numbers.py) * [Germain Primes](maths/germain_primes.py) * [Greatest Common Divisor](maths/greatest_common_divisor.py) * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py) * [Integer Square Root](maths/integer_square_root.py) * [Interquartile Range](maths/interquartile_range.py) * [Is Int Palindrome](maths/is_int_palindrome.py) * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py) * [Is Square Free](maths/is_square_free.py) * [Jaccard Similarity](maths/jaccard_similarity.py) * [Joint Probability Distribution](maths/joint_probability_distribution.py) * [Josephus Problem](maths/josephus_problem.py) * [Juggler Sequence](maths/juggler_sequence.py) * [Karatsuba](maths/karatsuba.py) * [Kth Lexicographic Permutation](maths/kth_lexicographic_permutation.py) * [Largest Of Very Large Numbers](maths/largest_of_very_large_numbers.py) * [Least Common Multiple](maths/least_common_multiple.py) * [Line Length](maths/line_length.py) * [Liouville Lambda](maths/liouville_lambda.py) * [Lucas Lehmer Primality Test](maths/lucas_lehmer_primality_test.py) * [Lucas Series](maths/lucas_series.py) * [Maclaurin Series](maths/maclaurin_series.py) * [Manhattan Distance](maths/manhattan_distance.py) * [Matrix Exponentiation](maths/matrix_exponentiation.py) * [Max Sum Sliding Window](maths/max_sum_sliding_window.py) * [Median Of Two Arrays](maths/median_of_two_arrays.py) * [Minkowski Distance](maths/minkowski_distance.py) * [Mobius Function](maths/mobius_function.py) * [Modular Division](maths/modular_division.py) * [Modular Exponential](maths/modular_exponential.py) * [Monte Carlo](maths/monte_carlo.py) * [Monte Carlo Dice](maths/monte_carlo_dice.py) * [Number Of Digits](maths/number_of_digits.py) * Numerical Analysis * [Adams Bashforth](maths/numerical_analysis/adams_bashforth.py) * [Bisection](maths/numerical_analysis/bisection.py) * [Bisection 2](maths/numerical_analysis/bisection_2.py) * [Integration By Simpson Approx](maths/numerical_analysis/integration_by_simpson_approx.py) * [Intersection](maths/numerical_analysis/intersection.py) * [Nevilles Method](maths/numerical_analysis/nevilles_method.py) * [Newton Forward Interpolation](maths/numerical_analysis/newton_forward_interpolation.py) * [Newton Raphson](maths/numerical_analysis/newton_raphson.py) * [Numerical Integration](maths/numerical_analysis/numerical_integration.py) * [Runge Kutta](maths/numerical_analysis/runge_kutta.py) * [Runge Kutta Fehlberg 45](maths/numerical_analysis/runge_kutta_fehlberg_45.py) * [Runge Kutta Gills](maths/numerical_analysis/runge_kutta_gills.py) * [Secant Method](maths/numerical_analysis/secant_method.py) * [Simpson Rule](maths/numerical_analysis/simpson_rule.py) * [Square Root](maths/numerical_analysis/square_root.py) * [Odd Sieve](maths/odd_sieve.py) * [Perfect Cube](maths/perfect_cube.py) * [Perfect Number](maths/perfect_number.py) * [Perfect Square](maths/perfect_square.py) * [Persistence](maths/persistence.py) * [Pi Generator](maths/pi_generator.py) * [Pi Monte Carlo Estimation](maths/pi_monte_carlo_estimation.py) * [Points Are Collinear 3D](maths/points_are_collinear_3d.py) * [Pollard Rho](maths/pollard_rho.py) * [Polynomial Evaluation](maths/polynomial_evaluation.py) * Polynomials * [Single Indeterminate Operations](maths/polynomials/single_indeterminate_operations.py) * [Power Using Recursion](maths/power_using_recursion.py) * [Prime Check](maths/prime_check.py) * [Prime Factors](maths/prime_factors.py) * [Prime Numbers](maths/prime_numbers.py) * [Prime Sieve Eratosthenes](maths/prime_sieve_eratosthenes.py) * [Primelib](maths/primelib.py) * [Print Multiplication Table](maths/print_multiplication_table.py) * [Pythagoras](maths/pythagoras.py) * [Qr Decomposition](maths/qr_decomposition.py) * [Quadratic Equations Complex Numbers](maths/quadratic_equations_complex_numbers.py) * [Radians](maths/radians.py) * [Radix2 Fft](maths/radix2_fft.py) * [Remove Digit](maths/remove_digit.py) * [Segmented Sieve](maths/segmented_sieve.py) * Series * [Arithmetic](maths/series/arithmetic.py) * [Geometric](maths/series/geometric.py) * [Geometric Series](maths/series/geometric_series.py) * [Harmonic](maths/series/harmonic.py) * [Harmonic Series](maths/series/harmonic_series.py) * [Hexagonal Numbers](maths/series/hexagonal_numbers.py) * [P Series](maths/series/p_series.py) * [Sieve Of Eratosthenes](maths/sieve_of_eratosthenes.py) * [Sigmoid](maths/sigmoid.py) * [Signum](maths/signum.py) * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py) * [Sin](maths/sin.py) * [Sock Merchant](maths/sock_merchant.py) * [Softmax](maths/softmax.py) * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py) * Special Numbers * [Armstrong Numbers](maths/special_numbers/armstrong_numbers.py) * [Automorphic Number](maths/special_numbers/automorphic_number.py) * [Bell Numbers](maths/special_numbers/bell_numbers.py) * [Carmichael Number](maths/special_numbers/carmichael_number.py) * [Catalan Number](maths/special_numbers/catalan_number.py) * [Hamming Numbers](maths/special_numbers/hamming_numbers.py) * [Happy Number](maths/special_numbers/happy_number.py) * [Harshad Numbers](maths/special_numbers/harshad_numbers.py) * [Hexagonal Number](maths/special_numbers/hexagonal_number.py) * [Krishnamurthy Number](maths/special_numbers/krishnamurthy_number.py) * [Perfect Number](maths/special_numbers/perfect_number.py) * [Polygonal Numbers](maths/special_numbers/polygonal_numbers.py) * [Pronic Number](maths/special_numbers/pronic_number.py) * [Proth Number](maths/special_numbers/proth_number.py) * [Triangular Numbers](maths/special_numbers/triangular_numbers.py) * [Ugly Numbers](maths/special_numbers/ugly_numbers.py) * [Weird Number](maths/special_numbers/weird_number.py) * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py) * [Sum Of Digits](maths/sum_of_digits.py) * [Sum Of Geometric Progression](maths/sum_of_geometric_progression.py) * [Sum Of Harmonic Series](maths/sum_of_harmonic_series.py) * [Sumset](maths/sumset.py) * [Sylvester Sequence](maths/sylvester_sequence.py) * [Tanh](maths/tanh.py) * [Test Prime Check](maths/test_prime_check.py) * [Three Sum](maths/three_sum.py) * [Trapezoidal Rule](maths/trapezoidal_rule.py) * [Triplet Sum](maths/triplet_sum.py) * [Twin Prime](maths/twin_prime.py) * [Two Pointer](maths/two_pointer.py) * [Two Sum](maths/two_sum.py) * [Volume](maths/volume.py) * [Zellers Congruence](maths/zellers_congruence.py) ## Matrix * [Binary Search Matrix](matrix/binary_search_matrix.py) * [Count Islands In Matrix](matrix/count_islands_in_matrix.py) * [Count Negative Numbers In Sorted Matrix](matrix/count_negative_numbers_in_sorted_matrix.py) * [Count Paths](matrix/count_paths.py) * [Cramers Rule 2X2](matrix/cramers_rule_2x2.py) * [Inverse Of Matrix](matrix/inverse_of_matrix.py) * [Largest Square Area In Matrix](matrix/largest_square_area_in_matrix.py) * [Matrix Class](matrix/matrix_class.py) * [Matrix Multiplication Recursion](matrix/matrix_multiplication_recursion.py) * [Matrix Operation](matrix/matrix_operation.py) * [Max Area Of Island](matrix/max_area_of_island.py) * [Median Matrix](matrix/median_matrix.py) * [Nth Fibonacci Using Matrix Exponentiation](matrix/nth_fibonacci_using_matrix_exponentiation.py) * [Pascal Triangle](matrix/pascal_triangle.py) * [Rotate Matrix](matrix/rotate_matrix.py) * [Searching In Sorted Matrix](matrix/searching_in_sorted_matrix.py) * [Sherman Morrison](matrix/sherman_morrison.py) * [Spiral Print](matrix/spiral_print.py) * Tests * [Test Matrix Operation](matrix/tests/test_matrix_operation.py) * [Validate Sudoku Board](matrix/validate_sudoku_board.py) ## Networking Flow * [Ford Fulkerson](networking_flow/ford_fulkerson.py) * [Minimum Cut](networking_flow/minimum_cut.py) ## Neural Network * [2 Hidden Layers Neural Network](neural_network/2_hidden_layers_neural_network.py) * Activation Functions * [Binary Step](neural_network/activation_functions/binary_step.py) * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py) * [Leaky Rectified Linear Unit](neural_network/activation_functions/leaky_rectified_linear_unit.py) * [Mish](neural_network/activation_functions/mish.py) * [Rectified Linear Unit](neural_network/activation_functions/rectified_linear_unit.py) * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py) * [Soboleva Modified Hyperbolic Tangent](neural_network/activation_functions/soboleva_modified_hyperbolic_tangent.py) * [Softplus](neural_network/activation_functions/softplus.py) * [Squareplus](neural_network/activation_functions/squareplus.py) * [Swish](neural_network/activation_functions/swish.py) * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py) * [Convolution Neural Network](neural_network/convolution_neural_network.py) * [Simple Neural Network](neural_network/simple_neural_network.py) ## Other * [Activity Selection](other/activity_selection.py) * [Alternative List Arrange](other/alternative_list_arrange.py) * [Bankers Algorithm](other/bankers_algorithm.py) * [Davis Putnam Logemann Loveland](other/davis_putnam_logemann_loveland.py) * [Doomsday](other/doomsday.py) * [Fischer Yates Shuffle](other/fischer_yates_shuffle.py) * [Gauss Easter](other/gauss_easter.py) * [Graham Scan](other/graham_scan.py) * [Greedy](other/greedy.py) * [Guess The Number Search](other/guess_the_number_search.py) * [H Index](other/h_index.py) * [Least Recently Used](other/least_recently_used.py) * [Lfu Cache](other/lfu_cache.py) * [Linear Congruential Generator](other/linear_congruential_generator.py) * [Lru Cache](other/lru_cache.py) * [Magicdiamondpattern](other/magicdiamondpattern.py) * [Majority Vote Algorithm](other/majority_vote_algorithm.py) * [Maximum Subsequence](other/maximum_subsequence.py) * [Nested Brackets](other/nested_brackets.py) * [Number Container System](other/number_container_system.py) * [Password](other/password.py) * [Quine](other/quine.py) * [Scoring Algorithm](other/scoring_algorithm.py) * [Sdes](other/sdes.py) * [Tower Of Hanoi](other/tower_of_hanoi.py) * [Word Search](other/word_search.py) ## Physics * [Altitude Pressure](physics/altitude_pressure.py) * [Archimedes Principle Of Buoyant Force](physics/archimedes_principle_of_buoyant_force.py) * [Basic Orbital Capture](physics/basic_orbital_capture.py) * [Casimir Effect](physics/casimir_effect.py) * [Center Of Mass](physics/center_of_mass.py) * [Centripetal Force](physics/centripetal_force.py) * [Coulombs Law](physics/coulombs_law.py) * [Doppler Frequency](physics/doppler_frequency.py) * [Grahams Law](physics/grahams_law.py) * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py) * [Hubble Parameter](physics/hubble_parameter.py) * [Ideal Gas Law](physics/ideal_gas_law.py) * [In Static Equilibrium](physics/in_static_equilibrium.py) * [Kinetic Energy](physics/kinetic_energy.py) * [Lens Formulae](physics/lens_formulae.py) * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py) * [Malus Law](physics/malus_law.py) * [Mass Energy Equivalence](physics/mass_energy_equivalence.py) * [Mirror Formulae](physics/mirror_formulae.py) * [N Body Simulation](physics/n_body_simulation.py) * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py) * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py) * [Photoelectric Effect](physics/photoelectric_effect.py) * [Potential Energy](physics/potential_energy.py) * [Reynolds Number](physics/reynolds_number.py) * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py) * [Shear Stress](physics/shear_stress.py) * [Speed Of Sound](physics/speed_of_sound.py) * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py) * [Terminal Velocity](physics/terminal_velocity.py) ## Project Euler * Problem 001 * [Sol1](project_euler/problem_001/sol1.py) * [Sol2](project_euler/problem_001/sol2.py) * [Sol3](project_euler/problem_001/sol3.py) * [Sol4](project_euler/problem_001/sol4.py) * [Sol5](project_euler/problem_001/sol5.py) * [Sol6](project_euler/problem_001/sol6.py) * [Sol7](project_euler/problem_001/sol7.py) * Problem 002 * [Sol1](project_euler/problem_002/sol1.py) * [Sol2](project_euler/problem_002/sol2.py) * [Sol3](project_euler/problem_002/sol3.py) * [Sol4](project_euler/problem_002/sol4.py) * [Sol5](project_euler/problem_002/sol5.py) * Problem 003 * [Sol1](project_euler/problem_003/sol1.py) * [Sol2](project_euler/problem_003/sol2.py) * [Sol3](project_euler/problem_003/sol3.py) * Problem 004 * [Sol1](project_euler/problem_004/sol1.py) * [Sol2](project_euler/problem_004/sol2.py) * Problem 005 * [Sol1](project_euler/problem_005/sol1.py) * [Sol2](project_euler/problem_005/sol2.py) * Problem 006 * [Sol1](project_euler/problem_006/sol1.py) * [Sol2](project_euler/problem_006/sol2.py) * [Sol3](project_euler/problem_006/sol3.py) * [Sol4](project_euler/problem_006/sol4.py) * Problem 007 * [Sol1](project_euler/problem_007/sol1.py) * [Sol2](project_euler/problem_007/sol2.py) * [Sol3](project_euler/problem_007/sol3.py) * Problem 008 * [Sol1](project_euler/problem_008/sol1.py) * [Sol2](project_euler/problem_008/sol2.py) * [Sol3](project_euler/problem_008/sol3.py) * Problem 009 * [Sol1](project_euler/problem_009/sol1.py) * [Sol2](project_euler/problem_009/sol2.py) * [Sol3](project_euler/problem_009/sol3.py) * Problem 010 * [Sol1](project_euler/problem_010/sol1.py) * [Sol2](project_euler/problem_010/sol2.py) * [Sol3](project_euler/problem_010/sol3.py) * Problem 011 * [Sol1](project_euler/problem_011/sol1.py) * [Sol2](project_euler/problem_011/sol2.py) * Problem 012 * [Sol1](project_euler/problem_012/sol1.py) * [Sol2](project_euler/problem_012/sol2.py) * Problem 013 * [Sol1](project_euler/problem_013/sol1.py) * Problem 014 * [Sol1](project_euler/problem_014/sol1.py) * [Sol2](project_euler/problem_014/sol2.py) * Problem 015 * [Sol1](project_euler/problem_015/sol1.py) * Problem 016 * [Sol1](project_euler/problem_016/sol1.py) * [Sol2](project_euler/problem_016/sol2.py) * Problem 017 * [Sol1](project_euler/problem_017/sol1.py) * Problem 018 * [Solution](project_euler/problem_018/solution.py) * Problem 019 * [Sol1](project_euler/problem_019/sol1.py) * Problem 020 * [Sol1](project_euler/problem_020/sol1.py) * [Sol2](project_euler/problem_020/sol2.py) * [Sol3](project_euler/problem_020/sol3.py) * [Sol4](project_euler/problem_020/sol4.py) * Problem 021 * [Sol1](project_euler/problem_021/sol1.py) * Problem 022 * [Sol1](project_euler/problem_022/sol1.py) * [Sol2](project_euler/problem_022/sol2.py) * Problem 023 * [Sol1](project_euler/problem_023/sol1.py) * Problem 024 * [Sol1](project_euler/problem_024/sol1.py) * Problem 025 * [Sol1](project_euler/problem_025/sol1.py) * [Sol2](project_euler/problem_025/sol2.py) * [Sol3](project_euler/problem_025/sol3.py) * Problem 026 * [Sol1](project_euler/problem_026/sol1.py) * Problem 027 * [Sol1](project_euler/problem_027/sol1.py) * Problem 028 * [Sol1](project_euler/problem_028/sol1.py) * Problem 029 * [Sol1](project_euler/problem_029/sol1.py) * Problem 030 * [Sol1](project_euler/problem_030/sol1.py) * Problem 031 * [Sol1](project_euler/problem_031/sol1.py) * [Sol2](project_euler/problem_031/sol2.py) * Problem 032 * [Sol32](project_euler/problem_032/sol32.py) * Problem 033 * [Sol1](project_euler/problem_033/sol1.py) * Problem 034 * [Sol1](project_euler/problem_034/sol1.py) * Problem 035 * [Sol1](project_euler/problem_035/sol1.py) * Problem 036 * [Sol1](project_euler/problem_036/sol1.py) * Problem 037 * [Sol1](project_euler/problem_037/sol1.py) * Problem 038 * [Sol1](project_euler/problem_038/sol1.py) * Problem 039 * [Sol1](project_euler/problem_039/sol1.py) * Problem 040 * [Sol1](project_euler/problem_040/sol1.py) * Problem 041 * [Sol1](project_euler/problem_041/sol1.py) * Problem 042 * [Solution42](project_euler/problem_042/solution42.py) * Problem 043 * [Sol1](project_euler/problem_043/sol1.py) * Problem 044 * [Sol1](project_euler/problem_044/sol1.py) * Problem 045 * [Sol1](project_euler/problem_045/sol1.py) * Problem 046 * [Sol1](project_euler/problem_046/sol1.py) * Problem 047 * [Sol1](project_euler/problem_047/sol1.py) * Problem 048 * [Sol1](project_euler/problem_048/sol1.py) * Problem 049 * [Sol1](project_euler/problem_049/sol1.py) * Problem 050 * [Sol1](project_euler/problem_050/sol1.py) * Problem 051 * [Sol1](project_euler/problem_051/sol1.py) * Problem 052 * [Sol1](project_euler/problem_052/sol1.py) * Problem 053 * [Sol1](project_euler/problem_053/sol1.py) * Problem 054 * [Sol1](project_euler/problem_054/sol1.py) * [Test Poker Hand](project_euler/problem_054/test_poker_hand.py) * Problem 055 * [Sol1](project_euler/problem_055/sol1.py) * Problem 056 * [Sol1](project_euler/problem_056/sol1.py) * Problem 057 * [Sol1](project_euler/problem_057/sol1.py) * Problem 058 * [Sol1](project_euler/problem_058/sol1.py) * Problem 059 * [Sol1](project_euler/problem_059/sol1.py) * Problem 062 * [Sol1](project_euler/problem_062/sol1.py) * Problem 063 * [Sol1](project_euler/problem_063/sol1.py) * Problem 064 * [Sol1](project_euler/problem_064/sol1.py) * Problem 065 * [Sol1](project_euler/problem_065/sol1.py) * Problem 067 * [Sol1](project_euler/problem_067/sol1.py) * [Sol2](project_euler/problem_067/sol2.py) * Problem 068 * [Sol1](project_euler/problem_068/sol1.py) * Problem 069 * [Sol1](project_euler/problem_069/sol1.py) * Problem 070 * [Sol1](project_euler/problem_070/sol1.py) * Problem 071 * [Sol1](project_euler/problem_071/sol1.py) * Problem 072 * [Sol1](project_euler/problem_072/sol1.py) * [Sol2](project_euler/problem_072/sol2.py) * Problem 073 * [Sol1](project_euler/problem_073/sol1.py) * Problem 074 * [Sol1](project_euler/problem_074/sol1.py) * [Sol2](project_euler/problem_074/sol2.py) * Problem 075 * [Sol1](project_euler/problem_075/sol1.py) * Problem 076 * [Sol1](project_euler/problem_076/sol1.py) * Problem 077 * [Sol1](project_euler/problem_077/sol1.py) * Problem 078 * [Sol1](project_euler/problem_078/sol1.py) * Problem 079 * [Sol1](project_euler/problem_079/sol1.py) * Problem 080 * [Sol1](project_euler/problem_080/sol1.py) * Problem 081 * [Sol1](project_euler/problem_081/sol1.py) * Problem 082 * [Sol1](project_euler/problem_082/sol1.py) * Problem 085 * [Sol1](project_euler/problem_085/sol1.py) * Problem 086 * [Sol1](project_euler/problem_086/sol1.py) * Problem 087 * [Sol1](project_euler/problem_087/sol1.py) * Problem 089 * [Sol1](project_euler/problem_089/sol1.py) * Problem 091 * [Sol1](project_euler/problem_091/sol1.py) * Problem 092 * [Sol1](project_euler/problem_092/sol1.py) * Problem 094 * [Sol1](project_euler/problem_094/sol1.py) * Problem 097 * [Sol1](project_euler/problem_097/sol1.py) * Problem 099 * [Sol1](project_euler/problem_099/sol1.py) * Problem 100 * [Sol1](project_euler/problem_100/sol1.py) * Problem 101 * [Sol1](project_euler/problem_101/sol1.py) * Problem 102 * [Sol1](project_euler/problem_102/sol1.py) * Problem 104 * [Sol1](project_euler/problem_104/sol1.py) * Problem 107 * [Sol1](project_euler/problem_107/sol1.py) * Problem 109 * [Sol1](project_euler/problem_109/sol1.py) * Problem 112 * [Sol1](project_euler/problem_112/sol1.py) * Problem 113 * [Sol1](project_euler/problem_113/sol1.py) * Problem 114 * [Sol1](project_euler/problem_114/sol1.py) * Problem 115 * [Sol1](project_euler/problem_115/sol1.py) * Problem 116 * [Sol1](project_euler/problem_116/sol1.py) * Problem 117 * [Sol1](project_euler/problem_117/sol1.py) * Problem 119 * [Sol1](project_euler/problem_119/sol1.py) * Problem 120 * [Sol1](project_euler/problem_120/sol1.py) * Problem 121 * [Sol1](project_euler/problem_121/sol1.py) * Problem 123 * [Sol1](project_euler/problem_123/sol1.py) * Problem 125 * [Sol1](project_euler/problem_125/sol1.py) * Problem 129 * [Sol1](project_euler/problem_129/sol1.py) * Problem 131 * [Sol1](project_euler/problem_131/sol1.py) * Problem 135 * [Sol1](project_euler/problem_135/sol1.py) * Problem 144 * [Sol1](project_euler/problem_144/sol1.py) * Problem 145 * [Sol1](project_euler/problem_145/sol1.py) * Problem 173 * [Sol1](project_euler/problem_173/sol1.py) * Problem 174 * [Sol1](project_euler/problem_174/sol1.py) * Problem 180 * [Sol1](project_euler/problem_180/sol1.py) * Problem 187 * [Sol1](project_euler/problem_187/sol1.py) * Problem 188 * [Sol1](project_euler/problem_188/sol1.py) * Problem 191 * [Sol1](project_euler/problem_191/sol1.py) * Problem 203 * [Sol1](project_euler/problem_203/sol1.py) * Problem 205 * [Sol1](project_euler/problem_205/sol1.py) * Problem 206 * [Sol1](project_euler/problem_206/sol1.py) * Problem 207 * [Sol1](project_euler/problem_207/sol1.py) * Problem 234 * [Sol1](project_euler/problem_234/sol1.py) * Problem 301 * [Sol1](project_euler/problem_301/sol1.py) * Problem 493 * [Sol1](project_euler/problem_493/sol1.py) * Problem 551 * [Sol1](project_euler/problem_551/sol1.py) * Problem 587 * [Sol1](project_euler/problem_587/sol1.py) * Problem 686 * [Sol1](project_euler/problem_686/sol1.py) * Problem 800 * [Sol1](project_euler/problem_800/sol1.py) ## Quantum * [Q Fourier Transform](quantum/q_fourier_transform.py) ## Scheduling * [First Come First Served](scheduling/first_come_first_served.py) * [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py) * [Job Sequence With Deadline](scheduling/job_sequence_with_deadline.py) * [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py) * [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py) * [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py) * [Round Robin](scheduling/round_robin.py) * [Shortest Job First](scheduling/shortest_job_first.py) ## Searches * [Binary Search](searches/binary_search.py) * [Binary Tree Traversal](searches/binary_tree_traversal.py) * [Double Linear Search](searches/double_linear_search.py) * [Double Linear Search Recursion](searches/double_linear_search_recursion.py) * [Fibonacci Search](searches/fibonacci_search.py) * [Hill Climbing](searches/hill_climbing.py) * [Interpolation Search](searches/interpolation_search.py) * [Jump Search](searches/jump_search.py) * [Linear Search](searches/linear_search.py) * [Median Of Medians](searches/median_of_medians.py) * [Quick Select](searches/quick_select.py) * [Sentinel Linear Search](searches/sentinel_linear_search.py) * [Simple Binary Search](searches/simple_binary_search.py) * [Simulated Annealing](searches/simulated_annealing.py) * [Tabu Search](searches/tabu_search.py) * [Ternary Search](searches/ternary_search.py) ## Sorts * [Bead Sort](sorts/bead_sort.py) * [Binary Insertion Sort](sorts/binary_insertion_sort.py) * [Bitonic Sort](sorts/bitonic_sort.py) * [Bogo Sort](sorts/bogo_sort.py) * [Bubble Sort](sorts/bubble_sort.py) * [Bucket Sort](sorts/bucket_sort.py) * [Circle Sort](sorts/circle_sort.py) * [Cocktail Shaker Sort](sorts/cocktail_shaker_sort.py) * [Comb Sort](sorts/comb_sort.py) * [Counting Sort](sorts/counting_sort.py) * [Cycle Sort](sorts/cycle_sort.py) * [Double Sort](sorts/double_sort.py) * [Dutch National Flag Sort](sorts/dutch_national_flag_sort.py) * [Exchange Sort](sorts/exchange_sort.py) * [External Sort](sorts/external_sort.py) * [Gnome Sort](sorts/gnome_sort.py) * [Heap Sort](sorts/heap_sort.py) * [Insertion Sort](sorts/insertion_sort.py) * [Intro Sort](sorts/intro_sort.py) * [Iterative Merge Sort](sorts/iterative_merge_sort.py) * [Merge Insertion Sort](sorts/merge_insertion_sort.py) * [Merge Sort](sorts/merge_sort.py) * [Msd Radix Sort](sorts/msd_radix_sort.py) * [Natural Sort](sorts/natural_sort.py) * [Odd Even Sort](sorts/odd_even_sort.py) * [Odd Even Transposition Parallel](sorts/odd_even_transposition_parallel.py) * [Odd Even Transposition Single Threaded](sorts/odd_even_transposition_single_threaded.py) * [Pancake Sort](sorts/pancake_sort.py) * [Patience Sort](sorts/patience_sort.py) * [Pigeon Sort](sorts/pigeon_sort.py) * [Pigeonhole Sort](sorts/pigeonhole_sort.py) * [Quick Sort](sorts/quick_sort.py) * [Quick Sort 3 Partition](sorts/quick_sort_3_partition.py) * [Radix Sort](sorts/radix_sort.py) * [Recursive Insertion Sort](sorts/recursive_insertion_sort.py) * [Recursive Mergesort Array](sorts/recursive_mergesort_array.py) * [Recursive Quick Sort](sorts/recursive_quick_sort.py) * [Selection Sort](sorts/selection_sort.py) * [Shell Sort](sorts/shell_sort.py) * [Shrink Shell Sort](sorts/shrink_shell_sort.py) * [Slowsort](sorts/slowsort.py) * [Stooge Sort](sorts/stooge_sort.py) * [Strand Sort](sorts/strand_sort.py) * [Tim Sort](sorts/tim_sort.py) * [Topological Sort](sorts/topological_sort.py) * [Tree Sort](sorts/tree_sort.py) * [Unknown Sort](sorts/unknown_sort.py) * [Wiggle Sort](sorts/wiggle_sort.py) ## Strings * [Aho Corasick](strings/aho_corasick.py) * [Alternative String Arrange](strings/alternative_string_arrange.py) * [Anagrams](strings/anagrams.py) * [Autocomplete Using Trie](strings/autocomplete_using_trie.py) * [Barcode Validator](strings/barcode_validator.py) * [Bitap String Match](strings/bitap_string_match.py) * [Boyer Moore Search](strings/boyer_moore_search.py) * [Camel Case To Snake Case](strings/camel_case_to_snake_case.py) * [Can String Be Rearranged As Palindrome](strings/can_string_be_rearranged_as_palindrome.py) * [Capitalize](strings/capitalize.py) * [Check Anagrams](strings/check_anagrams.py) * [Credit Card Validator](strings/credit_card_validator.py) * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py) * [Detecting English Programmatically](strings/detecting_english_programmatically.py) * [Dna](strings/dna.py) * [Edit Distance](strings/edit_distance.py) * [Frequency Finder](strings/frequency_finder.py) * [Hamming Distance](strings/hamming_distance.py) * [Indian Phone Validator](strings/indian_phone_validator.py) * [Is Contains Unique Chars](strings/is_contains_unique_chars.py) * [Is Isogram](strings/is_isogram.py) * [Is Pangram](strings/is_pangram.py) * [Is Polish National Id](strings/is_polish_national_id.py) * [Is Spain National Id](strings/is_spain_national_id.py) * [Is Srilankan Phone Number](strings/is_srilankan_phone_number.py) * [Is Valid Email Address](strings/is_valid_email_address.py) * [Jaro Winkler](strings/jaro_winkler.py) * [Join](strings/join.py) * [Knuth Morris Pratt](strings/knuth_morris_pratt.py) * [Levenshtein Distance](strings/levenshtein_distance.py) * [Lower](strings/lower.py) * [Manacher](strings/manacher.py) * [Min Cost String Conversion](strings/min_cost_string_conversion.py) * [Naive String Search](strings/naive_string_search.py) * [Ngram](strings/ngram.py) * [Palindrome](strings/palindrome.py) * [Pig Latin](strings/pig_latin.py) * [Prefix Function](strings/prefix_function.py) * [Rabin Karp](strings/rabin_karp.py) * [Remove Duplicate](strings/remove_duplicate.py) * [Reverse Letters](strings/reverse_letters.py) * [Reverse Words](strings/reverse_words.py) * [Snake Case To Camel Pascal Case](strings/snake_case_to_camel_pascal_case.py) * [Split](strings/split.py) * [String Switch Case](strings/string_switch_case.py) * [Strip](strings/strip.py) * [Text Justification](strings/text_justification.py) * [Title](strings/title.py) * [Top K Frequent Words](strings/top_k_frequent_words.py) * [Upper](strings/upper.py) * [Wave](strings/wave.py) * [Wildcard Pattern Matching](strings/wildcard_pattern_matching.py) * [Word Occurrence](strings/word_occurrence.py) * [Word Patterns](strings/word_patterns.py) * [Z Function](strings/z_function.py) ## Web Programming * [Co2 Emission](web_programming/co2_emission.py) * [Covid Stats Via Xpath](web_programming/covid_stats_via_xpath.py) * [Crawl Google Results](web_programming/crawl_google_results.py) * [Crawl Google Scholar Citation](web_programming/crawl_google_scholar_citation.py) * [Currency Converter](web_programming/currency_converter.py) * [Current Stock Price](web_programming/current_stock_price.py) * [Current Weather](web_programming/current_weather.py) * [Daily Horoscope](web_programming/daily_horoscope.py) * [Download Images From Google Query](web_programming/download_images_from_google_query.py) * [Emails From Url](web_programming/emails_from_url.py) * [Fetch Anime And Play](web_programming/fetch_anime_and_play.py) * [Fetch Bbc News](web_programming/fetch_bbc_news.py) * [Fetch Github Info](web_programming/fetch_github_info.py) * [Fetch Jobs](web_programming/fetch_jobs.py) * [Fetch Quotes](web_programming/fetch_quotes.py) * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py) * [Get Amazon Product Data](web_programming/get_amazon_product_data.py) * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py) * [Get Imdbtop](web_programming/get_imdbtop.py) * [Get Ip Geolocation](web_programming/get_ip_geolocation.py) * [Get Top Billionaires](web_programming/get_top_billionaires.py) * [Get Top Hn Posts](web_programming/get_top_hn_posts.py) * [Get User Tweets](web_programming/get_user_tweets.py) * [Giphy](web_programming/giphy.py) * [Instagram Crawler](web_programming/instagram_crawler.py) * [Instagram Pic](web_programming/instagram_pic.py) * [Instagram Video](web_programming/instagram_video.py) * [Nasa Data](web_programming/nasa_data.py) * [Open Google Results](web_programming/open_google_results.py) * [Random Anime Character](web_programming/random_anime_character.py) * [Recaptcha Verification](web_programming/recaptcha_verification.py) * [Reddit](web_programming/reddit.py) * [Search Books By Isbn](web_programming/search_books_by_isbn.py) * [Slack Message](web_programming/slack_message.py) * [Test Fetch Github Info](web_programming/test_fetch_github_info.py) * [World Covid19 Stats](web_programming/world_covid19_stats.py)

## Audio Filters * [Butterworth Filter](audio_filters/butterworth_filter.py) * [Iir Filter](audio_filters/iir_filter.py) * [Show Response](audio_filters/show_response.py) ## Backtracking * [All Combinations](backtracking/all_combinations.py) * [All Permutations](backtracking/all_permutations.py) * [All Subsequences](backtracking/all_subsequences.py) * [Coloring](backtracking/coloring.py) * [Combination Sum](backtracking/combination_sum.py) * [Crossword Puzzle Solver](backtracking/crossword_puzzle_solver.py) * [Generate Parentheses](backtracking/generate_parentheses.py) * [Hamiltonian Cycle](backtracking/hamiltonian_cycle.py) * [Knight Tour](backtracking/knight_tour.py) * [Match Word Pattern](backtracking/match_word_pattern.py) * [Minimax](backtracking/minimax.py) * [N Queens](backtracking/n_queens.py) * [N Queens Math](backtracking/n_queens_math.py) * [Power Sum](backtracking/power_sum.py) * [Rat In Maze](backtracking/rat_in_maze.py) * [Sudoku](backtracking/sudoku.py) * [Sum Of Subsets](backtracking/sum_of_subsets.py) * [Word Search](backtracking/word_search.py) ## Bit Manipulation * [Binary And Operator](bit_manipulation/binary_and_operator.py) * [Binary Coded Decimal](bit_manipulation/binary_coded_decimal.py) * [Binary Count Setbits](bit_manipulation/binary_count_setbits.py) * [Binary Count Trailing Zeros](bit_manipulation/binary_count_trailing_zeros.py) * [Binary Or Operator](bit_manipulation/binary_or_operator.py) * [Binary Shifts](bit_manipulation/binary_shifts.py) * [Binary Twos Complement](bit_manipulation/binary_twos_complement.py) * [Binary Xor Operator](bit_manipulation/binary_xor_operator.py) * [Bitwise Addition Recursive](bit_manipulation/bitwise_addition_recursive.py) * [Count 1S Brian Kernighan Method](bit_manipulation/count_1s_brian_kernighan_method.py) * [Count Number Of One Bits](bit_manipulation/count_number_of_one_bits.py) * [Excess 3 Code](bit_manipulation/excess_3_code.py) * [Find Previous Power Of Two](bit_manipulation/find_previous_power_of_two.py) * [Gray Code Sequence](bit_manipulation/gray_code_sequence.py) * [Highest Set Bit](bit_manipulation/highest_set_bit.py) * [Index Of Rightmost Set Bit](bit_manipulation/index_of_rightmost_set_bit.py) * [Is Even](bit_manipulation/is_even.py) * [Is Power Of Two](bit_manipulation/is_power_of_two.py) * [Largest Pow Of Two Le Num](bit_manipulation/largest_pow_of_two_le_num.py) * [Missing Number](bit_manipulation/missing_number.py) * [Numbers Different Signs](bit_manipulation/numbers_different_signs.py) * [Power Of 4](bit_manipulation/power_of_4.py) * [Reverse Bits](bit_manipulation/reverse_bits.py) * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py) * [Swap All Odd And Even Bits](bit_manipulation/swap_all_odd_and_even_bits.py) ## Blockchain * [Diophantine Equation](blockchain/diophantine_equation.py) ## Boolean Algebra * [And Gate](boolean_algebra/and_gate.py) * [Imply Gate](boolean_algebra/imply_gate.py) * [Karnaugh Map Simplification](boolean_algebra/karnaugh_map_simplification.py) * [Multiplexer](boolean_algebra/multiplexer.py) * [Nand Gate](boolean_algebra/nand_gate.py) * [Nimply Gate](boolean_algebra/nimply_gate.py) * [Nor Gate](boolean_algebra/nor_gate.py) * [Not Gate](boolean_algebra/not_gate.py) * [Or Gate](boolean_algebra/or_gate.py) * [Quine Mc Cluskey](boolean_algebra/quine_mc_cluskey.py) * [Xnor Gate](boolean_algebra/xnor_gate.py) * [Xor Gate](boolean_algebra/xor_gate.py) ## Cellular Automata * [Conways Game Of Life](cellular_automata/conways_game_of_life.py) * [Game Of Life](cellular_automata/game_of_life.py) * [Langtons Ant](cellular_automata/langtons_ant.py) * [Nagel Schrekenberg](cellular_automata/nagel_schrekenberg.py) * [One Dimensional](cellular_automata/one_dimensional.py) * [Wa Tor](cellular_automata/wa_tor.py) ## Ciphers * [A1Z26](ciphers/a1z26.py) * [Affine Cipher](ciphers/affine_cipher.py) * [Atbash](ciphers/atbash.py) * [Autokey](ciphers/autokey.py) * [Baconian Cipher](ciphers/baconian_cipher.py) * [Base16](ciphers/base16.py) * [Base32](ciphers/base32.py) * [Base64](ciphers/base64.py) * [Base85](ciphers/base85.py) * [Beaufort Cipher](ciphers/beaufort_cipher.py) * [Bifid](ciphers/bifid.py) * [Brute Force Caesar Cipher](ciphers/brute_force_caesar_cipher.py) * [Caesar Cipher](ciphers/caesar_cipher.py) * [Cryptomath Module](ciphers/cryptomath_module.py) * [Decrypt Caesar With Chi Squared](ciphers/decrypt_caesar_with_chi_squared.py) * [Deterministic Miller Rabin](ciphers/deterministic_miller_rabin.py) * [Diffie](ciphers/diffie.py) * [Diffie Hellman](ciphers/diffie_hellman.py) * [Elgamal Key Generator](ciphers/elgamal_key_generator.py) * [Enigma Machine2](ciphers/enigma_machine2.py) * [Fractionated Morse Cipher](ciphers/fractionated_morse_cipher.py) * [Hill Cipher](ciphers/hill_cipher.py) * [Mixed Keyword Cypher](ciphers/mixed_keyword_cypher.py) * [Mono Alphabetic Ciphers](ciphers/mono_alphabetic_ciphers.py) * [Morse Code](ciphers/morse_code.py) * [Onepad Cipher](ciphers/onepad_cipher.py) * [Permutation Cipher](ciphers/permutation_cipher.py) * [Playfair Cipher](ciphers/playfair_cipher.py) * [Polybius](ciphers/polybius.py) * [Porta Cipher](ciphers/porta_cipher.py) * [Rabin Miller](ciphers/rabin_miller.py) * [Rail Fence Cipher](ciphers/rail_fence_cipher.py) * [Rot13](ciphers/rot13.py) * [Rsa Cipher](ciphers/rsa_cipher.py) * [Rsa Factorization](ciphers/rsa_factorization.py) * [Rsa Key Generator](ciphers/rsa_key_generator.py) * [Running Key Cipher](ciphers/running_key_cipher.py) * [Shuffled Shift Cipher](ciphers/shuffled_shift_cipher.py) * [Simple Keyword Cypher](ciphers/simple_keyword_cypher.py) * [Simple Substitution Cipher](ciphers/simple_substitution_cipher.py) * [Transposition Cipher](ciphers/transposition_cipher.py) * [Transposition Cipher Encrypt Decrypt File](ciphers/transposition_cipher_encrypt_decrypt_file.py) * [Trifid Cipher](ciphers/trifid_cipher.py) * [Vernam Cipher](ciphers/vernam_cipher.py) * [Vigenere Cipher](ciphers/vigenere_cipher.py) * [Xor Cipher](ciphers/xor_cipher.py) ## Compression * [Burrows Wheeler](compression/burrows_wheeler.py) * [Huffman](compression/huffman.py) * [Lempel Ziv](compression/lempel_ziv.py) * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py) * [Lz77](compression/lz77.py) * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py) * [Run Length Encoding](compression/run_length_encoding.py) ## Computer Vision * [Flip Augmentation](computer_vision/flip_augmentation.py) * [Haralick Descriptors](computer_vision/haralick_descriptors.py) * [Harris Corner](computer_vision/harris_corner.py) * [Horn Schunck](computer_vision/horn_schunck.py) * [Mean Threshold](computer_vision/mean_threshold.py) * [Mosaic Augmentation](computer_vision/mosaic_augmentation.py) * [Pooling Functions](computer_vision/pooling_functions.py) ## Conversions * [Astronomical Length Scale Conversion](conversions/astronomical_length_scale_conversion.py) * [Binary To Decimal](conversions/binary_to_decimal.py) * [Binary To Hexadecimal](conversions/binary_to_hexadecimal.py) * [Binary To Octal](conversions/binary_to_octal.py) * [Convert Number To Words](conversions/convert_number_to_words.py) * [Decimal To Any](conversions/decimal_to_any.py) * [Decimal To Binary](conversions/decimal_to_binary.py) * [Decimal To Hexadecimal](conversions/decimal_to_hexadecimal.py) * [Decimal To Octal](conversions/decimal_to_octal.py) * [Energy Conversions](conversions/energy_conversions.py) * [Excel Title To Column](conversions/excel_title_to_column.py) * [Hex To Bin](conversions/hex_to_bin.py) * [Hexadecimal To Decimal](conversions/hexadecimal_to_decimal.py) * [Ipv4 Conversion](conversions/ipv4_conversion.py) * [Length Conversion](conversions/length_conversion.py) * [Molecular Chemistry](conversions/molecular_chemistry.py) * [Octal To Binary](conversions/octal_to_binary.py) * [Octal To Decimal](conversions/octal_to_decimal.py) * [Octal To Hexadecimal](conversions/octal_to_hexadecimal.py) * [Prefix Conversions](conversions/prefix_conversions.py) * [Prefix Conversions String](conversions/prefix_conversions_string.py) * [Pressure Conversions](conversions/pressure_conversions.py) * [Rgb Cmyk Conversion](conversions/rgb_cmyk_conversion.py) * [Rgb Hsv Conversion](conversions/rgb_hsv_conversion.py) * [Roman Numerals](conversions/roman_numerals.py) * [Speed Conversions](conversions/speed_conversions.py) * [Temperature Conversions](conversions/temperature_conversions.py) * [Time Conversions](conversions/time_conversions.py) * [Volume Conversions](conversions/volume_conversions.py) * [Weight Conversion](conversions/weight_conversion.py) ## Data Structures * Arrays * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py) * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py) * [Index 2D Array In 1D](data_structures/arrays/index_2d_array_in_1d.py) * [Kth Largest Element](data_structures/arrays/kth_largest_element.py) * [Median Two Array](data_structures/arrays/median_two_array.py) * [Monotonic Array](data_structures/arrays/monotonic_array.py) * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py) * [Permutations](data_structures/arrays/permutations.py) * [Prefix Sum](data_structures/arrays/prefix_sum.py) * [Product Sum](data_structures/arrays/product_sum.py) * [Sparse Table](data_structures/arrays/sparse_table.py) * [Sudoku Solver](data_structures/arrays/sudoku_solver.py) * Binary Tree * [Avl Tree](data_structures/binary_tree/avl_tree.py) * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py) * [Binary Search Tree](data_structures/binary_tree/binary_search_tree.py) * [Binary Search Tree Recursive](data_structures/binary_tree/binary_search_tree_recursive.py) * [Binary Tree Mirror](data_structures/binary_tree/binary_tree_mirror.py) * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py) * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py) * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py) * [Diameter Of Binary Tree](data_structures/binary_tree/diameter_of_binary_tree.py) * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py) * [Distribute Coins](data_structures/binary_tree/distribute_coins.py) * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py) * [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py) * [Floor And Ceiling](data_structures/binary_tree/floor_and_ceiling.py) * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py) * [Is Sorted](data_structures/binary_tree/is_sorted.py) * [Is Sum Tree](data_structures/binary_tree/is_sum_tree.py) * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py) * [Lowest Common Ancestor](data_structures/binary_tree/lowest_common_ancestor.py) * [Maximum Fenwick Tree](data_structures/binary_tree/maximum_fenwick_tree.py) * [Merge Two Binary Trees](data_structures/binary_tree/merge_two_binary_trees.py) * [Mirror Binary Tree](data_structures/binary_tree/mirror_binary_tree.py) * [Non Recursive Segment Tree](data_structures/binary_tree/non_recursive_segment_tree.py) * [Number Of Possible Binary Trees](data_structures/binary_tree/number_of_possible_binary_trees.py) * [Red Black Tree](data_structures/binary_tree/red_black_tree.py) * [Segment Tree](data_structures/binary_tree/segment_tree.py) * [Segment Tree Other](data_structures/binary_tree/segment_tree_other.py) * [Serialize Deserialize Binary Tree](data_structures/binary_tree/serialize_deserialize_binary_tree.py) * [Symmetric Tree](data_structures/binary_tree/symmetric_tree.py) * [Treap](data_structures/binary_tree/treap.py) * [Wavelet Tree](data_structures/binary_tree/wavelet_tree.py) * Disjoint Set * [Alternate Disjoint Set](data_structures/disjoint_set/alternate_disjoint_set.py) * [Disjoint Set](data_structures/disjoint_set/disjoint_set.py) * Hashing * [Bloom Filter](data_structures/hashing/bloom_filter.py) * [Double Hash](data_structures/hashing/double_hash.py) * [Hash Map](data_structures/hashing/hash_map.py) * [Hash Table](data_structures/hashing/hash_table.py) * [Hash Table With Linked List](data_structures/hashing/hash_table_with_linked_list.py) * Number Theory * [Prime Numbers](data_structures/hashing/number_theory/prime_numbers.py) * [Quadratic Probing](data_structures/hashing/quadratic_probing.py) * Tests * [Test Hash Map](data_structures/hashing/tests/test_hash_map.py) * Heap * [Binomial Heap](data_structures/heap/binomial_heap.py) * [Heap](data_structures/heap/heap.py) * [Heap Generic](data_structures/heap/heap_generic.py) * [Max Heap](data_structures/heap/max_heap.py) * [Min Heap](data_structures/heap/min_heap.py) * [Randomized Heap](data_structures/heap/randomized_heap.py) * [Skew Heap](data_structures/heap/skew_heap.py) * Linked List * [Circular Linked List](data_structures/linked_list/circular_linked_list.py) * [Deque Doubly](data_structures/linked_list/deque_doubly.py) * [Doubly Linked List](data_structures/linked_list/doubly_linked_list.py) * [Doubly Linked List Two](data_structures/linked_list/doubly_linked_list_two.py) * [Floyds Cycle Detection](data_structures/linked_list/floyds_cycle_detection.py) * [From Sequence](data_structures/linked_list/from_sequence.py) * [Has Loop](data_structures/linked_list/has_loop.py) * [Is Palindrome](data_structures/linked_list/is_palindrome.py) * [Merge Two Lists](data_structures/linked_list/merge_two_lists.py) * [Middle Element Of Linked List](data_structures/linked_list/middle_element_of_linked_list.py) * [Print Reverse](data_structures/linked_list/print_reverse.py) * [Reverse K Group](data_structures/linked_list/reverse_k_group.py) * [Rotate To The Right](data_structures/linked_list/rotate_to_the_right.py) * [Singly Linked List](data_structures/linked_list/singly_linked_list.py) * [Skip List](data_structures/linked_list/skip_list.py) * [Swap Nodes](data_structures/linked_list/swap_nodes.py) * Queue * [Circular Queue](data_structures/queue/circular_queue.py) * [Circular Queue Linked List](data_structures/queue/circular_queue_linked_list.py) * [Double Ended Queue](data_structures/queue/double_ended_queue.py) * [Linked Queue](data_structures/queue/linked_queue.py) * [Priority Queue Using List](data_structures/queue/priority_queue_using_list.py) * [Queue By List](data_structures/queue/queue_by_list.py) * [Queue By Two Stacks](data_structures/queue/queue_by_two_stacks.py) * [Queue On Pseudo Stack](data_structures/queue/queue_on_pseudo_stack.py) * Stacks * [Balanced Parentheses](data_structures/stacks/balanced_parentheses.py) * [Dijkstras Two Stack Algorithm](data_structures/stacks/dijkstras_two_stack_algorithm.py) * [Infix To Postfix Conversion](data_structures/stacks/infix_to_postfix_conversion.py) * [Infix To Prefix Conversion](data_structures/stacks/infix_to_prefix_conversion.py) * [Next Greater Element](data_structures/stacks/next_greater_element.py) * [Postfix Evaluation](data_structures/stacks/postfix_evaluation.py) * [Prefix Evaluation](data_structures/stacks/prefix_evaluation.py) * [Stack](data_structures/stacks/stack.py) * [Stack Using Two Queues](data_structures/stacks/stack_using_two_queues.py) * [Stack With Doubly Linked List](data_structures/stacks/stack_with_doubly_linked_list.py) * [Stack With Singly Linked List](data_structures/stacks/stack_with_singly_linked_list.py) * [Stock Span Problem](data_structures/stacks/stock_span_problem.py) * Trie * [Radix Tree](data_structures/trie/radix_tree.py) * [Trie](data_structures/trie/trie.py) ## Digital Image Processing * [Change Brightness](digital_image_processing/change_brightness.py) * [Change Contrast](digital_image_processing/change_contrast.py) * [Convert To Negative](digital_image_processing/convert_to_negative.py) * Dithering * [Burkes](digital_image_processing/dithering/burkes.py) * Edge Detection * [Canny](digital_image_processing/edge_detection/canny.py) * Filters * [Bilateral Filter](digital_image_processing/filters/bilateral_filter.py) * [Convolve](digital_image_processing/filters/convolve.py) * [Gabor Filter](digital_image_processing/filters/gabor_filter.py) * [Gaussian Filter](digital_image_processing/filters/gaussian_filter.py) * [Laplacian Filter](digital_image_processing/filters/laplacian_filter.py) * [Local Binary Pattern](digital_image_processing/filters/local_binary_pattern.py) * [Median Filter](digital_image_processing/filters/median_filter.py) * [Sobel Filter](digital_image_processing/filters/sobel_filter.py) * Histogram Equalization * [Histogram Stretch](digital_image_processing/histogram_equalization/histogram_stretch.py) * [Index Calculation](digital_image_processing/index_calculation.py) * Morphological Operations * [Dilation Operation](digital_image_processing/morphological_operations/dilation_operation.py) * [Erosion Operation](digital_image_processing/morphological_operations/erosion_operation.py) * Resize * [Resize](digital_image_processing/resize/resize.py) * Rotation * [Rotation](digital_image_processing/rotation/rotation.py) * [Sepia](digital_image_processing/sepia.py) * [Test Digital Image Processing](digital_image_processing/test_digital_image_processing.py) ## Divide And Conquer * [Closest Pair Of Points](divide_and_conquer/closest_pair_of_points.py) * [Convex Hull](divide_and_conquer/convex_hull.py) * [Heaps Algorithm](divide_and_conquer/heaps_algorithm.py) * [Heaps Algorithm Iterative](divide_and_conquer/heaps_algorithm_iterative.py) * [Inversions](divide_and_conquer/inversions.py) * [Kth Order Statistic](divide_and_conquer/kth_order_statistic.py) * [Max Difference Pair](divide_and_conquer/max_difference_pair.py) * [Max Subarray](divide_and_conquer/max_subarray.py) * [Mergesort](divide_and_conquer/mergesort.py) * [Peak](divide_and_conquer/peak.py) * [Power](divide_and_conquer/power.py) * [Strassen Matrix Multiplication](divide_and_conquer/strassen_matrix_multiplication.py) ## Dynamic Programming * [Abbreviation](dynamic_programming/abbreviation.py) * [All Construct](dynamic_programming/all_construct.py) * [Bitmask](dynamic_programming/bitmask.py) * [Catalan Numbers](dynamic_programming/catalan_numbers.py) * [Climbing Stairs](dynamic_programming/climbing_stairs.py) * [Combination Sum Iv](dynamic_programming/combination_sum_iv.py) * [Edit Distance](dynamic_programming/edit_distance.py) * [Factorial](dynamic_programming/factorial.py) * [Fast Fibonacci](dynamic_programming/fast_fibonacci.py) * [Fibonacci](dynamic_programming/fibonacci.py) * [Fizz Buzz](dynamic_programming/fizz_buzz.py) * [Floyd Warshall](dynamic_programming/floyd_warshall.py) * [Integer Partition](dynamic_programming/integer_partition.py) * [Iterating Through Submasks](dynamic_programming/iterating_through_submasks.py) * [Knapsack](dynamic_programming/knapsack.py) * [Largest Divisible Subset](dynamic_programming/largest_divisible_subset.py) * [Longest Common Subsequence](dynamic_programming/longest_common_subsequence.py) * [Longest Common Substring](dynamic_programming/longest_common_substring.py) * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py) * [Longest Increasing Subsequence O(Nlogn)](dynamic_programming/longest_increasing_subsequence_o(nlogn).py) * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py) * [Matrix Chain Multiplication](dynamic_programming/matrix_chain_multiplication.py) * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py) * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py) * [Max Product Subarray](dynamic_programming/max_product_subarray.py) * [Max Subarray Sum](dynamic_programming/max_subarray_sum.py) * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py) * [Minimum Coin Change](dynamic_programming/minimum_coin_change.py) * [Minimum Cost Path](dynamic_programming/minimum_cost_path.py) * [Minimum Partition](dynamic_programming/minimum_partition.py) * [Minimum Size Subarray Sum](dynamic_programming/minimum_size_subarray_sum.py) * [Minimum Squares To Represent A Number](dynamic_programming/minimum_squares_to_represent_a_number.py) * [Minimum Steps To One](dynamic_programming/minimum_steps_to_one.py) * [Minimum Tickets Cost](dynamic_programming/minimum_tickets_cost.py) * [Optimal Binary Search Tree](dynamic_programming/optimal_binary_search_tree.py) * [Palindrome Partitioning](dynamic_programming/palindrome_partitioning.py) * [Regex Match](dynamic_programming/regex_match.py) * [Rod Cutting](dynamic_programming/rod_cutting.py) * [Smith Waterman](dynamic_programming/smith_waterman.py) * [Subset Generation](dynamic_programming/subset_generation.py) * [Sum Of Subset](dynamic_programming/sum_of_subset.py) * [Trapped Water](dynamic_programming/trapped_water.py) * [Tribonacci](dynamic_programming/tribonacci.py) * [Viterbi](dynamic_programming/viterbi.py) * [Wildcard Matching](dynamic_programming/wildcard_matching.py) * [Word Break](dynamic_programming/word_break.py) ## Electronics * [Apparent Power](electronics/apparent_power.py) * [Builtin Voltage](electronics/builtin_voltage.py) * [Capacitor Equivalence](electronics/capacitor_equivalence.py) * [Carrier Concentration](electronics/carrier_concentration.py) * [Charging Capacitor](electronics/charging_capacitor.py) * [Charging Inductor](electronics/charging_inductor.py) * [Circular Convolution](electronics/circular_convolution.py) * [Coulombs Law](electronics/coulombs_law.py) * [Electric Conductivity](electronics/electric_conductivity.py) * [Electric Power](electronics/electric_power.py) * [Electrical Impedance](electronics/electrical_impedance.py) * [Ic 555 Timer](electronics/ic_555_timer.py) * [Ind Reactance](electronics/ind_reactance.py) * [Ohms Law](electronics/ohms_law.py) * [Real And Reactive Power](electronics/real_and_reactive_power.py) * [Resistor Color Code](electronics/resistor_color_code.py) * [Resistor Equivalence](electronics/resistor_equivalence.py) * [Resonant Frequency](electronics/resonant_frequency.py) * [Wheatstone Bridge](electronics/wheatstone_bridge.py) ## File Transfer * [Receive File](file_transfer/receive_file.py) * [Send File](file_transfer/send_file.py) * Tests * [Test Send File](file_transfer/tests/test_send_file.py) ## Financial * [Equated Monthly Installments](financial/equated_monthly_installments.py) * [Exponential Moving Average](financial/exponential_moving_average.py) * [Interest](financial/interest.py) * [Present Value](financial/present_value.py) * [Price Plus Tax](financial/price_plus_tax.py) * [Simple Moving Average](financial/simple_moving_average.py) ## Fractals * [Julia Sets](fractals/julia_sets.py) * [Koch Snowflake](fractals/koch_snowflake.py) * [Mandelbrot](fractals/mandelbrot.py) * [Sierpinski Triangle](fractals/sierpinski_triangle.py) ## Fuzzy Logic * [Fuzzy Operations](fuzzy_logic/fuzzy_operations.py) ## Genetic Algorithm * [Basic String](genetic_algorithm/basic_string.py) ## Geodesy * [Haversine Distance](geodesy/haversine_distance.py) * [Lamberts Ellipsoidal Distance](geodesy/lamberts_ellipsoidal_distance.py) ## Graphics * [Bezier Curve](graphics/bezier_curve.py) * [Vector3 For 2D Rendering](graphics/vector3_for_2d_rendering.py) ## Graphs * [A Star](graphs/a_star.py) * [Articulation Points](graphs/articulation_points.py) * [Basic Graphs](graphs/basic_graphs.py) * [Bellman Ford](graphs/bellman_ford.py) * [Bi Directional Dijkstra](graphs/bi_directional_dijkstra.py) * [Bidirectional A Star](graphs/bidirectional_a_star.py) * [Bidirectional Breadth First Search](graphs/bidirectional_breadth_first_search.py) * [Boruvka](graphs/boruvka.py) * [Breadth First Search](graphs/breadth_first_search.py) * [Breadth First Search 2](graphs/breadth_first_search_2.py) * [Breadth First Search Shortest Path](graphs/breadth_first_search_shortest_path.py) * [Breadth First Search Shortest Path 2](graphs/breadth_first_search_shortest_path_2.py) * [Breadth First Search Zero One Shortest Path](graphs/breadth_first_search_zero_one_shortest_path.py) * [Check Bipatrite](graphs/check_bipatrite.py) * [Check Cycle](graphs/check_cycle.py) * [Connected Components](graphs/connected_components.py) * [Deep Clone Graph](graphs/deep_clone_graph.py) * [Depth First Search](graphs/depth_first_search.py) * [Depth First Search 2](graphs/depth_first_search_2.py) * [Dijkstra](graphs/dijkstra.py) * [Dijkstra 2](graphs/dijkstra_2.py) * [Dijkstra Algorithm](graphs/dijkstra_algorithm.py) * [Dijkstra Alternate](graphs/dijkstra_alternate.py) * [Dijkstra Binary Grid](graphs/dijkstra_binary_grid.py) * [Dinic](graphs/dinic.py) * [Directed And Undirected (Weighted) Graph](graphs/directed_and_undirected_(weighted)_graph.py) * [Edmonds Karp Multiple Source And Sink](graphs/edmonds_karp_multiple_source_and_sink.py) * [Eulerian Path And Circuit For Undirected Graph](graphs/eulerian_path_and_circuit_for_undirected_graph.py) * [Even Tree](graphs/even_tree.py) * [Finding Bridges](graphs/finding_bridges.py) * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py) * [G Topological Sort](graphs/g_topological_sort.py) * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py) * [Graph Adjacency List](graphs/graph_adjacency_list.py) * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py) * [Graph List](graphs/graph_list.py) * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py) * [Greedy Best First](graphs/greedy_best_first.py) * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py) * [Kahns Algorithm Long](graphs/kahns_algorithm_long.py) * [Kahns Algorithm Topo](graphs/kahns_algorithm_topo.py) * [Karger](graphs/karger.py) * [Markov Chain](graphs/markov_chain.py) * [Matching Min Vertex Cover](graphs/matching_min_vertex_cover.py) * [Minimum Path Sum](graphs/minimum_path_sum.py) * [Minimum Spanning Tree Boruvka](graphs/minimum_spanning_tree_boruvka.py) * [Minimum Spanning Tree Kruskal](graphs/minimum_spanning_tree_kruskal.py) * [Minimum Spanning Tree Kruskal2](graphs/minimum_spanning_tree_kruskal2.py) * [Minimum Spanning Tree Prims](graphs/minimum_spanning_tree_prims.py) * [Minimum Spanning Tree Prims2](graphs/minimum_spanning_tree_prims2.py) * [Multi Heuristic Astar](graphs/multi_heuristic_astar.py) * [Page Rank](graphs/page_rank.py) * [Prim](graphs/prim.py) * [Random Graph Generator](graphs/random_graph_generator.py) * [Scc Kosaraju](graphs/scc_kosaraju.py) * [Strongly Connected Components](graphs/strongly_connected_components.py) * [Tarjans Scc](graphs/tarjans_scc.py) * Tests * [Test Min Spanning Tree Kruskal](graphs/tests/test_min_spanning_tree_kruskal.py) * [Test Min Spanning Tree Prim](graphs/tests/test_min_spanning_tree_prim.py) ## Greedy Methods * [Best Time To Buy And Sell Stock](greedy_methods/best_time_to_buy_and_sell_stock.py) * [Fractional Cover Problem](greedy_methods/fractional_cover_problem.py) * [Fractional Knapsack](greedy_methods/fractional_knapsack.py) * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py) * [Gas Station](greedy_methods/gas_station.py) * [Minimum Coin Change](greedy_methods/minimum_coin_change.py) * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py) * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py) ## Hashes * [Adler32](hashes/adler32.py) * [Chaos Machine](hashes/chaos_machine.py) * [Djb2](hashes/djb2.py) * [Elf](hashes/elf.py) * [Enigma Machine](hashes/enigma_machine.py) * [Fletcher16](hashes/fletcher16.py) * [Hamming Code](hashes/hamming_code.py) * [Luhn](hashes/luhn.py) * [Md5](hashes/md5.py) * [Sdbm](hashes/sdbm.py) * [Sha1](hashes/sha1.py) * [Sha256](hashes/sha256.py) ## Knapsack * [Greedy Knapsack](knapsack/greedy_knapsack.py) * [Knapsack](knapsack/knapsack.py) * [Recursive Approach Knapsack](knapsack/recursive_approach_knapsack.py) * Tests * [Test Greedy Knapsack](knapsack/tests/test_greedy_knapsack.py) * [Test Knapsack](knapsack/tests/test_knapsack.py) ## Linear Algebra * [Gaussian Elimination](linear_algebra/gaussian_elimination.py) * [Jacobi Iteration Method](linear_algebra/jacobi_iteration_method.py) * [Lu Decomposition](linear_algebra/lu_decomposition.py) * Src * [Conjugate Gradient](linear_algebra/src/conjugate_gradient.py) * Gaussian Elimination Pivoting * [Gaussian Elimination Pivoting](linear_algebra/src/gaussian_elimination_pivoting/gaussian_elimination_pivoting.py) * [Lib](linear_algebra/src/lib.py) * [Polynom For Points](linear_algebra/src/polynom_for_points.py) * [Power Iteration](linear_algebra/src/power_iteration.py) * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py) * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py) * [Schur Complement](linear_algebra/src/schur_complement.py) * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py) * [Transformations 2D](linear_algebra/src/transformations_2d.py) ## Linear Programming * [Simplex](linear_programming/simplex.py) ## Machine Learning * [Apriori Algorithm](machine_learning/apriori_algorithm.py) * [Astar](machine_learning/astar.py) * [Automatic Differentiation](machine_learning/automatic_differentiation.py) * [Data Transformations](machine_learning/data_transformations.py) * [Decision Tree](machine_learning/decision_tree.py) * [Dimensionality Reduction](machine_learning/dimensionality_reduction.py) * Forecasting * [Run](machine_learning/forecasting/run.py) * [Frequent Pattern Growth](machine_learning/frequent_pattern_growth.py) * [Gradient Boosting Classifier](machine_learning/gradient_boosting_classifier.py) * [Gradient Descent](machine_learning/gradient_descent.py) * [K Means Clust](machine_learning/k_means_clust.py) * [K Nearest Neighbours](machine_learning/k_nearest_neighbours.py) * [Linear Discriminant Analysis](machine_learning/linear_discriminant_analysis.py) * [Linear Regression](machine_learning/linear_regression.py) * Local Weighted Learning * [Local Weighted Learning](machine_learning/local_weighted_learning/local_weighted_learning.py) * [Logistic Regression](machine_learning/logistic_regression.py) * [Loss Functions](machine_learning/loss_functions.py) * [Mfcc](machine_learning/mfcc.py) * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py) * [Polynomial Regression](machine_learning/polynomial_regression.py) * [Scoring Functions](machine_learning/scoring_functions.py) * [Self Organizing Map](machine_learning/self_organizing_map.py) * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py) * [Similarity Search](machine_learning/similarity_search.py) * [Support Vector Machines](machine_learning/support_vector_machines.py) * [Word Frequency Functions](machine_learning/word_frequency_functions.py) * [Xgboost Classifier](machine_learning/xgboost_classifier.py) * [Xgboost Regressor](machine_learning/xgboost_regressor.py) ## Maths * [Abs](maths/abs.py) * [Addition Without Arithmetic](maths/addition_without_arithmetic.py) * [Aliquot Sum](maths/aliquot_sum.py) * [Allocation Number](maths/allocation_number.py) * [Arc Length](maths/arc_length.py) * [Area](maths/area.py) * [Area Under Curve](maths/area_under_curve.py) * [Average Absolute Deviation](maths/average_absolute_deviation.py) * [Average Mean](maths/average_mean.py) * [Average Median](maths/average_median.py) * [Average Mode](maths/average_mode.py) * [Bailey Borwein Plouffe](maths/bailey_borwein_plouffe.py) * [Base Neg2 Conversion](maths/base_neg2_conversion.py) * [Basic Maths](maths/basic_maths.py) * [Binary Exponentiation](maths/binary_exponentiation.py) * [Binary Multiplication](maths/binary_multiplication.py) * [Binomial Coefficient](maths/binomial_coefficient.py) * [Binomial Distribution](maths/binomial_distribution.py) * [Ceil](maths/ceil.py) * [Chebyshev Distance](maths/chebyshev_distance.py) * [Check Polygon](maths/check_polygon.py) * [Chinese Remainder Theorem](maths/chinese_remainder_theorem.py) * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py) * [Collatz Sequence](maths/collatz_sequence.py) * [Combinations](maths/combinations.py) * [Continued Fraction](maths/continued_fraction.py) * [Decimal Isolate](maths/decimal_isolate.py) * [Decimal To Fraction](maths/decimal_to_fraction.py) * [Dodecahedron](maths/dodecahedron.py) * [Double Factorial](maths/double_factorial.py) * [Dual Number Automatic Differentiation](maths/dual_number_automatic_differentiation.py) * [Entropy](maths/entropy.py) * [Euclidean Distance](maths/euclidean_distance.py) * [Euler Method](maths/euler_method.py) * [Euler Modified](maths/euler_modified.py) * [Eulers Totient](maths/eulers_totient.py) * [Extended Euclidean Algorithm](maths/extended_euclidean_algorithm.py) * [Factorial](maths/factorial.py) * [Factors](maths/factors.py) * [Fast Inverse Sqrt](maths/fast_inverse_sqrt.py) * [Fermat Little Theorem](maths/fermat_little_theorem.py) * [Fibonacci](maths/fibonacci.py) * [Find Max](maths/find_max.py) * [Find Min](maths/find_min.py) * [Floor](maths/floor.py) * [Gamma](maths/gamma.py) * [Gaussian](maths/gaussian.py) * [Gaussian Error Linear Unit](maths/gaussian_error_linear_unit.py) * [Gcd Of N Numbers](maths/gcd_of_n_numbers.py) * [Germain Primes](maths/germain_primes.py) * [Greatest Common Divisor](maths/greatest_common_divisor.py) * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py) * [Integer Square Root](maths/integer_square_root.py) * [Interquartile Range](maths/interquartile_range.py) * [Is Int Palindrome](maths/is_int_palindrome.py) * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py) * [Is Square Free](maths/is_square_free.py) * [Jaccard Similarity](maths/jaccard_similarity.py) * [Joint Probability Distribution](maths/joint_probability_distribution.py) * [Josephus Problem](maths/josephus_problem.py) * [Juggler Sequence](maths/juggler_sequence.py) * [Karatsuba](maths/karatsuba.py) * [Kth Lexicographic Permutation](maths/kth_lexicographic_permutation.py) * [Largest Of Very Large Numbers](maths/largest_of_very_large_numbers.py) * [Least Common Multiple](maths/least_common_multiple.py) * [Line Length](maths/line_length.py) * [Liouville Lambda](maths/liouville_lambda.py) * [Lucas Lehmer Primality Test](maths/lucas_lehmer_primality_test.py) * [Lucas Series](maths/lucas_series.py) * [Maclaurin Series](maths/maclaurin_series.py) * [Manhattan Distance](maths/manhattan_distance.py) * [Matrix Exponentiation](maths/matrix_exponentiation.py) * [Max Sum Sliding Window](maths/max_sum_sliding_window.py) * [Median Of Two Arrays](maths/median_of_two_arrays.py) * [Minkowski Distance](maths/minkowski_distance.py) * [Mobius Function](maths/mobius_function.py) * [Modular Division](maths/modular_division.py) * [Modular Exponential](maths/modular_exponential.py) * [Monte Carlo](maths/monte_carlo.py) * [Monte Carlo Dice](maths/monte_carlo_dice.py) * [Number Of Digits](maths/number_of_digits.py) * Numerical Analysis * [Adams Bashforth](maths/numerical_analysis/adams_bashforth.py) * [Bisection](maths/numerical_analysis/bisection.py) * [Bisection 2](maths/numerical_analysis/bisection_2.py) * [Integration By Simpson Approx](maths/numerical_analysis/integration_by_simpson_approx.py) * [Intersection](maths/numerical_analysis/intersection.py) * [Nevilles Method](maths/numerical_analysis/nevilles_method.py) * [Newton Forward Interpolation](maths/numerical_analysis/newton_forward_interpolation.py) * [Newton Raphson](maths/numerical_analysis/newton_raphson.py) * [Numerical Integration](maths/numerical_analysis/numerical_integration.py) * [Runge Kutta](maths/numerical_analysis/runge_kutta.py) * [Runge Kutta Fehlberg 45](maths/numerical_analysis/runge_kutta_fehlberg_45.py) * [Runge Kutta Gills](maths/numerical_analysis/runge_kutta_gills.py) * [Secant Method](maths/numerical_analysis/secant_method.py) * [Simpson Rule](maths/numerical_analysis/simpson_rule.py) * [Square Root](maths/numerical_analysis/square_root.py) * [Odd Sieve](maths/odd_sieve.py) * [Perfect Cube](maths/perfect_cube.py) * [Perfect Number](maths/perfect_number.py) * [Perfect Square](maths/perfect_square.py) * [Persistence](maths/persistence.py) * [Pi Generator](maths/pi_generator.py) * [Pi Monte Carlo Estimation](maths/pi_monte_carlo_estimation.py) * [Points Are Collinear 3D](maths/points_are_collinear_3d.py) * [Pollard Rho](maths/pollard_rho.py) * [Polynomial Evaluation](maths/polynomial_evaluation.py) * Polynomials * [Single Indeterminate Operations](maths/polynomials/single_indeterminate_operations.py) * [Power Using Recursion](maths/power_using_recursion.py) * [Prime Check](maths/prime_check.py) * [Prime Factors](maths/prime_factors.py) * [Prime Numbers](maths/prime_numbers.py) * [Prime Sieve Eratosthenes](maths/prime_sieve_eratosthenes.py) * [Primelib](maths/primelib.py) * [Print Multiplication Table](maths/print_multiplication_table.py) * [Pythagoras](maths/pythagoras.py) * [Qr Decomposition](maths/qr_decomposition.py) * [Quadratic Equations Complex Numbers](maths/quadratic_equations_complex_numbers.py) * [Radians](maths/radians.py) * [Radix2 Fft](maths/radix2_fft.py) * [Remove Digit](maths/remove_digit.py) * [Segmented Sieve](maths/segmented_sieve.py) * Series * [Arithmetic](maths/series/arithmetic.py) * [Geometric](maths/series/geometric.py) * [Geometric Series](maths/series/geometric_series.py) * [Harmonic](maths/series/harmonic.py) * [Harmonic Series](maths/series/harmonic_series.py) * [Hexagonal Numbers](maths/series/hexagonal_numbers.py) * [P Series](maths/series/p_series.py) * [Sieve Of Eratosthenes](maths/sieve_of_eratosthenes.py) * [Sigmoid](maths/sigmoid.py) * [Signum](maths/signum.py) * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py) * [Sin](maths/sin.py) * [Sock Merchant](maths/sock_merchant.py) * [Softmax](maths/softmax.py) * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py) * Special Numbers * [Armstrong Numbers](maths/special_numbers/armstrong_numbers.py) * [Automorphic Number](maths/special_numbers/automorphic_number.py) * [Bell Numbers](maths/special_numbers/bell_numbers.py) * [Carmichael Number](maths/special_numbers/carmichael_number.py) * [Catalan Number](maths/special_numbers/catalan_number.py) * [Hamming Numbers](maths/special_numbers/hamming_numbers.py) * [Happy Number](maths/special_numbers/happy_number.py) * [Harshad Numbers](maths/special_numbers/harshad_numbers.py) * [Hexagonal Number](maths/special_numbers/hexagonal_number.py) * [Krishnamurthy Number](maths/special_numbers/krishnamurthy_number.py) * [Perfect Number](maths/special_numbers/perfect_number.py) * [Polygonal Numbers](maths/special_numbers/polygonal_numbers.py) * [Pronic Number](maths/special_numbers/pronic_number.py) * [Proth Number](maths/special_numbers/proth_number.py) * [Triangular Numbers](maths/special_numbers/triangular_numbers.py) * [Ugly Numbers](maths/special_numbers/ugly_numbers.py) * [Weird Number](maths/special_numbers/weird_number.py) * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py) * [Sum Of Digits](maths/sum_of_digits.py) * [Sum Of Geometric Progression](maths/sum_of_geometric_progression.py) * [Sum Of Harmonic Series](maths/sum_of_harmonic_series.py) * [Sumset](maths/sumset.py) * [Sylvester Sequence](maths/sylvester_sequence.py) * [Tanh](maths/tanh.py) * [Test Prime Check](maths/test_prime_check.py) * [Three Sum](maths/three_sum.py) * [Trapezoidal Rule](maths/trapezoidal_rule.py) * [Triplet Sum](maths/triplet_sum.py) * [Twin Prime](maths/twin_prime.py) * [Two Pointer](maths/two_pointer.py) * [Two Sum](maths/two_sum.py) * [Volume](maths/volume.py) * [Zellers Congruence](maths/zellers_congruence.py) ## Matrix * [Binary Search Matrix](matrix/binary_search_matrix.py) * [Count Islands In Matrix](matrix/count_islands_in_matrix.py) * [Count Negative Numbers In Sorted Matrix](matrix/count_negative_numbers_in_sorted_matrix.py) * [Count Paths](matrix/count_paths.py) * [Cramers Rule 2X2](matrix/cramers_rule_2x2.py) * [Inverse Of Matrix](matrix/inverse_of_matrix.py) * [Largest Square Area In Matrix](matrix/largest_square_area_in_matrix.py) * [Matrix Class](matrix/matrix_class.py) * [Matrix Multiplication Recursion](matrix/matrix_multiplication_recursion.py) * [Matrix Operation](matrix/matrix_operation.py) * [Max Area Of Island](matrix/max_area_of_island.py) * [Median Matrix](matrix/median_matrix.py) * [Nth Fibonacci Using Matrix Exponentiation](matrix/nth_fibonacci_using_matrix_exponentiation.py) * [Pascal Triangle](matrix/pascal_triangle.py) * [Rotate Matrix](matrix/rotate_matrix.py) * [Searching In Sorted Matrix](matrix/searching_in_sorted_matrix.py) * [Sherman Morrison](matrix/sherman_morrison.py) * [Spiral Print](matrix/spiral_print.py) * Tests * [Test Matrix Operation](matrix/tests/test_matrix_operation.py) * [Validate Sudoku Board](matrix/validate_sudoku_board.py) ## Networking Flow * [Ford Fulkerson](networking_flow/ford_fulkerson.py) * [Minimum Cut](networking_flow/minimum_cut.py) ## Neural Network * [2 Hidden Layers Neural Network](neural_network/2_hidden_layers_neural_network.py) * Activation Functions * [Binary Step](neural_network/activation_functions/binary_step.py) * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py) * [Leaky Rectified Linear Unit](neural_network/activation_functions/leaky_rectified_linear_unit.py) * [Mish](neural_network/activation_functions/mish.py) * [Rectified Linear Unit](neural_network/activation_functions/rectified_linear_unit.py) * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py) * [Soboleva Modified Hyperbolic Tangent](neural_network/activation_functions/soboleva_modified_hyperbolic_tangent.py) * [Softplus](neural_network/activation_functions/softplus.py) * [Squareplus](neural_network/activation_functions/squareplus.py) * [Swish](neural_network/activation_functions/swish.py) * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py) * [Convolution Neural Network](neural_network/convolution_neural_network.py) * [Simple Neural Network](neural_network/simple_neural_network.py) ## Other * [Activity Selection](other/activity_selection.py) * [Alternative List Arrange](other/alternative_list_arrange.py) * [Bankers Algorithm](other/bankers_algorithm.py) * [Davis Putnam Logemann Loveland](other/davis_putnam_logemann_loveland.py) * [Doomsday](other/doomsday.py) * [Fischer Yates Shuffle](other/fischer_yates_shuffle.py) * [Gauss Easter](other/gauss_easter.py) * [Graham Scan](other/graham_scan.py) * [Greedy](other/greedy.py) * [Guess The Number Search](other/guess_the_number_search.py) * [H Index](other/h_index.py) * [Least Recently Used](other/least_recently_used.py) * [Lfu Cache](other/lfu_cache.py) * [Linear Congruential Generator](other/linear_congruential_generator.py) * [Lru Cache](other/lru_cache.py) * [Magicdiamondpattern](other/magicdiamondpattern.py) * [Majority Vote Algorithm](other/majority_vote_algorithm.py) * [Maximum Subsequence](other/maximum_subsequence.py) * [Nested Brackets](other/nested_brackets.py) * [Number Container System](other/number_container_system.py) * [Password](other/password.py) * [Quine](other/quine.py) * [Scoring Algorithm](other/scoring_algorithm.py) * [Sdes](other/sdes.py) * [Tower Of Hanoi](other/tower_of_hanoi.py) * [Word Search](other/word_search.py) ## Physics * [Altitude Pressure](physics/altitude_pressure.py) * [Archimedes Principle Of Buoyant Force](physics/archimedes_principle_of_buoyant_force.py) * [Basic Orbital Capture](physics/basic_orbital_capture.py) * [Casimir Effect](physics/casimir_effect.py) * [Center Of Mass](physics/center_of_mass.py) * [Centripetal Force](physics/centripetal_force.py) * [Coulombs Law](physics/coulombs_law.py) * [Doppler Frequency](physics/doppler_frequency.py) * [Grahams Law](physics/grahams_law.py) * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py) * [Hubble Parameter](physics/hubble_parameter.py) * [Ideal Gas Law](physics/ideal_gas_law.py) * [In Static Equilibrium](physics/in_static_equilibrium.py) * [Kinetic Energy](physics/kinetic_energy.py) * [Lens Formulae](physics/lens_formulae.py) * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py) * [Malus Law](physics/malus_law.py) * [Mass Energy Equivalence](physics/mass_energy_equivalence.py) * [Mirror Formulae](physics/mirror_formulae.py) * [N Body Simulation](physics/n_body_simulation.py) * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py) * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py) * [Photoelectric Effect](physics/photoelectric_effect.py) * [Potential Energy](physics/potential_energy.py) * [Reynolds Number](physics/reynolds_number.py) * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py) * [Shear Stress](physics/shear_stress.py) * [Speed Of Sound](physics/speed_of_sound.py) * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py) * [Terminal Velocity](physics/terminal_velocity.py) ## Project Euler * Problem 001 * [Sol1](project_euler/problem_001/sol1.py) * [Sol2](project_euler/problem_001/sol2.py) * [Sol3](project_euler/problem_001/sol3.py) * [Sol4](project_euler/problem_001/sol4.py) * [Sol5](project_euler/problem_001/sol5.py) * [Sol6](project_euler/problem_001/sol6.py) * [Sol7](project_euler/problem_001/sol7.py) * Problem 002 * [Sol1](project_euler/problem_002/sol1.py) * [Sol2](project_euler/problem_002/sol2.py) * [Sol3](project_euler/problem_002/sol3.py) * [Sol4](project_euler/problem_002/sol4.py) * [Sol5](project_euler/problem_002/sol5.py) * Problem 003 * [Sol1](project_euler/problem_003/sol1.py) * [Sol2](project_euler/problem_003/sol2.py) * [Sol3](project_euler/problem_003/sol3.py) * Problem 004 * [Sol1](project_euler/problem_004/sol1.py) * [Sol2](project_euler/problem_004/sol2.py) * Problem 005 * [Sol1](project_euler/problem_005/sol1.py) * [Sol2](project_euler/problem_005/sol2.py) * Problem 006 * [Sol1](project_euler/problem_006/sol1.py) * [Sol2](project_euler/problem_006/sol2.py) * [Sol3](project_euler/problem_006/sol3.py) * [Sol4](project_euler/problem_006/sol4.py) * Problem 007 * [Sol1](project_euler/problem_007/sol1.py) * [Sol2](project_euler/problem_007/sol2.py) * [Sol3](project_euler/problem_007/sol3.py) * Problem 008 * [Sol1](project_euler/problem_008/sol1.py) * [Sol2](project_euler/problem_008/sol2.py) * [Sol3](project_euler/problem_008/sol3.py) * Problem 009 * [Sol1](project_euler/problem_009/sol1.py) * [Sol2](project_euler/problem_009/sol2.py) * [Sol3](project_euler/problem_009/sol3.py) * Problem 010 * [Sol1](project_euler/problem_010/sol1.py) * [Sol2](project_euler/problem_010/sol2.py) * [Sol3](project_euler/problem_010/sol3.py) * Problem 011 * [Sol1](project_euler/problem_011/sol1.py) * [Sol2](project_euler/problem_011/sol2.py) * Problem 012 * [Sol1](project_euler/problem_012/sol1.py) * [Sol2](project_euler/problem_012/sol2.py) * Problem 013 * [Sol1](project_euler/problem_013/sol1.py) * Problem 014 * [Sol1](project_euler/problem_014/sol1.py) * [Sol2](project_euler/problem_014/sol2.py) * Problem 015 * [Sol1](project_euler/problem_015/sol1.py) * Problem 016 * [Sol1](project_euler/problem_016/sol1.py) * [Sol2](project_euler/problem_016/sol2.py) * Problem 017 * [Sol1](project_euler/problem_017/sol1.py) * Problem 018 * [Solution](project_euler/problem_018/solution.py) * Problem 019 * [Sol1](project_euler/problem_019/sol1.py) * Problem 020 * [Sol1](project_euler/problem_020/sol1.py) * [Sol2](project_euler/problem_020/sol2.py) * [Sol3](project_euler/problem_020/sol3.py) * [Sol4](project_euler/problem_020/sol4.py) * Problem 021 * [Sol1](project_euler/problem_021/sol1.py) * Problem 022 * [Sol1](project_euler/problem_022/sol1.py) * [Sol2](project_euler/problem_022/sol2.py) * Problem 023 * [Sol1](project_euler/problem_023/sol1.py) * Problem 024 * [Sol1](project_euler/problem_024/sol1.py) * Problem 025 * [Sol1](project_euler/problem_025/sol1.py) * [Sol2](project_euler/problem_025/sol2.py) * [Sol3](project_euler/problem_025/sol3.py) * Problem 026 * [Sol1](project_euler/problem_026/sol1.py) * Problem 027 * [Sol1](project_euler/problem_027/sol1.py) * Problem 028 * [Sol1](project_euler/problem_028/sol1.py) * Problem 029 * [Sol1](project_euler/problem_029/sol1.py) * Problem 030 * [Sol1](project_euler/problem_030/sol1.py) * Problem 031 * [Sol1](project_euler/problem_031/sol1.py) * [Sol2](project_euler/problem_031/sol2.py) * Problem 032 * [Sol32](project_euler/problem_032/sol32.py) * Problem 033 * [Sol1](project_euler/problem_033/sol1.py) * Problem 034 * [Sol1](project_euler/problem_034/sol1.py) * Problem 035 * [Sol1](project_euler/problem_035/sol1.py) * Problem 036 * [Sol1](project_euler/problem_036/sol1.py) * Problem 037 * [Sol1](project_euler/problem_037/sol1.py) * Problem 038 * [Sol1](project_euler/problem_038/sol1.py) * Problem 039 * [Sol1](project_euler/problem_039/sol1.py) * Problem 040 * [Sol1](project_euler/problem_040/sol1.py) * Problem 041 * [Sol1](project_euler/problem_041/sol1.py) * Problem 042 * [Solution42](project_euler/problem_042/solution42.py) * Problem 043 * [Sol1](project_euler/problem_043/sol1.py) * Problem 044 * [Sol1](project_euler/problem_044/sol1.py) * Problem 045 * [Sol1](project_euler/problem_045/sol1.py) * Problem 046 * [Sol1](project_euler/problem_046/sol1.py) * Problem 047 * [Sol1](project_euler/problem_047/sol1.py) * Problem 048 * [Sol1](project_euler/problem_048/sol1.py) * Problem 049 * [Sol1](project_euler/problem_049/sol1.py) * Problem 050 * [Sol1](project_euler/problem_050/sol1.py) * Problem 051 * [Sol1](project_euler/problem_051/sol1.py) * Problem 052 * [Sol1](project_euler/problem_052/sol1.py) * Problem 053 * [Sol1](project_euler/problem_053/sol1.py) * Problem 054 * [Sol1](project_euler/problem_054/sol1.py) * [Test Poker Hand](project_euler/problem_054/test_poker_hand.py) * Problem 055 * [Sol1](project_euler/problem_055/sol1.py) * Problem 056 * [Sol1](project_euler/problem_056/sol1.py) * Problem 057 * [Sol1](project_euler/problem_057/sol1.py) * Problem 058 * [Sol1](project_euler/problem_058/sol1.py) * Problem 059 * [Sol1](project_euler/problem_059/sol1.py) * Problem 062 * [Sol1](project_euler/problem_062/sol1.py) * Problem 063 * [Sol1](project_euler/problem_063/sol1.py) * Problem 064 * [Sol1](project_euler/problem_064/sol1.py) * Problem 065 * [Sol1](project_euler/problem_065/sol1.py) * Problem 067 * [Sol1](project_euler/problem_067/sol1.py) * [Sol2](project_euler/problem_067/sol2.py) * Problem 068 * [Sol1](project_euler/problem_068/sol1.py) * Problem 069 * [Sol1](project_euler/problem_069/sol1.py) * Problem 070 * [Sol1](project_euler/problem_070/sol1.py) * Problem 071 * [Sol1](project_euler/problem_071/sol1.py) * Problem 072 * [Sol1](project_euler/problem_072/sol1.py) * [Sol2](project_euler/problem_072/sol2.py) * Problem 073 * [Sol1](project_euler/problem_073/sol1.py) * Problem 074 * [Sol1](project_euler/problem_074/sol1.py) * [Sol2](project_euler/problem_074/sol2.py) * Problem 075 * [Sol1](project_euler/problem_075/sol1.py) * Problem 076 * [Sol1](project_euler/problem_076/sol1.py) * Problem 077 * [Sol1](project_euler/problem_077/sol1.py) * Problem 078 * [Sol1](project_euler/problem_078/sol1.py) * Problem 079 * [Sol1](project_euler/problem_079/sol1.py) * Problem 080 * [Sol1](project_euler/problem_080/sol1.py) * Problem 081 * [Sol1](project_euler/problem_081/sol1.py) * Problem 082 * [Sol1](project_euler/problem_082/sol1.py) * Problem 085 * [Sol1](project_euler/problem_085/sol1.py) * Problem 086 * [Sol1](project_euler/problem_086/sol1.py) * Problem 087 * [Sol1](project_euler/problem_087/sol1.py) * Problem 089 * [Sol1](project_euler/problem_089/sol1.py) * Problem 091 * [Sol1](project_euler/problem_091/sol1.py) * Problem 092 * [Sol1](project_euler/problem_092/sol1.py) * Problem 094 * [Sol1](project_euler/problem_094/sol1.py) * Problem 097 * [Sol1](project_euler/problem_097/sol1.py) * Problem 099 * [Sol1](project_euler/problem_099/sol1.py) * Problem 100 * [Sol1](project_euler/problem_100/sol1.py) * Problem 101 * [Sol1](project_euler/problem_101/sol1.py) * Problem 102 * [Sol1](project_euler/problem_102/sol1.py) * Problem 104 * [Sol1](project_euler/problem_104/sol1.py) * Problem 107 * [Sol1](project_euler/problem_107/sol1.py) * Problem 109 * [Sol1](project_euler/problem_109/sol1.py) * Problem 112 * [Sol1](project_euler/problem_112/sol1.py) * Problem 113 * [Sol1](project_euler/problem_113/sol1.py) * Problem 114 * [Sol1](project_euler/problem_114/sol1.py) * Problem 115 * [Sol1](project_euler/problem_115/sol1.py) * Problem 116 * [Sol1](project_euler/problem_116/sol1.py) * Problem 117 * [Sol1](project_euler/problem_117/sol1.py) * Problem 119 * [Sol1](project_euler/problem_119/sol1.py) * Problem 120 * [Sol1](project_euler/problem_120/sol1.py) * Problem 121 * [Sol1](project_euler/problem_121/sol1.py) * Problem 123 * [Sol1](project_euler/problem_123/sol1.py) * Problem 125 * [Sol1](project_euler/problem_125/sol1.py) * Problem 129 * [Sol1](project_euler/problem_129/sol1.py) * Problem 131 * [Sol1](project_euler/problem_131/sol1.py) * Problem 135 * [Sol1](project_euler/problem_135/sol1.py) * Problem 144 * [Sol1](project_euler/problem_144/sol1.py) * Problem 145 * [Sol1](project_euler/problem_145/sol1.py) * Problem 173 * [Sol1](project_euler/problem_173/sol1.py) * Problem 174 * [Sol1](project_euler/problem_174/sol1.py) * Problem 180 * [Sol1](project_euler/problem_180/sol1.py) * Problem 187 * [Sol1](project_euler/problem_187/sol1.py) * Problem 188 * [Sol1](project_euler/problem_188/sol1.py) * Problem 191 * [Sol1](project_euler/problem_191/sol1.py) * Problem 203 * [Sol1](project_euler/problem_203/sol1.py) * Problem 205 * [Sol1](project_euler/problem_205/sol1.py) * Problem 206 * [Sol1](project_euler/problem_206/sol1.py) * Problem 207 * [Sol1](project_euler/problem_207/sol1.py) * Problem 234 * [Sol1](project_euler/problem_234/sol1.py) * Problem 301 * [Sol1](project_euler/problem_301/sol1.py) * Problem 493 * [Sol1](project_euler/problem_493/sol1.py) * Problem 551 * [Sol1](project_euler/problem_551/sol1.py) * Problem 587 * [Sol1](project_euler/problem_587/sol1.py) * Problem 686 * [Sol1](project_euler/problem_686/sol1.py) * Problem 800 * [Sol1](project_euler/problem_800/sol1.py) ## Quantum * [Q Fourier Transform](quantum/q_fourier_transform.py) ## Scheduling * [First Come First Served](scheduling/first_come_first_served.py) * [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py) * [Job Sequence With Deadline](scheduling/job_sequence_with_deadline.py) * [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py) * [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py) * [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py) * [Round Robin](scheduling/round_robin.py) * [Shortest Job First](scheduling/shortest_job_first.py) ## Searches * [Binary Search](searches/binary_search.py) * [Binary Tree Traversal](searches/binary_tree_traversal.py) * [Double Linear Search](searches/double_linear_search.py) * [Double Linear Search Recursion](searches/double_linear_search_recursion.py) * [Fibonacci Search](searches/fibonacci_search.py) * [Hill Climbing](searches/hill_climbing.py) * [Interpolation Search](searches/interpolation_search.py) * [Jump Search](searches/jump_search.py) * [Linear Search](searches/linear_search.py) * [Median Of Medians](searches/median_of_medians.py) * [Quick Select](searches/quick_select.py) * [Sentinel Linear Search](searches/sentinel_linear_search.py) * [Simple Binary Search](searches/simple_binary_search.py) * [Simulated Annealing](searches/simulated_annealing.py) * [Tabu Search](searches/tabu_search.py) * [Ternary Search](searches/ternary_search.py) ## Sorts * [Bead Sort](sorts/bead_sort.py) * [Binary Insertion Sort](sorts/binary_insertion_sort.py) * [Bitonic Sort](sorts/bitonic_sort.py) * [Bogo Sort](sorts/bogo_sort.py) * [Bubble Sort](sorts/bubble_sort.py) * [Bucket Sort](sorts/bucket_sort.py) * [Circle Sort](sorts/circle_sort.py) * [Cocktail Shaker Sort](sorts/cocktail_shaker_sort.py) * [Comb Sort](sorts/comb_sort.py) * [Counting Sort](sorts/counting_sort.py) * [Cycle Sort](sorts/cycle_sort.py) * [Double Sort](sorts/double_sort.py) * [Dutch National Flag Sort](sorts/dutch_national_flag_sort.py) * [Exchange Sort](sorts/exchange_sort.py) * [External Sort](sorts/external_sort.py) * [Gnome Sort](sorts/gnome_sort.py) * [Heap Sort](sorts/heap_sort.py) * [Insertion Sort](sorts/insertion_sort.py) * [Intro Sort](sorts/intro_sort.py) * [Iterative Merge Sort](sorts/iterative_merge_sort.py) * [Merge Insertion Sort](sorts/merge_insertion_sort.py) * [Merge Sort](sorts/merge_sort.py) * [Msd Radix Sort](sorts/msd_radix_sort.py) * [Natural Sort](sorts/natural_sort.py) * [Odd Even Sort](sorts/odd_even_sort.py) * [Odd Even Transposition Parallel](sorts/odd_even_transposition_parallel.py) * [Odd Even Transposition Single Threaded](sorts/odd_even_transposition_single_threaded.py) * [Pancake Sort](sorts/pancake_sort.py) * [Patience Sort](sorts/patience_sort.py) * [Pigeon Sort](sorts/pigeon_sort.py) * [Pigeonhole Sort](sorts/pigeonhole_sort.py) * [Quick Sort](sorts/quick_sort.py) * [Quick Sort 3 Partition](sorts/quick_sort_3_partition.py) * [Radix Sort](sorts/radix_sort.py) * [Recursive Insertion Sort](sorts/recursive_insertion_sort.py) * [Recursive Mergesort Array](sorts/recursive_mergesort_array.py) * [Recursive Quick Sort](sorts/recursive_quick_sort.py) * [Selection Sort](sorts/selection_sort.py) * [Shell Sort](sorts/shell_sort.py) * [Shrink Shell Sort](sorts/shrink_shell_sort.py) * [Slowsort](sorts/slowsort.py) * [Stooge Sort](sorts/stooge_sort.py) * [Strand Sort](sorts/strand_sort.py) * [Tim Sort](sorts/tim_sort.py) * [Topological Sort](sorts/topological_sort.py) * [Tree Sort](sorts/tree_sort.py) * [Unknown Sort](sorts/unknown_sort.py) * [Wiggle Sort](sorts/wiggle_sort.py) ## Strings * [Aho Corasick](strings/aho_corasick.py) * [Alternative String Arrange](strings/alternative_string_arrange.py) * [Anagrams](strings/anagrams.py) * [Autocomplete Using Trie](strings/autocomplete_using_trie.py) * [Barcode Validator](strings/barcode_validator.py) * [Bitap String Match](strings/bitap_string_match.py) * [Boyer Moore Search](strings/boyer_moore_search.py) * [Camel Case To Snake Case](strings/camel_case_to_snake_case.py) * [Can String Be Rearranged As Palindrome](strings/can_string_be_rearranged_as_palindrome.py) * [Capitalize](strings/capitalize.py) * [Check Anagrams](strings/check_anagrams.py) * [Credit Card Validator](strings/credit_card_validator.py) * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py) * [Detecting English Programmatically](strings/detecting_english_programmatically.py) * [Dna](strings/dna.py) * [Edit Distance](strings/edit_distance.py) * [Frequency Finder](strings/frequency_finder.py) * [Hamming Distance](strings/hamming_distance.py) * [Indian Phone Validator](strings/indian_phone_validator.py) * [Is Contains Unique Chars](strings/is_contains_unique_chars.py) * [Is Isogram](strings/is_isogram.py) * [Is Pangram](strings/is_pangram.py) * [Is Polish National Id](strings/is_polish_national_id.py) * [Is Spain National Id](strings/is_spain_national_id.py) * [Is Srilankan Phone Number](strings/is_srilankan_phone_number.py) * [Is Valid Email Address](strings/is_valid_email_address.py) * [Jaro Winkler](strings/jaro_winkler.py) * [Join](strings/join.py) * [Knuth Morris Pratt](strings/knuth_morris_pratt.py) * [Levenshtein Distance](strings/levenshtein_distance.py) * [Lower](strings/lower.py) * [Manacher](strings/manacher.py) * [Min Cost String Conversion](strings/min_cost_string_conversion.py) * [Naive String Search](strings/naive_string_search.py) * [Ngram](strings/ngram.py) * [Palindrome](strings/palindrome.py) * [Pig Latin](strings/pig_latin.py) * [Prefix Function](strings/prefix_function.py) * [Rabin Karp](strings/rabin_karp.py) * [Remove Duplicate](strings/remove_duplicate.py) * [Reverse Letters](strings/reverse_letters.py) * [Reverse Words](strings/reverse_words.py) * [Snake Case To Camel Pascal Case](strings/snake_case_to_camel_pascal_case.py) * [Split](strings/split.py) * [String Switch Case](strings/string_switch_case.py) * [Strip](strings/strip.py) * [Text Justification](strings/text_justification.py) * [Title](strings/title.py) * [Top K Frequent Words](strings/top_k_frequent_words.py) * [Upper](strings/upper.py) * [Wave](strings/wave.py) * [Wildcard Pattern Matching](strings/wildcard_pattern_matching.py) * [Word Occurrence](strings/word_occurrence.py) * [Word Patterns](strings/word_patterns.py) * [Z Function](strings/z_function.py) ## Web Programming * [Co2 Emission](web_programming/co2_emission.py) * [Covid Stats Via Xpath](web_programming/covid_stats_via_xpath.py) * [Crawl Google Results](web_programming/crawl_google_results.py) * [Crawl Google Scholar Citation](web_programming/crawl_google_scholar_citation.py) * [Currency Converter](web_programming/currency_converter.py) * [Current Stock Price](web_programming/current_stock_price.py) * [Current Weather](web_programming/current_weather.py) * [Daily Horoscope](web_programming/daily_horoscope.py) * [Download Images From Google Query](web_programming/download_images_from_google_query.py) * [Emails From Url](web_programming/emails_from_url.py) * [Fetch Anime And Play](web_programming/fetch_anime_and_play.py) * [Fetch Bbc News](web_programming/fetch_bbc_news.py) * [Fetch Github Info](web_programming/fetch_github_info.py) * [Fetch Jobs](web_programming/fetch_jobs.py) * [Fetch Quotes](web_programming/fetch_quotes.py) * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py) * [Get Amazon Product Data](web_programming/get_amazon_product_data.py) * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py) * [Get Ip Geolocation](web_programming/get_ip_geolocation.py) * [Get Top Billionaires](web_programming/get_top_billionaires.py) * [Get Top Hn Posts](web_programming/get_top_hn_posts.py) * [Get User Tweets](web_programming/get_user_tweets.py) * [Giphy](web_programming/giphy.py) * [Instagram Crawler](web_programming/instagram_crawler.py) * [Instagram Pic](web_programming/instagram_pic.py) * [Instagram Video](web_programming/instagram_video.py) * [Nasa Data](web_programming/nasa_data.py) * [Open Google Results](web_programming/open_google_results.py) * [Random Anime Character](web_programming/random_anime_character.py) * [Recaptcha Verification](web_programming/recaptcha_verification.py) * [Reddit](web_programming/reddit.py) * [Search Books By Isbn](web_programming/search_books_by_isbn.py) * [Slack Message](web_programming/slack_message.py) * [Test Fetch Github Info](web_programming/test_fetch_github_info.py) * [World Covid19 Stats](web_programming/world_covid19_stats.py)

TheAlgorithms/Python

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""" This program print the matrix in spiral form. This problem has been solved through recursive way. Matrix must satisfy below conditions i) matrix should be only one or two dimensional ii) number of column of all rows should be equal """ def check_matrix(matrix: list[list[int]]) -> bool: # must be matrix = [list(row) for row in matrix] if matrix and isinstance(matrix, list): if isinstance(matrix[0], list): prev_len = 0 for row in matrix: if prev_len == 0: prev_len = len(row) result = True else: result = prev_len == len(row) else: result = True else: result = False return result def spiral_print_clockwise(a: list[list[int]]) -> None: """ >>> spiral_print_clockwise([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) 1 2 3 4 8 12 11 10 9 5 6 7 """ if check_matrix(a) and len(a) > 0: a = [list(row) for row in a] mat_row = len(a) if isinstance(a[0], list): mat_col = len(a[0]) else: for dat in a: print(dat) return # horizotal printing increasing for i in range(mat_col): print(a[0][i]) # vertical printing down for i in range(1, mat_row): print(a[i][mat_col - 1]) # horizotal printing decreasing if mat_row > 1: for i in range(mat_col - 2, -1, -1): print(a[mat_row - 1][i]) # vertical printing up for i in range(mat_row - 2, 0, -1): print(a[i][0]) remain_mat = [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]] if len(remain_mat) > 0: spiral_print_clockwise(remain_mat) else: return else: print("Not a valid matrix") return # Other Easy to understand Approach def spiral_traversal(matrix: list[list]) -> list[int]: """ >>> spiral_traversal([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] Example: matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] Algorithm: Step 1. first pop the 0 index list. (which is [1,2,3,4] and concatenate the output of [step 2]) Step 2. Now perform matrix’s Transpose operation (Change rows to column and vice versa) and reverse the resultant matrix. Step 3. Pass the output of [2nd step], to same recursive function till base case hits. Dry Run: Stage 1. [1, 2, 3, 4] + spiral_traversal([ [8, 12], [7, 11], [6, 10], [5, 9]] ]) Stage 2. [1, 2, 3, 4, 8, 12] + spiral_traversal([ [11, 10, 9], [7, 6, 5] ]) Stage 3. [1, 2, 3, 4, 8, 12, 11, 10, 9] + spiral_traversal([ [5], [6], [7] ]) Stage 4. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([ [5], [6], [7] ]) Stage 5. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([[6, 7]]) Stage 6. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] + spiral_traversal([]) """ if matrix: return list(matrix.pop(0)) + spiral_traversal(list(zip(*matrix))[::-1]) else: return [] # driver code if __name__ == "__main__": import doctest doctest.testmod() a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] spiral_print_clockwise(a)

""" This program print the matrix in spiral form. This problem has been solved through recursive way. Matrix must satisfy below conditions i) matrix should be only one or two dimensional ii) number of column of all rows should be equal """ def check_matrix(matrix: list[list[int]]) -> bool: # must be matrix = [list(row) for row in matrix] if matrix and isinstance(matrix, list): if isinstance(matrix[0], list): prev_len = 0 for row in matrix: if prev_len == 0: prev_len = len(row) result = True else: result = prev_len == len(row) else: result = True else: result = False return result def spiral_print_clockwise(a: list[list[int]]) -> None: """ >>> spiral_print_clockwise([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) 1 2 3 4 8 12 11 10 9 5 6 7 """ if check_matrix(a) and len(a) > 0: a = [list(row) for row in a] mat_row = len(a) if isinstance(a[0], list): mat_col = len(a[0]) else: for dat in a: print(dat) return # horizotal printing increasing for i in range(mat_col): print(a[0][i]) # vertical printing down for i in range(1, mat_row): print(a[i][mat_col - 1]) # horizotal printing decreasing if mat_row > 1: for i in range(mat_col - 2, -1, -1): print(a[mat_row - 1][i]) # vertical printing up for i in range(mat_row - 2, 0, -1): print(a[i][0]) remain_mat = [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]] if len(remain_mat) > 0: spiral_print_clockwise(remain_mat) else: return else: print("Not a valid matrix") return # Other Easy to understand Approach def spiral_traversal(matrix: list[list]) -> list[int]: """ >>> spiral_traversal([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] Example: matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] Algorithm: Step 1. first pop the 0 index list. (which is [1,2,3,4] and concatenate the output of [step 2]) Step 2. Now perform matrix’s Transpose operation (Change rows to column and vice versa) and reverse the resultant matrix. Step 3. Pass the output of [2nd step], to same recursive function till base case hits. Dry Run: Stage 1. [1, 2, 3, 4] + spiral_traversal([ [8, 12], [7, 11], [6, 10], [5, 9]] ]) Stage 2. [1, 2, 3, 4, 8, 12] + spiral_traversal([ [11, 10, 9], [7, 6, 5] ]) Stage 3. [1, 2, 3, 4, 8, 12, 11, 10, 9] + spiral_traversal([ [5], [6], [7] ]) Stage 4. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([ [5], [6], [7] ]) Stage 5. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([[6, 7]]) Stage 6. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] + spiral_traversal([]) """ if matrix: return list(matrix.pop(0)) + spiral_traversal(list(zip(*matrix))[::-1]) # type: ignore else: return [] # driver code if __name__ == "__main__": import doctest doctest.testmod() a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] spiral_print_clockwise(a)

TheAlgorithms/Python

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# https://farside.ph.utexas.edu/teaching/316/lectures/node46.html from __future__ import annotations def capacitor_parallel(capacitors: list[float]) -> float: """ Ceq = C1 + C2 + ... + Cn Calculate the equivalent resistance for any number of capacitors in parallel. >>> capacitor_parallel([5.71389, 12, 3]) 20.71389 >>> capacitor_parallel([5.71389, 12, -3]) Traceback (most recent call last): ... ValueError: Capacitor at index 2 has a negative value! """ sum_c = 0.0 for index, capacitor in enumerate(capacitors): if capacitor < 0: msg = f"Capacitor at index {index} has a negative value!" raise ValueError(msg) sum_c += capacitor return sum_c def capacitor_series(capacitors: list[float]) -> float: """ Ceq = 1/ (1/C1 + 1/C2 + ... + 1/Cn) >>> capacitor_series([5.71389, 12, 3]) 1.6901062252507735 >>> capacitor_series([5.71389, 12, -3]) Traceback (most recent call last): ... ValueError: Capacitor at index 2 has a negative or zero value! >>> capacitor_series([5.71389, 12, 0.000]) Traceback (most recent call last): ... ValueError: Capacitor at index 2 has a negative or zero value! """ first_sum = 0.0 for index, capacitor in enumerate(capacitors): if capacitor <= 0: msg = f"Capacitor at index {index} has a negative or zero value!" raise ValueError(msg) first_sum += 1 / capacitor return 1 / first_sum if __name__ == "__main__": import doctest doctest.testmod()

# https://farside.ph.utexas.edu/teaching/316/lectures/node46.html from __future__ import annotations def capacitor_parallel(capacitors: list[float]) -> float: """ Ceq = C1 + C2 + ... + Cn Calculate the equivalent resistance for any number of capacitors in parallel. >>> capacitor_parallel([5.71389, 12, 3]) 20.71389 >>> capacitor_parallel([5.71389, 12, -3]) Traceback (most recent call last): ... ValueError: Capacitor at index 2 has a negative value! """ sum_c = 0.0 for index, capacitor in enumerate(capacitors): if capacitor < 0: msg = f"Capacitor at index {index} has a negative value!" raise ValueError(msg) sum_c += capacitor return sum_c def capacitor_series(capacitors: list[float]) -> float: """ Ceq = 1/ (1/C1 + 1/C2 + ... + 1/Cn) >>> capacitor_series([5.71389, 12, 3]) 1.6901062252507735 >>> capacitor_series([5.71389, 12, -3]) Traceback (most recent call last): ... ValueError: Capacitor at index 2 has a negative or zero value! >>> capacitor_series([5.71389, 12, 0.000]) Traceback (most recent call last): ... ValueError: Capacitor at index 2 has a negative or zero value! """ first_sum = 0.0 for index, capacitor in enumerate(capacitors): if capacitor <= 0: msg = f"Capacitor at index {index} has a negative or zero value!" raise ValueError(msg) first_sum += 1 / capacitor return 1 / first_sum if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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"""Breath First Search (BFS) can be used when finding the shortest path from a given source node to a target node in an unweighted graph. """ from __future__ import annotations graph = { "A": ["B", "C", "E"], "B": ["A", "D", "E"], "C": ["A", "F", "G"], "D": ["B"], "E": ["A", "B", "D"], "F": ["C"], "G": ["C"], } class Graph: def __init__(self, graph: dict[str, list[str]], source_vertex: str) -> None: """ Graph is implemented as dictionary of adjacency lists. Also, Source vertex have to be defined upon initialization. """ self.graph = graph # mapping node to its parent in resulting breadth first tree self.parent: dict[str, str | None] = {} self.source_vertex = source_vertex def breath_first_search(self) -> None: """ This function is a helper for running breath first search on this graph. >>> g = Graph(graph, "G") >>> g.breath_first_search() >>> g.parent {'G': None, 'C': 'G', 'A': 'C', 'F': 'C', 'B': 'A', 'E': 'A', 'D': 'B'} """ visited = {self.source_vertex} self.parent[self.source_vertex] = None queue = [self.source_vertex] # first in first out queue while queue: vertex = queue.pop(0) for adjacent_vertex in self.graph[vertex]: if adjacent_vertex not in visited: visited.add(adjacent_vertex) self.parent[adjacent_vertex] = vertex queue.append(adjacent_vertex) def shortest_path(self, target_vertex: str) -> str: """ This shortest path function returns a string, describing the result: 1.) No path is found. The string is a human readable message to indicate this. 2.) The shortest path is found. The string is in the form `v1(->v2->v3->...->vn)`, where v1 is the source vertex and vn is the target vertex, if it exists separately. >>> g = Graph(graph, "G") >>> g.breath_first_search() Case 1 - No path is found. >>> g.shortest_path("Foo") Traceback (most recent call last): ... ValueError: No path from vertex: G to vertex: Foo Case 2 - The path is found. >>> g.shortest_path("D") 'G->C->A->B->D' >>> g.shortest_path("G") 'G' """ if target_vertex == self.source_vertex: return self.source_vertex target_vertex_parent = self.parent.get(target_vertex) if target_vertex_parent is None: msg = ( f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}" ) raise ValueError(msg) return self.shortest_path(target_vertex_parent) + f"->{target_vertex}" if __name__ == "__main__": g = Graph(graph, "G") g.breath_first_search() print(g.shortest_path("D")) print(g.shortest_path("G")) print(g.shortest_path("Foo"))

"""Breath First Search (BFS) can be used when finding the shortest path from a given source node to a target node in an unweighted graph. """ from __future__ import annotations graph = { "A": ["B", "C", "E"], "B": ["A", "D", "E"], "C": ["A", "F", "G"], "D": ["B"], "E": ["A", "B", "D"], "F": ["C"], "G": ["C"], } class Graph: def __init__(self, graph: dict[str, list[str]], source_vertex: str) -> None: """ Graph is implemented as dictionary of adjacency lists. Also, Source vertex have to be defined upon initialization. """ self.graph = graph # mapping node to its parent in resulting breadth first tree self.parent: dict[str, str | None] = {} self.source_vertex = source_vertex def breath_first_search(self) -> None: """ This function is a helper for running breath first search on this graph. >>> g = Graph(graph, "G") >>> g.breath_first_search() >>> g.parent {'G': None, 'C': 'G', 'A': 'C', 'F': 'C', 'B': 'A', 'E': 'A', 'D': 'B'} """ visited = {self.source_vertex} self.parent[self.source_vertex] = None queue = [self.source_vertex] # first in first out queue while queue: vertex = queue.pop(0) for adjacent_vertex in self.graph[vertex]: if adjacent_vertex not in visited: visited.add(adjacent_vertex) self.parent[adjacent_vertex] = vertex queue.append(adjacent_vertex) def shortest_path(self, target_vertex: str) -> str: """ This shortest path function returns a string, describing the result: 1.) No path is found. The string is a human readable message to indicate this. 2.) The shortest path is found. The string is in the form `v1(->v2->v3->...->vn)`, where v1 is the source vertex and vn is the target vertex, if it exists separately. >>> g = Graph(graph, "G") >>> g.breath_first_search() Case 1 - No path is found. >>> g.shortest_path("Foo") Traceback (most recent call last): ... ValueError: No path from vertex: G to vertex: Foo Case 2 - The path is found. >>> g.shortest_path("D") 'G->C->A->B->D' >>> g.shortest_path("G") 'G' """ if target_vertex == self.source_vertex: return self.source_vertex target_vertex_parent = self.parent.get(target_vertex) if target_vertex_parent is None: msg = ( f"No path from vertex: {self.source_vertex} to vertex: {target_vertex}" ) raise ValueError(msg) return self.shortest_path(target_vertex_parent) + f"->{target_vertex}" if __name__ == "__main__": g = Graph(graph, "G") g.breath_first_search() print(g.shortest_path("D")) print(g.shortest_path("G")) print(g.shortest_path("Foo"))

TheAlgorithms/Python

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""" Fast inverse square root (1/sqrt(x)) using the Quake III algorithm. Reference: https://en.wikipedia.org/wiki/Fast_inverse_square_root Accuracy: https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy """ import struct def fast_inverse_sqrt(number: float) -> float: """ Compute the fast inverse square root of a floating-point number using the famous Quake III algorithm. :param float number: Input number for which to calculate the inverse square root. :return float: The fast inverse square root of the input number. Example: >>> fast_inverse_sqrt(10) 0.3156857923527257 >>> fast_inverse_sqrt(4) 0.49915357479239103 >>> fast_inverse_sqrt(4.1) 0.4932849504615651 >>> fast_inverse_sqrt(0) Traceback (most recent call last): ... ValueError: Input must be a positive number. >>> fast_inverse_sqrt(-1) Traceback (most recent call last): ... ValueError: Input must be a positive number. >>> from math import isclose, sqrt >>> all(isclose(fast_inverse_sqrt(i), 1 / sqrt(i), rel_tol=0.00132) ... for i in range(50, 60)) True """ if number <= 0: raise ValueError("Input must be a positive number.") i = struct.unpack(">i", struct.pack(">f", number))[0] i = 0x5F3759DF - (i >> 1) y = struct.unpack(">f", struct.pack(">i", i))[0] return y * (1.5 - 0.5 * number * y * y) if __name__ == "__main__": from doctest import testmod testmod() # https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy from math import sqrt for i in range(5, 101, 5): print(f"{i:>3}: {(1 / sqrt(i)) - fast_inverse_sqrt(i):.5f}")

""" Fast inverse square root (1/sqrt(x)) using the Quake III algorithm. Reference: https://en.wikipedia.org/wiki/Fast_inverse_square_root Accuracy: https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy """ import struct def fast_inverse_sqrt(number: float) -> float: """ Compute the fast inverse square root of a floating-point number using the famous Quake III algorithm. :param float number: Input number for which to calculate the inverse square root. :return float: The fast inverse square root of the input number. Example: >>> fast_inverse_sqrt(10) 0.3156857923527257 >>> fast_inverse_sqrt(4) 0.49915357479239103 >>> fast_inverse_sqrt(4.1) 0.4932849504615651 >>> fast_inverse_sqrt(0) Traceback (most recent call last): ... ValueError: Input must be a positive number. >>> fast_inverse_sqrt(-1) Traceback (most recent call last): ... ValueError: Input must be a positive number. >>> from math import isclose, sqrt >>> all(isclose(fast_inverse_sqrt(i), 1 / sqrt(i), rel_tol=0.00132) ... for i in range(50, 60)) True """ if number <= 0: raise ValueError("Input must be a positive number.") i = struct.unpack(">i", struct.pack(">f", number))[0] i = 0x5F3759DF - (i >> 1) y = struct.unpack(">f", struct.pack(">i", i))[0] return y * (1.5 - 0.5 * number * y * y) if __name__ == "__main__": from doctest import testmod testmod() # https://en.wikipedia.org/wiki/Fast_inverse_square_root#Accuracy from math import sqrt for i in range(5, 101, 5): print(f"{i:>3}: {(1 / sqrt(i)) - fast_inverse_sqrt(i):.5f}")

TheAlgorithms/Python

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import math """ In cryptography, the TRANSPOSITION cipher is a method of encryption where the positions of plaintext are shifted a certain number(determined by the key) that follows a regular system that results in the permuted text, known as the encrypted text. The type of transposition cipher demonstrated under is the ROUTE cipher. """ def main() -> None: message = input("Enter message: ") key = int(input(f"Enter key [2-{len(message) - 1}]: ")) mode = input("Encryption/Decryption [e/d]: ") if mode.lower().startswith("e"): text = encrypt_message(key, message) elif mode.lower().startswith("d"): text = decrypt_message(key, message) # Append pipe symbol (vertical bar) to identify spaces at the end. print(f"Output:\n{text + '|'}") def encrypt_message(key: int, message: str) -> str: """ >>> encrypt_message(6, 'Harshil Darji') 'Hlia rDsahrij' """ cipher_text = [""] * key for col in range(key): pointer = col while pointer < len(message): cipher_text[col] += message[pointer] pointer += key return "".join(cipher_text) def decrypt_message(key: int, message: str) -> str: """ >>> decrypt_message(6, 'Hlia rDsahrij') 'Harshil Darji' """ num_cols = math.ceil(len(message) / key) num_rows = key num_shaded_boxes = (num_cols * num_rows) - len(message) plain_text = [""] * num_cols col = 0 row = 0 for symbol in message: plain_text[col] += symbol col += 1 if ( (col == num_cols) or (col == num_cols - 1) and (row >= num_rows - num_shaded_boxes) ): col = 0 row += 1 return "".join(plain_text) if __name__ == "__main__": import doctest doctest.testmod() main()

import math """ In cryptography, the TRANSPOSITION cipher is a method of encryption where the positions of plaintext are shifted a certain number(determined by the key) that follows a regular system that results in the permuted text, known as the encrypted text. The type of transposition cipher demonstrated under is the ROUTE cipher. """ def main() -> None: message = input("Enter message: ") key = int(input(f"Enter key [2-{len(message) - 1}]: ")) mode = input("Encryption/Decryption [e/d]: ") if mode.lower().startswith("e"): text = encrypt_message(key, message) elif mode.lower().startswith("d"): text = decrypt_message(key, message) # Append pipe symbol (vertical bar) to identify spaces at the end. print(f"Output:\n{text + '|'}") def encrypt_message(key: int, message: str) -> str: """ >>> encrypt_message(6, 'Harshil Darji') 'Hlia rDsahrij' """ cipher_text = [""] * key for col in range(key): pointer = col while pointer < len(message): cipher_text[col] += message[pointer] pointer += key return "".join(cipher_text) def decrypt_message(key: int, message: str) -> str: """ >>> decrypt_message(6, 'Hlia rDsahrij') 'Harshil Darji' """ num_cols = math.ceil(len(message) / key) num_rows = key num_shaded_boxes = (num_cols * num_rows) - len(message) plain_text = [""] * num_cols col = 0 row = 0 for symbol in message: plain_text[col] += symbol col += 1 if ( (col == num_cols) or (col == num_cols - 1) and (row >= num_rows - num_shaded_boxes) ): col = 0 row += 1 return "".join(plain_text) if __name__ == "__main__": import doctest doctest.testmod() main()

TheAlgorithms/Python

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""" PyTest's for Digital Image Processing """ import numpy as np from cv2 import COLOR_BGR2GRAY, cvtColor, imread from numpy import array, uint8 from PIL import Image from digital_image_processing import change_contrast as cc from digital_image_processing import convert_to_negative as cn from digital_image_processing import sepia as sp from digital_image_processing.dithering import burkes as bs from digital_image_processing.edge_detection import canny from digital_image_processing.filters import convolve as conv from digital_image_processing.filters import gaussian_filter as gg from digital_image_processing.filters import local_binary_pattern as lbp from digital_image_processing.filters import median_filter as med from digital_image_processing.filters import sobel_filter as sob from digital_image_processing.resize import resize as rs img = imread(r"digital_image_processing/image_data/lena_small.jpg") gray = cvtColor(img, COLOR_BGR2GRAY) # Test: convert_to_negative() def test_convert_to_negative(): negative_img = cn.convert_to_negative(img) # assert negative_img array for at least one True assert negative_img.any() # Test: change_contrast() def test_change_contrast(): with Image.open("digital_image_processing/image_data/lena_small.jpg") as img: # Work around assertion for response assert str(cc.change_contrast(img, 110)).startswith( "<PIL.Image.Image image mode=RGB size=100x100 at" ) # canny.gen_gaussian_kernel() def test_gen_gaussian_kernel(): resp = canny.gen_gaussian_kernel(9, sigma=1.4) # Assert ambiguous array assert resp.all() # canny.py def test_canny(): canny_img = imread("digital_image_processing/image_data/lena_small.jpg", 0) # assert ambiguous array for all == True assert canny_img.all() canny_array = canny.canny(canny_img) # assert canny array for at least one True assert canny_array.any() # filters/gaussian_filter.py def test_gen_gaussian_kernel_filter(): assert gg.gaussian_filter(gray, 5, sigma=0.9).all() def test_convolve_filter(): # laplace diagonals laplace = array([[0.25, 0.5, 0.25], [0.5, -3, 0.5], [0.25, 0.5, 0.25]]) res = conv.img_convolve(gray, laplace).astype(uint8) assert res.any() def test_median_filter(): assert med.median_filter(gray, 3).any() def test_sobel_filter(): grad, theta = sob.sobel_filter(gray) assert grad.any() assert theta.any() def test_sepia(): sepia = sp.make_sepia(img, 20) assert sepia.all() def test_burkes(file_path: str = "digital_image_processing/image_data/lena_small.jpg"): burkes = bs.Burkes(imread(file_path, 1), 120) burkes.process() assert burkes.output_img.any() def test_nearest_neighbour( file_path: str = "digital_image_processing/image_data/lena_small.jpg", ): nn = rs.NearestNeighbour(imread(file_path, 1), 400, 200) nn.process() assert nn.output.any() def test_local_binary_pattern(): # pull request 10161 before: # "digital_image_processing/image_data/lena.jpg" # after: "digital_image_processing/image_data/lena_small.jpg" from os import getenv # Speed up our Continuous Integration tests file_name = "lena_small.jpg" if getenv("CI") else "lena.jpg" file_path = f"digital_image_processing/image_data/{file_name}" # Reading the image and converting it to grayscale image = imread(file_path, 0) # Test for get_neighbors_pixel function() return not None x_coordinate = 0 y_coordinate = 0 center = image[x_coordinate][y_coordinate] neighbors_pixels = lbp.get_neighbors_pixel( image, x_coordinate, y_coordinate, center ) assert neighbors_pixels is not None # Test for local_binary_pattern function() # Create a numpy array as the same height and width of read image lbp_image = np.zeros((image.shape[0], image.shape[1])) # Iterating through the image and calculating the local binary pattern value # for each pixel. for i in range(image.shape[0]): for j in range(image.shape[1]): lbp_image[i][j] = lbp.local_binary_value(image, i, j) assert lbp_image.any()

""" PyTest's for Digital Image Processing """ import numpy as np from cv2 import COLOR_BGR2GRAY, cvtColor, imread from numpy import array, uint8 from PIL import Image from digital_image_processing import change_contrast as cc from digital_image_processing import convert_to_negative as cn from digital_image_processing import sepia as sp from digital_image_processing.dithering import burkes as bs from digital_image_processing.edge_detection import canny from digital_image_processing.filters import convolve as conv from digital_image_processing.filters import gaussian_filter as gg from digital_image_processing.filters import local_binary_pattern as lbp from digital_image_processing.filters import median_filter as med from digital_image_processing.filters import sobel_filter as sob from digital_image_processing.resize import resize as rs img = imread(r"digital_image_processing/image_data/lena_small.jpg") gray = cvtColor(img, COLOR_BGR2GRAY) # Test: convert_to_negative() def test_convert_to_negative(): negative_img = cn.convert_to_negative(img) # assert negative_img array for at least one True assert negative_img.any() # Test: change_contrast() def test_change_contrast(): with Image.open("digital_image_processing/image_data/lena_small.jpg") as img: # Work around assertion for response assert str(cc.change_contrast(img, 110)).startswith( "<PIL.Image.Image image mode=RGB size=100x100 at" ) # canny.gen_gaussian_kernel() def test_gen_gaussian_kernel(): resp = canny.gen_gaussian_kernel(9, sigma=1.4) # Assert ambiguous array assert resp.all() # canny.py def test_canny(): canny_img = imread("digital_image_processing/image_data/lena_small.jpg", 0) # assert ambiguous array for all == True assert canny_img.all() canny_array = canny.canny(canny_img) # assert canny array for at least one True assert canny_array.any() # filters/gaussian_filter.py def test_gen_gaussian_kernel_filter(): assert gg.gaussian_filter(gray, 5, sigma=0.9).all() def test_convolve_filter(): # laplace diagonals laplace = array([[0.25, 0.5, 0.25], [0.5, -3, 0.5], [0.25, 0.5, 0.25]]) res = conv.img_convolve(gray, laplace).astype(uint8) assert res.any() def test_median_filter(): assert med.median_filter(gray, 3).any() def test_sobel_filter(): grad, theta = sob.sobel_filter(gray) assert grad.any() assert theta.any() def test_sepia(): sepia = sp.make_sepia(img, 20) assert sepia.all() def test_burkes(file_path: str = "digital_image_processing/image_data/lena_small.jpg"): burkes = bs.Burkes(imread(file_path, 1), 120) burkes.process() assert burkes.output_img.any() def test_nearest_neighbour( file_path: str = "digital_image_processing/image_data/lena_small.jpg", ): nn = rs.NearestNeighbour(imread(file_path, 1), 400, 200) nn.process() assert nn.output.any() def test_local_binary_pattern(): # pull request 10161 before: # "digital_image_processing/image_data/lena.jpg" # after: "digital_image_processing/image_data/lena_small.jpg" from os import getenv # Speed up our Continuous Integration tests file_name = "lena_small.jpg" if getenv("CI") else "lena.jpg" file_path = f"digital_image_processing/image_data/{file_name}" # Reading the image and converting it to grayscale image = imread(file_path, 0) # Test for get_neighbors_pixel function() return not None x_coordinate = 0 y_coordinate = 0 center = image[x_coordinate][y_coordinate] neighbors_pixels = lbp.get_neighbors_pixel( image, x_coordinate, y_coordinate, center ) assert neighbors_pixels is not None # Test for local_binary_pattern function() # Create a numpy array as the same height and width of read image lbp_image = np.zeros((image.shape[0], image.shape[1])) # Iterating through the image and calculating the local binary pattern value # for each pixel. for i in range(image.shape[0]): for j in range(image.shape[1]): lbp_image[i][j] = lbp.local_binary_value(image, i, j) assert lbp_image.any()

TheAlgorithms/Python

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def rgb_to_cmyk(r_input: int, g_input: int, b_input: int) -> tuple[int, int, int, int]: """ Simple RGB to CMYK conversion. Returns percentages of CMYK paint. https://www.programmingalgorithms.com/algorithm/rgb-to-cmyk/ Note: this is a very popular algorithm that converts colors linearly and gives only approximate results. Actual preparation for printing requires advanced color conversion considering the color profiles and parameters of the target device. >>> rgb_to_cmyk(255, 200, "a") Traceback (most recent call last): ... ValueError: Expected int, found (<class 'int'>, <class 'int'>, <class 'str'>) >>> rgb_to_cmyk(255, 255, 999) Traceback (most recent call last): ... ValueError: Expected int of the range 0..255 >>> rgb_to_cmyk(255, 255, 255) # white (0, 0, 0, 0) >>> rgb_to_cmyk(128, 128, 128) # gray (0, 0, 0, 50) >>> rgb_to_cmyk(0, 0, 0) # black (0, 0, 0, 100) >>> rgb_to_cmyk(255, 0, 0) # red (0, 100, 100, 0) >>> rgb_to_cmyk(0, 255, 0) # green (100, 0, 100, 0) >>> rgb_to_cmyk(0, 0, 255) # blue (100, 100, 0, 0) """ if ( not isinstance(r_input, int) or not isinstance(g_input, int) or not isinstance(b_input, int) ): msg = f"Expected int, found {type(r_input), type(g_input), type(b_input)}" raise ValueError(msg) if not 0 <= r_input < 256 or not 0 <= g_input < 256 or not 0 <= b_input < 256: raise ValueError("Expected int of the range 0..255") # changing range from 0..255 to 0..1 r = r_input / 255 g = g_input / 255 b = b_input / 255 k = 1 - max(r, g, b) if k == 1: # pure black return 0, 0, 0, 100 c = round(100 * (1 - r - k) / (1 - k)) m = round(100 * (1 - g - k) / (1 - k)) y = round(100 * (1 - b - k) / (1 - k)) k = round(100 * k) return c, m, y, k if __name__ == "__main__": from doctest import testmod testmod()

def rgb_to_cmyk(r_input: int, g_input: int, b_input: int) -> tuple[int, int, int, int]: """ Simple RGB to CMYK conversion. Returns percentages of CMYK paint. https://www.programmingalgorithms.com/algorithm/rgb-to-cmyk/ Note: this is a very popular algorithm that converts colors linearly and gives only approximate results. Actual preparation for printing requires advanced color conversion considering the color profiles and parameters of the target device. >>> rgb_to_cmyk(255, 200, "a") Traceback (most recent call last): ... ValueError: Expected int, found (<class 'int'>, <class 'int'>, <class 'str'>) >>> rgb_to_cmyk(255, 255, 999) Traceback (most recent call last): ... ValueError: Expected int of the range 0..255 >>> rgb_to_cmyk(255, 255, 255) # white (0, 0, 0, 0) >>> rgb_to_cmyk(128, 128, 128) # gray (0, 0, 0, 50) >>> rgb_to_cmyk(0, 0, 0) # black (0, 0, 0, 100) >>> rgb_to_cmyk(255, 0, 0) # red (0, 100, 100, 0) >>> rgb_to_cmyk(0, 255, 0) # green (100, 0, 100, 0) >>> rgb_to_cmyk(0, 0, 255) # blue (100, 100, 0, 0) """ if ( not isinstance(r_input, int) or not isinstance(g_input, int) or not isinstance(b_input, int) ): msg = f"Expected int, found {type(r_input), type(g_input), type(b_input)}" raise ValueError(msg) if not 0 <= r_input < 256 or not 0 <= g_input < 256 or not 0 <= b_input < 256: raise ValueError("Expected int of the range 0..255") # changing range from 0..255 to 0..1 r = r_input / 255 g = g_input / 255 b = b_input / 255 k = 1 - max(r, g, b) if k == 1: # pure black return 0, 0, 0, 100 c = round(100 * (1 - r - k) / (1 - k)) m = round(100 * (1 - g - k) / (1 - k)) y = round(100 * (1 - b - k) / (1 - k)) k = round(100 * k) return c, m, y, k if __name__ == "__main__": from doctest import testmod testmod()

TheAlgorithms/Python

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# Minimum cut on Ford_Fulkerson algorithm. test_graph = [ [0, 16, 13, 0, 0, 0], [0, 0, 10, 12, 0, 0], [0, 4, 0, 0, 14, 0], [0, 0, 9, 0, 0, 20], [0, 0, 0, 7, 0, 4], [0, 0, 0, 0, 0, 0], ] def bfs(graph, s, t, parent): # Return True if there is node that has not iterated. visited = [False] * len(graph) queue = [s] visited[s] = True while queue: u = queue.pop(0) for ind in range(len(graph[u])): if visited[ind] is False and graph[u][ind] > 0: queue.append(ind) visited[ind] = True parent[ind] = u return visited[t] def mincut(graph, source, sink): """This array is filled by BFS and to store path >>> mincut(test_graph, source=0, sink=5) [(1, 3), (4, 3), (4, 5)] """ parent = [-1] * (len(graph)) max_flow = 0 res = [] temp = [i[:] for i in graph] # Record original cut, copy. while bfs(graph, source, sink, parent): path_flow = float("Inf") s = sink while s != source: # Find the minimum value in select path path_flow = min(path_flow, graph[parent[s]][s]) s = parent[s] max_flow += path_flow v = sink while v != source: u = parent[v] graph[u][v] -= path_flow graph[v][u] += path_flow v = parent[v] for i in range(len(graph)): for j in range(len(graph[0])): if graph[i][j] == 0 and temp[i][j] > 0: res.append((i, j)) return res if __name__ == "__main__": print(mincut(test_graph, source=0, sink=5))

# Minimum cut on Ford_Fulkerson algorithm. test_graph = [ [0, 16, 13, 0, 0, 0], [0, 0, 10, 12, 0, 0], [0, 4, 0, 0, 14, 0], [0, 0, 9, 0, 0, 20], [0, 0, 0, 7, 0, 4], [0, 0, 0, 0, 0, 0], ] def bfs(graph, s, t, parent): # Return True if there is node that has not iterated. visited = [False] * len(graph) queue = [s] visited[s] = True while queue: u = queue.pop(0) for ind in range(len(graph[u])): if visited[ind] is False and graph[u][ind] > 0: queue.append(ind) visited[ind] = True parent[ind] = u return visited[t] def mincut(graph, source, sink): """This array is filled by BFS and to store path >>> mincut(test_graph, source=0, sink=5) [(1, 3), (4, 3), (4, 5)] """ parent = [-1] * (len(graph)) max_flow = 0 res = [] temp = [i[:] for i in graph] # Record original cut, copy. while bfs(graph, source, sink, parent): path_flow = float("Inf") s = sink while s != source: # Find the minimum value in select path path_flow = min(path_flow, graph[parent[s]][s]) s = parent[s] max_flow += path_flow v = sink while v != source: u = parent[v] graph[u][v] -= path_flow graph[v][u] += path_flow v = parent[v] for i in range(len(graph)): for j in range(len(graph[0])): if graph[i][j] == 0 and temp[i][j] > 0: res.append((i, j)) return res if __name__ == "__main__": print(mincut(test_graph, source=0, sink=5))

TheAlgorithms/Python

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""" Problem 43: https://projecteuler.net/problem=43 The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property. Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following: d2d3d4=406 is divisible by 2 d3d4d5=063 is divisible by 3 d4d5d6=635 is divisible by 5 d5d6d7=357 is divisible by 7 d6d7d8=572 is divisible by 11 d7d8d9=728 is divisible by 13 d8d9d10=289 is divisible by 17 Find the sum of all 0 to 9 pandigital numbers with this property. """ from itertools import permutations def is_substring_divisible(num: tuple) -> bool: """ Returns True if the pandigital number passes all the divisibility tests. >>> is_substring_divisible((0, 1, 2, 4, 6, 5, 7, 3, 8, 9)) False >>> is_substring_divisible((5, 1, 2, 4, 6, 0, 7, 8, 3, 9)) False >>> is_substring_divisible((1, 4, 0, 6, 3, 5, 7, 2, 8, 9)) True """ if num[3] % 2 != 0: return False if (num[2] + num[3] + num[4]) % 3 != 0: return False if num[5] % 5 != 0: return False tests = [7, 11, 13, 17] for i, test in enumerate(tests): if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0: return False return True def solution(n: int = 10) -> int: """ Returns the sum of all pandigital numbers which pass the divisibility tests. >>> solution(10) 16695334890 """ return sum( int("".join(map(str, num))) for num in permutations(range(n)) if is_substring_divisible(num) ) if __name__ == "__main__": print(f"{solution() = }")

""" Problem 43: https://projecteuler.net/problem=43 The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property. Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following: d2d3d4=406 is divisible by 2 d3d4d5=063 is divisible by 3 d4d5d6=635 is divisible by 5 d5d6d7=357 is divisible by 7 d6d7d8=572 is divisible by 11 d7d8d9=728 is divisible by 13 d8d9d10=289 is divisible by 17 Find the sum of all 0 to 9 pandigital numbers with this property. """ from itertools import permutations def is_substring_divisible(num: tuple) -> bool: """ Returns True if the pandigital number passes all the divisibility tests. >>> is_substring_divisible((0, 1, 2, 4, 6, 5, 7, 3, 8, 9)) False >>> is_substring_divisible((5, 1, 2, 4, 6, 0, 7, 8, 3, 9)) False >>> is_substring_divisible((1, 4, 0, 6, 3, 5, 7, 2, 8, 9)) True """ if num[3] % 2 != 0: return False if (num[2] + num[3] + num[4]) % 3 != 0: return False if num[5] % 5 != 0: return False tests = [7, 11, 13, 17] for i, test in enumerate(tests): if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0: return False return True def solution(n: int = 10) -> int: """ Returns the sum of all pandigital numbers which pass the divisibility tests. >>> solution(10) 16695334890 """ return sum( int("".join(map(str, num))) for num in permutations(range(n)) if is_substring_divisible(num) ) if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

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""" Approximates the area under the curve using the trapezoidal rule """ from __future__ import annotations from collections.abc import Callable def trapezoidal_area( fnc: Callable[[float], float], x_start: float, x_end: float, steps: int = 100, ) -> float: """ Treats curve as a collection of linear lines and sums the area of the trapezium shape they form :param fnc: a function which defines a curve :param x_start: left end point to indicate the start of line segment :param x_end: right end point to indicate end of line segment :param steps: an accuracy gauge; more steps increases the accuracy :return: a float representing the length of the curve >>> def f(x): ... return 5 >>> '%.3f' % trapezoidal_area(f, 12.0, 14.0, 1000) '10.000' >>> def f(x): ... return 9*x**2 >>> '%.4f' % trapezoidal_area(f, -4.0, 0, 10000) '192.0000' >>> '%.4f' % trapezoidal_area(f, -4.0, 4.0, 10000) '384.0000' """ x1 = x_start fx1 = fnc(x_start) area = 0.0 for _ in range(steps): # Approximates small segments of curve as linear and solve # for trapezoidal area x2 = (x_end - x_start) / steps + x1 fx2 = fnc(x2) area += abs(fx2 + fx1) * (x2 - x1) / 2 # Increment step x1 = x2 fx1 = fx2 return area if __name__ == "__main__": def f(x): return x**3 print("f(x) = x^3") print("The area between the curve, x = -10, x = 10 and the x axis is:") i = 10 while i <= 100000: area = trapezoidal_area(f, -5, 5, i) print(f"with {i} steps: {area}") i *= 10

""" Approximates the area under the curve using the trapezoidal rule """ from __future__ import annotations from collections.abc import Callable def trapezoidal_area( fnc: Callable[[float], float], x_start: float, x_end: float, steps: int = 100, ) -> float: """ Treats curve as a collection of linear lines and sums the area of the trapezium shape they form :param fnc: a function which defines a curve :param x_start: left end point to indicate the start of line segment :param x_end: right end point to indicate end of line segment :param steps: an accuracy gauge; more steps increases the accuracy :return: a float representing the length of the curve >>> def f(x): ... return 5 >>> '%.3f' % trapezoidal_area(f, 12.0, 14.0, 1000) '10.000' >>> def f(x): ... return 9*x**2 >>> '%.4f' % trapezoidal_area(f, -4.0, 0, 10000) '192.0000' >>> '%.4f' % trapezoidal_area(f, -4.0, 4.0, 10000) '384.0000' """ x1 = x_start fx1 = fnc(x_start) area = 0.0 for _ in range(steps): # Approximates small segments of curve as linear and solve # for trapezoidal area x2 = (x_end - x_start) / steps + x1 fx2 = fnc(x2) area += abs(fx2 + fx1) * (x2 - x1) / 2 # Increment step x1 = x2 fx1 = fx2 return area if __name__ == "__main__": def f(x): return x**3 print("f(x) = x^3") print("The area between the curve, x = -10, x = 10 and the x axis is:") i = 10 while i <= 100000: area = trapezoidal_area(f, -5, 5, i) print(f"with {i} steps: {area}") i *= 10

TheAlgorithms/Python

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""" * Author: Manuel Di Lullo (https://github.com/manueldilullo) * Description: Random graphs generator. Uses graphs represented with an adjacency list. URL: https://en.wikipedia.org/wiki/Random_graph """ import random def random_graph( vertices_number: int, probability: float, directed: bool = False ) -> dict: """ Generate a random graph @input: vertices_number (number of vertices), probability (probability that a generic edge (u,v) exists), directed (if True: graph will be a directed graph, otherwise it will be an undirected graph) @examples: >>> random.seed(1) >>> random_graph(4, 0.5) {0: [1], 1: [0, 2, 3], 2: [1, 3], 3: [1, 2]} >>> random.seed(1) >>> random_graph(4, 0.5, True) {0: [1], 1: [2, 3], 2: [3], 3: []} """ graph: dict = {i: [] for i in range(vertices_number)} # if probability is greater or equal than 1, then generate a complete graph if probability >= 1: return complete_graph(vertices_number) # if probability is lower or equal than 0, then return a graph without edges if probability <= 0: return graph # for each couple of nodes, add an edge from u to v # if the number randomly generated is greater than probability probability for i in range(vertices_number): for j in range(i + 1, vertices_number): if random.random() < probability: graph[i].append(j) if not directed: # if the graph is undirected, add an edge in from j to i, either graph[j].append(i) return graph def complete_graph(vertices_number: int) -> dict: """ Generate a complete graph with vertices_number vertices. @input: vertices_number (number of vertices), directed (False if the graph is undirected, True otherwise) @example: >>> complete_graph(3) {0: [1, 2], 1: [0, 2], 2: [0, 1]} """ return { i: [j for j in range(vertices_number) if i != j] for i in range(vertices_number) } if __name__ == "__main__": import doctest doctest.testmod()

""" * Author: Manuel Di Lullo (https://github.com/manueldilullo) * Description: Random graphs generator. Uses graphs represented with an adjacency list. URL: https://en.wikipedia.org/wiki/Random_graph """ import random def random_graph( vertices_number: int, probability: float, directed: bool = False ) -> dict: """ Generate a random graph @input: vertices_number (number of vertices), probability (probability that a generic edge (u,v) exists), directed (if True: graph will be a directed graph, otherwise it will be an undirected graph) @examples: >>> random.seed(1) >>> random_graph(4, 0.5) {0: [1], 1: [0, 2, 3], 2: [1, 3], 3: [1, 2]} >>> random.seed(1) >>> random_graph(4, 0.5, True) {0: [1], 1: [2, 3], 2: [3], 3: []} """ graph: dict = {i: [] for i in range(vertices_number)} # if probability is greater or equal than 1, then generate a complete graph if probability >= 1: return complete_graph(vertices_number) # if probability is lower or equal than 0, then return a graph without edges if probability <= 0: return graph # for each couple of nodes, add an edge from u to v # if the number randomly generated is greater than probability probability for i in range(vertices_number): for j in range(i + 1, vertices_number): if random.random() < probability: graph[i].append(j) if not directed: # if the graph is undirected, add an edge in from j to i, either graph[j].append(i) return graph def complete_graph(vertices_number: int) -> dict: """ Generate a complete graph with vertices_number vertices. @input: vertices_number (number of vertices), directed (False if the graph is undirected, True otherwise) @example: >>> complete_graph(3) {0: [1, 2], 1: [0, 2], 2: [0, 1]} """ return { i: [j for j in range(vertices_number) if i != j] for i in range(vertices_number) } if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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""" Given an array of integer elements and an integer 'k', we are required to find the maximum sum of 'k' consecutive elements in the array. Instead of using a nested for loop, in a Brute force approach we will use a technique called 'Window sliding technique' where the nested loops can be converted to a single loop to reduce time complexity. """ from __future__ import annotations def max_sum_in_array(array: list[int], k: int) -> int: """ Returns the maximum sum of k consecutive elements >>> arr = [1, 4, 2, 10, 2, 3, 1, 0, 20] >>> k = 4 >>> max_sum_in_array(arr, k) 24 >>> k = 10 >>> max_sum_in_array(arr,k) Traceback (most recent call last): ... ValueError: Invalid Input >>> arr = [1, 4, 2, 10, 2, 13, 1, 0, 2] >>> k = 4 >>> max_sum_in_array(arr, k) 27 """ if len(array) < k or k < 0: raise ValueError("Invalid Input") max_sum = current_sum = sum(array[:k]) for i in range(len(array) - k): current_sum = current_sum - array[i] + array[i + k] max_sum = max(max_sum, current_sum) return max_sum if __name__ == "__main__": from doctest import testmod from random import randint testmod() array = [randint(-1000, 1000) for i in range(100)] k = randint(0, 110) print(f"The maximum sum of {k} consecutive elements is {max_sum_in_array(array,k)}")

""" Given an array of integer elements and an integer 'k', we are required to find the maximum sum of 'k' consecutive elements in the array. Instead of using a nested for loop, in a Brute force approach we will use a technique called 'Window sliding technique' where the nested loops can be converted to a single loop to reduce time complexity. """ from __future__ import annotations def max_sum_in_array(array: list[int], k: int) -> int: """ Returns the maximum sum of k consecutive elements >>> arr = [1, 4, 2, 10, 2, 3, 1, 0, 20] >>> k = 4 >>> max_sum_in_array(arr, k) 24 >>> k = 10 >>> max_sum_in_array(arr,k) Traceback (most recent call last): ... ValueError: Invalid Input >>> arr = [1, 4, 2, 10, 2, 13, 1, 0, 2] >>> k = 4 >>> max_sum_in_array(arr, k) 27 """ if len(array) < k or k < 0: raise ValueError("Invalid Input") max_sum = current_sum = sum(array[:k]) for i in range(len(array) - k): current_sum = current_sum - array[i] + array[i + k] max_sum = max(max_sum, current_sum) return max_sum if __name__ == "__main__": from doctest import testmod from random import randint testmod() array = [randint(-1000, 1000) for i in range(100)] k = randint(0, 110) print(f"The maximum sum of {k} consecutive elements is {max_sum_in_array(array,k)}")

TheAlgorithms/Python

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class FlowNetwork: def __init__(self, graph, sources, sinks): self.source_index = None self.sink_index = None self.graph = graph self._normalize_graph(sources, sinks) self.vertices_count = len(graph) self.maximum_flow_algorithm = None # make only one source and one sink def _normalize_graph(self, sources, sinks): if sources is int: sources = [sources] if sinks is int: sinks = [sinks] if len(sources) == 0 or len(sinks) == 0: return self.source_index = sources[0] self.sink_index = sinks[0] # make fake vertex if there are more # than one source or sink if len(sources) > 1 or len(sinks) > 1: max_input_flow = 0 for i in sources: max_input_flow += sum(self.graph[i]) size = len(self.graph) + 1 for room in self.graph: room.insert(0, 0) self.graph.insert(0, [0] * size) for i in sources: self.graph[0][i + 1] = max_input_flow self.source_index = 0 size = len(self.graph) + 1 for room in self.graph: room.append(0) self.graph.append([0] * size) for i in sinks: self.graph[i + 1][size - 1] = max_input_flow self.sink_index = size - 1 def find_maximum_flow(self): if self.maximum_flow_algorithm is None: raise Exception("You need to set maximum flow algorithm before.") if self.source_index is None or self.sink_index is None: return 0 self.maximum_flow_algorithm.execute() return self.maximum_flow_algorithm.getMaximumFlow() def set_maximum_flow_algorithm(self, algorithm): self.maximum_flow_algorithm = algorithm(self) class FlowNetworkAlgorithmExecutor: def __init__(self, flow_network): self.flow_network = flow_network self.verticies_count = flow_network.verticesCount self.source_index = flow_network.sourceIndex self.sink_index = flow_network.sinkIndex # it's just a reference, so you shouldn't change # it in your algorithms, use deep copy before doing that self.graph = flow_network.graph self.executed = False def execute(self): if not self.executed: self._algorithm() self.executed = True # You should override it def _algorithm(self): pass class MaximumFlowAlgorithmExecutor(FlowNetworkAlgorithmExecutor): def __init__(self, flow_network): super().__init__(flow_network) # use this to save your result self.maximum_flow = -1 def get_maximum_flow(self): if not self.executed: raise Exception("You should execute algorithm before using its result!") return self.maximum_flow class PushRelabelExecutor(MaximumFlowAlgorithmExecutor): def __init__(self, flow_network): super().__init__(flow_network) self.preflow = [[0] * self.verticies_count for i in range(self.verticies_count)] self.heights = [0] * self.verticies_count self.excesses = [0] * self.verticies_count def _algorithm(self): self.heights[self.source_index] = self.verticies_count # push some substance to graph for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]): self.preflow[self.source_index][nextvertex_index] += bandwidth self.preflow[nextvertex_index][self.source_index] -= bandwidth self.excesses[nextvertex_index] += bandwidth # Relabel-to-front selection rule vertices_list = [ i for i in range(self.verticies_count) if i not in {self.source_index, self.sink_index} ] # move through list i = 0 while i < len(vertices_list): vertex_index = vertices_list[i] previous_height = self.heights[vertex_index] self.process_vertex(vertex_index) if self.heights[vertex_index] > previous_height: # if it was relabeled, swap elements # and start from 0 index vertices_list.insert(0, vertices_list.pop(i)) i = 0 else: i += 1 self.maximum_flow = sum(self.preflow[self.source_index]) def process_vertex(self, vertex_index): while self.excesses[vertex_index] > 0: for neighbour_index in range(self.verticies_count): # if it's neighbour and current vertex is higher if ( self.graph[vertex_index][neighbour_index] - self.preflow[vertex_index][neighbour_index] > 0 and self.heights[vertex_index] > self.heights[neighbour_index] ): self.push(vertex_index, neighbour_index) self.relabel(vertex_index) def push(self, from_index, to_index): preflow_delta = min( self.excesses[from_index], self.graph[from_index][to_index] - self.preflow[from_index][to_index], ) self.preflow[from_index][to_index] += preflow_delta self.preflow[to_index][from_index] -= preflow_delta self.excesses[from_index] -= preflow_delta self.excesses[to_index] += preflow_delta def relabel(self, vertex_index): min_height = None for to_index in range(self.verticies_count): if ( self.graph[vertex_index][to_index] - self.preflow[vertex_index][to_index] > 0 ) and (min_height is None or self.heights[to_index] < min_height): min_height = self.heights[to_index] if min_height is not None: self.heights[vertex_index] = min_height + 1 if __name__ == "__main__": entrances = [0] exits = [3] # graph = [ # [0, 0, 4, 6, 0, 0], # [0, 0, 5, 2, 0, 0], # [0, 0, 0, 0, 4, 4], # [0, 0, 0, 0, 6, 6], # [0, 0, 0, 0, 0, 0], # [0, 0, 0, 0, 0, 0], # ] graph = [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]] # prepare our network flow_network = FlowNetwork(graph, entrances, exits) # set algorithm flow_network.set_maximum_flow_algorithm(PushRelabelExecutor) # and calculate maximum_flow = flow_network.find_maximum_flow() print(f"maximum flow is {maximum_flow}")

class FlowNetwork: def __init__(self, graph, sources, sinks): self.source_index = None self.sink_index = None self.graph = graph self._normalize_graph(sources, sinks) self.vertices_count = len(graph) self.maximum_flow_algorithm = None # make only one source and one sink def _normalize_graph(self, sources, sinks): if sources is int: sources = [sources] if sinks is int: sinks = [sinks] if len(sources) == 0 or len(sinks) == 0: return self.source_index = sources[0] self.sink_index = sinks[0] # make fake vertex if there are more # than one source or sink if len(sources) > 1 or len(sinks) > 1: max_input_flow = 0 for i in sources: max_input_flow += sum(self.graph[i]) size = len(self.graph) + 1 for room in self.graph: room.insert(0, 0) self.graph.insert(0, [0] * size) for i in sources: self.graph[0][i + 1] = max_input_flow self.source_index = 0 size = len(self.graph) + 1 for room in self.graph: room.append(0) self.graph.append([0] * size) for i in sinks: self.graph[i + 1][size - 1] = max_input_flow self.sink_index = size - 1 def find_maximum_flow(self): if self.maximum_flow_algorithm is None: raise Exception("You need to set maximum flow algorithm before.") if self.source_index is None or self.sink_index is None: return 0 self.maximum_flow_algorithm.execute() return self.maximum_flow_algorithm.getMaximumFlow() def set_maximum_flow_algorithm(self, algorithm): self.maximum_flow_algorithm = algorithm(self) class FlowNetworkAlgorithmExecutor: def __init__(self, flow_network): self.flow_network = flow_network self.verticies_count = flow_network.verticesCount self.source_index = flow_network.sourceIndex self.sink_index = flow_network.sinkIndex # it's just a reference, so you shouldn't change # it in your algorithms, use deep copy before doing that self.graph = flow_network.graph self.executed = False def execute(self): if not self.executed: self._algorithm() self.executed = True # You should override it def _algorithm(self): pass class MaximumFlowAlgorithmExecutor(FlowNetworkAlgorithmExecutor): def __init__(self, flow_network): super().__init__(flow_network) # use this to save your result self.maximum_flow = -1 def get_maximum_flow(self): if not self.executed: raise Exception("You should execute algorithm before using its result!") return self.maximum_flow class PushRelabelExecutor(MaximumFlowAlgorithmExecutor): def __init__(self, flow_network): super().__init__(flow_network) self.preflow = [[0] * self.verticies_count for i in range(self.verticies_count)] self.heights = [0] * self.verticies_count self.excesses = [0] * self.verticies_count def _algorithm(self): self.heights[self.source_index] = self.verticies_count # push some substance to graph for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]): self.preflow[self.source_index][nextvertex_index] += bandwidth self.preflow[nextvertex_index][self.source_index] -= bandwidth self.excesses[nextvertex_index] += bandwidth # Relabel-to-front selection rule vertices_list = [ i for i in range(self.verticies_count) if i not in {self.source_index, self.sink_index} ] # move through list i = 0 while i < len(vertices_list): vertex_index = vertices_list[i] previous_height = self.heights[vertex_index] self.process_vertex(vertex_index) if self.heights[vertex_index] > previous_height: # if it was relabeled, swap elements # and start from 0 index vertices_list.insert(0, vertices_list.pop(i)) i = 0 else: i += 1 self.maximum_flow = sum(self.preflow[self.source_index]) def process_vertex(self, vertex_index): while self.excesses[vertex_index] > 0: for neighbour_index in range(self.verticies_count): # if it's neighbour and current vertex is higher if ( self.graph[vertex_index][neighbour_index] - self.preflow[vertex_index][neighbour_index] > 0 and self.heights[vertex_index] > self.heights[neighbour_index] ): self.push(vertex_index, neighbour_index) self.relabel(vertex_index) def push(self, from_index, to_index): preflow_delta = min( self.excesses[from_index], self.graph[from_index][to_index] - self.preflow[from_index][to_index], ) self.preflow[from_index][to_index] += preflow_delta self.preflow[to_index][from_index] -= preflow_delta self.excesses[from_index] -= preflow_delta self.excesses[to_index] += preflow_delta def relabel(self, vertex_index): min_height = None for to_index in range(self.verticies_count): if ( self.graph[vertex_index][to_index] - self.preflow[vertex_index][to_index] > 0 ) and (min_height is None or self.heights[to_index] < min_height): min_height = self.heights[to_index] if min_height is not None: self.heights[vertex_index] = min_height + 1 if __name__ == "__main__": entrances = [0] exits = [3] # graph = [ # [0, 0, 4, 6, 0, 0], # [0, 0, 5, 2, 0, 0], # [0, 0, 0, 0, 4, 4], # [0, 0, 0, 0, 6, 6], # [0, 0, 0, 0, 0, 0], # [0, 0, 0, 0, 0, 0], # ] graph = [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]] # prepare our network flow_network = FlowNetwork(graph, entrances, exits) # set algorithm flow_network.set_maximum_flow_algorithm(PushRelabelExecutor) # and calculate maximum_flow = flow_network.find_maximum_flow() print(f"maximum flow is {maximum_flow}")

TheAlgorithms/Python

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""" An implementation of interquartile range (IQR) which is a measure of statistical dispersion, which is the spread of the data. The function takes the list of numeric values as input and returns the IQR. Script inspired by this Wikipedia article: https://en.wikipedia.org/wiki/Interquartile_range """ from __future__ import annotations def find_median(nums: list[int | float]) -> float: """ This is the implementation of the median. :param nums: The list of numeric nums :return: Median of the list >>> find_median(nums=([1, 2, 2, 3, 4])) 2 >>> find_median(nums=([1, 2, 2, 3, 4, 4])) 2.5 >>> find_median(nums=([-1, 2, 0, 3, 4, -4])) 1.5 >>> find_median(nums=([1.1, 2.2, 2, 3.3, 4.4, 4])) 2.65 """ div, mod = divmod(len(nums), 2) if mod: return nums[div] return (nums[div] + nums[(div) - 1]) / 2 def interquartile_range(nums: list[int | float]) -> float: """ Return the interquartile range for a list of numeric values. :param nums: The list of numeric values. :return: interquartile range >>> interquartile_range(nums=[4, 1, 2, 3, 2]) 2.0 >>> interquartile_range(nums = [-2, -7, -10, 9, 8, 4, -67, 45]) 17.0 >>> interquartile_range(nums = [-2.1, -7.1, -10.1, 9.1, 8.1, 4.1, -67.1, 45.1]) 17.2 >>> interquartile_range(nums = [0, 0, 0, 0, 0]) 0.0 >>> interquartile_range(nums=[]) Traceback (most recent call last): ... ValueError: The list is empty. Provide a non-empty list. """ if not nums: raise ValueError("The list is empty. Provide a non-empty list.") nums.sort() length = len(nums) div, mod = divmod(length, 2) q1 = find_median(nums[:div]) half_length = sum((div, mod)) q3 = find_median(nums[half_length:length]) return q3 - q1 if __name__ == "__main__": import doctest doctest.testmod()

""" An implementation of interquartile range (IQR) which is a measure of statistical dispersion, which is the spread of the data. The function takes the list of numeric values as input and returns the IQR. Script inspired by this Wikipedia article: https://en.wikipedia.org/wiki/Interquartile_range """ from __future__ import annotations def find_median(nums: list[int | float]) -> float: """ This is the implementation of the median. :param nums: The list of numeric nums :return: Median of the list >>> find_median(nums=([1, 2, 2, 3, 4])) 2 >>> find_median(nums=([1, 2, 2, 3, 4, 4])) 2.5 >>> find_median(nums=([-1, 2, 0, 3, 4, -4])) 1.5 >>> find_median(nums=([1.1, 2.2, 2, 3.3, 4.4, 4])) 2.65 """ div, mod = divmod(len(nums), 2) if mod: return nums[div] return (nums[div] + nums[(div) - 1]) / 2 def interquartile_range(nums: list[int | float]) -> float: """ Return the interquartile range for a list of numeric values. :param nums: The list of numeric values. :return: interquartile range >>> interquartile_range(nums=[4, 1, 2, 3, 2]) 2.0 >>> interquartile_range(nums = [-2, -7, -10, 9, 8, 4, -67, 45]) 17.0 >>> interquartile_range(nums = [-2.1, -7.1, -10.1, 9.1, 8.1, 4.1, -67.1, 45.1]) 17.2 >>> interquartile_range(nums = [0, 0, 0, 0, 0]) 0.0 >>> interquartile_range(nums=[]) Traceback (most recent call last): ... ValueError: The list is empty. Provide a non-empty list. """ if not nums: raise ValueError("The list is empty. Provide a non-empty list.") nums.sort() length = len(nums) div, mod = divmod(length, 2) q1 = find_median(nums[:div]) half_length = sum((div, mod)) q3 = find_median(nums[half_length:length]) return q3 - q1 if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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from math import atan, cos, radians, sin, tan from .haversine_distance import haversine_distance AXIS_A = 6378137.0 AXIS_B = 6356752.314245 EQUATORIAL_RADIUS = 6378137 def lamberts_ellipsoidal_distance( lat1: float, lon1: float, lat2: float, lon2: float ) -> float: """ Calculate the shortest distance along the surface of an ellipsoid between two points on the surface of earth given longitudes and latitudes https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines NOTE: This algorithm uses geodesy/haversine_distance.py to compute central angle, sigma Representing the earth as an ellipsoid allows us to approximate distances between points on the surface much better than a sphere. Ellipsoidal formulas treat the Earth as an oblate ellipsoid which means accounting for the flattening that happens at the North and South poles. Lambert's formulae provide accuracy on the order of 10 meteres over thousands of kilometeres. Other methods can provide millimeter-level accuracy but this is a simpler method to calculate long range distances without increasing computational intensity. Args: lat1, lon1: latitude and longitude of coordinate 1 lat2, lon2: latitude and longitude of coordinate 2 Returns: geographical distance between two points in metres >>> from collections import namedtuple >>> point_2d = namedtuple("point_2d", "lat lon") >>> SAN_FRANCISCO = point_2d(37.774856, -122.424227) >>> YOSEMITE = point_2d(37.864742, -119.537521) >>> NEW_YORK = point_2d(40.713019, -74.012647) >>> VENICE = point_2d(45.443012, 12.313071) >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters" '254,351 meters' >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters" '4,138,992 meters' >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters" '9,737,326 meters' """ # CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System # Distance in metres(m) # Equation Parameters # https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines flattening = (AXIS_A - AXIS_B) / AXIS_A # Parametric latitudes # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude b_lat1 = atan((1 - flattening) * tan(radians(lat1))) b_lat2 = atan((1 - flattening) * tan(radians(lat2))) # Compute central angle between two points # using haversine theta. sigma = haversine_distance / equatorial radius sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS # Intermediate P and Q values p_value = (b_lat1 + b_lat2) / 2 q_value = (b_lat2 - b_lat1) / 2 # Intermediate X value # X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2) x_numerator = (sin(p_value) ** 2) * (cos(q_value) ** 2) x_demonimator = cos(sigma / 2) ** 2 x_value = (sigma - sin(sigma)) * (x_numerator / x_demonimator) # Intermediate Y value # Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2) y_numerator = (cos(p_value) ** 2) * (sin(q_value) ** 2) y_denominator = sin(sigma / 2) ** 2 y_value = (sigma + sin(sigma)) * (y_numerator / y_denominator) return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value))) if __name__ == "__main__": import doctest doctest.testmod()

from math import atan, cos, radians, sin, tan from .haversine_distance import haversine_distance AXIS_A = 6378137.0 AXIS_B = 6356752.314245 EQUATORIAL_RADIUS = 6378137 def lamberts_ellipsoidal_distance( lat1: float, lon1: float, lat2: float, lon2: float ) -> float: """ Calculate the shortest distance along the surface of an ellipsoid between two points on the surface of earth given longitudes and latitudes https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines NOTE: This algorithm uses geodesy/haversine_distance.py to compute central angle, sigma Representing the earth as an ellipsoid allows us to approximate distances between points on the surface much better than a sphere. Ellipsoidal formulas treat the Earth as an oblate ellipsoid which means accounting for the flattening that happens at the North and South poles. Lambert's formulae provide accuracy on the order of 10 meteres over thousands of kilometeres. Other methods can provide millimeter-level accuracy but this is a simpler method to calculate long range distances without increasing computational intensity. Args: lat1, lon1: latitude and longitude of coordinate 1 lat2, lon2: latitude and longitude of coordinate 2 Returns: geographical distance between two points in metres >>> from collections import namedtuple >>> point_2d = namedtuple("point_2d", "lat lon") >>> SAN_FRANCISCO = point_2d(37.774856, -122.424227) >>> YOSEMITE = point_2d(37.864742, -119.537521) >>> NEW_YORK = point_2d(40.713019, -74.012647) >>> VENICE = point_2d(45.443012, 12.313071) >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *YOSEMITE):0,.0f} meters" '254,351 meters' >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *NEW_YORK):0,.0f} meters" '4,138,992 meters' >>> f"{lamberts_ellipsoidal_distance(*SAN_FRANCISCO, *VENICE):0,.0f} meters" '9,737,326 meters' """ # CONSTANTS per WGS84 https://en.wikipedia.org/wiki/World_Geodetic_System # Distance in metres(m) # Equation Parameters # https://en.wikipedia.org/wiki/Geographical_distance#Lambert's_formula_for_long_lines flattening = (AXIS_A - AXIS_B) / AXIS_A # Parametric latitudes # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude b_lat1 = atan((1 - flattening) * tan(radians(lat1))) b_lat2 = atan((1 - flattening) * tan(radians(lat2))) # Compute central angle between two points # using haversine theta. sigma = haversine_distance / equatorial radius sigma = haversine_distance(lat1, lon1, lat2, lon2) / EQUATORIAL_RADIUS # Intermediate P and Q values p_value = (b_lat1 + b_lat2) / 2 q_value = (b_lat2 - b_lat1) / 2 # Intermediate X value # X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2) x_numerator = (sin(p_value) ** 2) * (cos(q_value) ** 2) x_demonimator = cos(sigma / 2) ** 2 x_value = (sigma - sin(sigma)) * (x_numerator / x_demonimator) # Intermediate Y value # Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2) y_numerator = (cos(p_value) ** 2) * (sin(q_value) ** 2) y_denominator = sin(sigma / 2) ** 2 y_value = (sigma + sin(sigma)) * (y_numerator / y_denominator) return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value))) if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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TheAlgorithms/Python

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TheAlgorithms/Python

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import math def perfect_square(num: int) -> bool: """ Check if a number is perfect square number or not :param num: the number to be checked :return: True if number is square number, otherwise False >>> perfect_square(9) True >>> perfect_square(16) True >>> perfect_square(1) True >>> perfect_square(0) True >>> perfect_square(10) False """ return math.sqrt(num) * math.sqrt(num) == num def perfect_square_binary_search(n: int) -> bool: """ Check if a number is perfect square using binary search. Time complexity : O(Log(n)) Space complexity: O(1) >>> perfect_square_binary_search(9) True >>> perfect_square_binary_search(16) True >>> perfect_square_binary_search(1) True >>> perfect_square_binary_search(0) True >>> perfect_square_binary_search(10) False >>> perfect_square_binary_search(-1) False >>> perfect_square_binary_search(1.1) False >>> perfect_square_binary_search("a") Traceback (most recent call last): ... TypeError: '<=' not supported between instances of 'int' and 'str' >>> perfect_square_binary_search(None) Traceback (most recent call last): ... TypeError: '<=' not supported between instances of 'int' and 'NoneType' >>> perfect_square_binary_search([]) Traceback (most recent call last): ... TypeError: '<=' not supported between instances of 'int' and 'list' """ left = 0 right = n while left <= right: mid = (left + right) // 2 if mid**2 == n: return True elif mid**2 > n: right = mid - 1 else: left = mid + 1 return False if __name__ == "__main__": import doctest doctest.testmod()

import math def perfect_square(num: int) -> bool: """ Check if a number is perfect square number or not :param num: the number to be checked :return: True if number is square number, otherwise False >>> perfect_square(9) True >>> perfect_square(16) True >>> perfect_square(1) True >>> perfect_square(0) True >>> perfect_square(10) False """ return math.sqrt(num) * math.sqrt(num) == num def perfect_square_binary_search(n: int) -> bool: """ Check if a number is perfect square using binary search. Time complexity : O(Log(n)) Space complexity: O(1) >>> perfect_square_binary_search(9) True >>> perfect_square_binary_search(16) True >>> perfect_square_binary_search(1) True >>> perfect_square_binary_search(0) True >>> perfect_square_binary_search(10) False >>> perfect_square_binary_search(-1) False >>> perfect_square_binary_search(1.1) False >>> perfect_square_binary_search("a") Traceback (most recent call last): ... TypeError: '<=' not supported between instances of 'int' and 'str' >>> perfect_square_binary_search(None) Traceback (most recent call last): ... TypeError: '<=' not supported between instances of 'int' and 'NoneType' >>> perfect_square_binary_search([]) Traceback (most recent call last): ... TypeError: '<=' not supported between instances of 'int' and 'list' """ left = 0 right = n while left <= right: mid = (left + right) // 2 if mid**2 == n: return True elif mid**2 > n: right = mid - 1 else: left = mid + 1 return False if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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""" Checks if a system of forces is in static equilibrium. """ from __future__ import annotations from numpy import array, cos, cross, float64, radians, sin from numpy.typing import NDArray def polar_force( magnitude: float, angle: float, radian_mode: bool = False ) -> list[float]: """ Resolves force along rectangular components. (force, angle) => (force_x, force_y) >>> import math >>> force = polar_force(10, 45) >>> math.isclose(force[0], 7.071067811865477) True >>> math.isclose(force[1], 7.0710678118654755) True >>> force = polar_force(10, 3.14, radian_mode=True) >>> math.isclose(force[0], -9.999987317275396) True >>> math.isclose(force[1], 0.01592652916486828) True """ if radian_mode: return [magnitude * cos(angle), magnitude * sin(angle)] return [magnitude * cos(radians(angle)), magnitude * sin(radians(angle))] def in_static_equilibrium( forces: NDArray[float64], location: NDArray[float64], eps: float = 10**-1 ) -> bool: """ Check if a system is in equilibrium. It takes two numpy.array objects. forces ==> [ [force1_x, force1_y], [force2_x, force2_y], ....] location ==> [ [x1, y1], [x2, y2], ....] >>> force = array([[1, 1], [-1, 2]]) >>> location = array([[1, 0], [10, 0]]) >>> in_static_equilibrium(force, location) False """ # summation of moments is zero moments: NDArray[float64] = cross(location, forces) sum_moments: float = sum(moments) return abs(sum_moments) < eps if __name__ == "__main__": # Test to check if it works forces = array( [ polar_force(718.4, 180 - 30), polar_force(879.54, 45), polar_force(100, -90), ] ) location: NDArray[float64] = array([[0, 0], [0, 0], [0, 0]]) assert in_static_equilibrium(forces, location) # Problem 1 in image_data/2D_problems.jpg forces = array( [ polar_force(30 * 9.81, 15), polar_force(215, 180 - 45), polar_force(264, 90 - 30), ] ) location = array([[0, 0], [0, 0], [0, 0]]) assert in_static_equilibrium(forces, location) # Problem in image_data/2D_problems_1.jpg forces = array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]]) location = array([[0, 0], [6, 0], [10, 0], [12, 0]]) assert in_static_equilibrium(forces, location) import doctest doctest.testmod()

""" Checks if a system of forces is in static equilibrium. """ from __future__ import annotations from numpy import array, cos, cross, float64, radians, sin from numpy.typing import NDArray def polar_force( magnitude: float, angle: float, radian_mode: bool = False ) -> list[float]: """ Resolves force along rectangular components. (force, angle) => (force_x, force_y) >>> import math >>> force = polar_force(10, 45) >>> math.isclose(force[0], 7.071067811865477) True >>> math.isclose(force[1], 7.0710678118654755) True >>> force = polar_force(10, 3.14, radian_mode=True) >>> math.isclose(force[0], -9.999987317275396) True >>> math.isclose(force[1], 0.01592652916486828) True """ if radian_mode: return [magnitude * cos(angle), magnitude * sin(angle)] return [magnitude * cos(radians(angle)), magnitude * sin(radians(angle))] def in_static_equilibrium( forces: NDArray[float64], location: NDArray[float64], eps: float = 10**-1 ) -> bool: """ Check if a system is in equilibrium. It takes two numpy.array objects. forces ==> [ [force1_x, force1_y], [force2_x, force2_y], ....] location ==> [ [x1, y1], [x2, y2], ....] >>> force = array([[1, 1], [-1, 2]]) >>> location = array([[1, 0], [10, 0]]) >>> in_static_equilibrium(force, location) False """ # summation of moments is zero moments: NDArray[float64] = cross(location, forces) sum_moments: float = sum(moments) return abs(sum_moments) < eps if __name__ == "__main__": # Test to check if it works forces = array( [ polar_force(718.4, 180 - 30), polar_force(879.54, 45), polar_force(100, -90), ] ) location: NDArray[float64] = array([[0, 0], [0, 0], [0, 0]]) assert in_static_equilibrium(forces, location) # Problem 1 in image_data/2D_problems.jpg forces = array( [ polar_force(30 * 9.81, 15), polar_force(215, 180 - 45), polar_force(264, 90 - 30), ] ) location = array([[0, 0], [0, 0], [0, 0]]) assert in_static_equilibrium(forces, location) # Problem in image_data/2D_problems_1.jpg forces = array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]]) location = array([[0, 0], [6, 0], [10, 0], [12, 0]]) assert in_static_equilibrium(forces, location) import doctest doctest.testmod()

TheAlgorithms/Python

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""" Normalization. Wikipedia: https://en.wikipedia.org/wiki/Normalization Normalization is the process of converting numerical data to a standard range of values. This range is typically between [0, 1] or [-1, 1]. The equation for normalization is x_norm = (x - x_min)/(x_max - x_min) where x_norm is the normalized value, x is the value, x_min is the minimum value within the column or list of data, and x_max is the maximum value within the column or list of data. Normalization is used to speed up the training of data and put all of the data on a similar scale. This is useful because variance in the range of values of a dataset can heavily impact optimization (particularly Gradient Descent). Standardization Wikipedia: https://en.wikipedia.org/wiki/Standardization Standardization is the process of converting numerical data to a normally distributed range of values. This range will have a mean of 0 and standard deviation of 1. This is also known as z-score normalization. The equation for standardization is x_std = (x - mu)/(sigma) where mu is the mean of the column or list of values and sigma is the standard deviation of the column or list of values. Choosing between Normalization & Standardization is more of an art of a science, but it is often recommended to run experiments with both to see which performs better. Additionally, a few rules of thumb are: 1. gaussian (normal) distributions work better with standardization 2. non-gaussian (non-normal) distributions work better with normalization 3. If a column or list of values has extreme values / outliers, use standardization """ from statistics import mean, stdev def normalization(data: list, ndigits: int = 3) -> list: """ Return a normalized list of values. @params: data, a list of values to normalize @returns: a list of normalized values (rounded to ndigits decimal places) @examples: >>> normalization([2, 7, 10, 20, 30, 50]) [0.0, 0.104, 0.167, 0.375, 0.583, 1.0] >>> normalization([5, 10, 15, 20, 25]) [0.0, 0.25, 0.5, 0.75, 1.0] """ # variables for calculation x_min = min(data) x_max = max(data) # normalize data return [round((x - x_min) / (x_max - x_min), ndigits) for x in data] def standardization(data: list, ndigits: int = 3) -> list: """ Return a standardized list of values. @params: data, a list of values to standardize @returns: a list of standardized values (rounded to ndigits decimal places) @examples: >>> standardization([2, 7, 10, 20, 30, 50]) [-0.999, -0.719, -0.551, 0.009, 0.57, 1.69] >>> standardization([5, 10, 15, 20, 25]) [-1.265, -0.632, 0.0, 0.632, 1.265] """ # variables for calculation mu = mean(data) sigma = stdev(data) # standardize data return [round((x - mu) / (sigma), ndigits) for x in data]

""" Normalization. Wikipedia: https://en.wikipedia.org/wiki/Normalization Normalization is the process of converting numerical data to a standard range of values. This range is typically between [0, 1] or [-1, 1]. The equation for normalization is x_norm = (x - x_min)/(x_max - x_min) where x_norm is the normalized value, x is the value, x_min is the minimum value within the column or list of data, and x_max is the maximum value within the column or list of data. Normalization is used to speed up the training of data and put all of the data on a similar scale. This is useful because variance in the range of values of a dataset can heavily impact optimization (particularly Gradient Descent). Standardization Wikipedia: https://en.wikipedia.org/wiki/Standardization Standardization is the process of converting numerical data to a normally distributed range of values. This range will have a mean of 0 and standard deviation of 1. This is also known as z-score normalization. The equation for standardization is x_std = (x - mu)/(sigma) where mu is the mean of the column or list of values and sigma is the standard deviation of the column or list of values. Choosing between Normalization & Standardization is more of an art of a science, but it is often recommended to run experiments with both to see which performs better. Additionally, a few rules of thumb are: 1. gaussian (normal) distributions work better with standardization 2. non-gaussian (non-normal) distributions work better with normalization 3. If a column or list of values has extreme values / outliers, use standardization """ from statistics import mean, stdev def normalization(data: list, ndigits: int = 3) -> list: """ Return a normalized list of values. @params: data, a list of values to normalize @returns: a list of normalized values (rounded to ndigits decimal places) @examples: >>> normalization([2, 7, 10, 20, 30, 50]) [0.0, 0.104, 0.167, 0.375, 0.583, 1.0] >>> normalization([5, 10, 15, 20, 25]) [0.0, 0.25, 0.5, 0.75, 1.0] """ # variables for calculation x_min = min(data) x_max = max(data) # normalize data return [round((x - x_min) / (x_max - x_min), ndigits) for x in data] def standardization(data: list, ndigits: int = 3) -> list: """ Return a standardized list of values. @params: data, a list of values to standardize @returns: a list of standardized values (rounded to ndigits decimal places) @examples: >>> standardization([2, 7, 10, 20, 30, 50]) [-0.999, -0.719, -0.551, 0.009, 0.57, 1.69] >>> standardization([5, 10, 15, 20, 25]) [-1.265, -0.632, 0.0, 0.632, 1.265] """ # variables for calculation mu = mean(data) sigma = stdev(data) # standardize data return [round((x - mu) / (sigma), ndigits) for x in data]

TheAlgorithms/Python

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""" https://en.wikipedia.org/wiki/Rayleigh_quotient """ from typing import Any import numpy as np def is_hermitian(matrix: np.ndarray) -> bool: """ Checks if a matrix is Hermitian. >>> import numpy as np >>> A = np.array([ ... [2, 2+1j, 4], ... [2-1j, 3, 1j], ... [4, -1j, 1]]) >>> is_hermitian(A) True >>> A = np.array([ ... [2, 2+1j, 4+1j], ... [2-1j, 3, 1j], ... [4, -1j, 1]]) >>> is_hermitian(A) False """ return np.array_equal(matrix, matrix.conjugate().T) def rayleigh_quotient(a: np.ndarray, v: np.ndarray) -> Any: """ Returns the Rayleigh quotient of a Hermitian matrix A and vector v. >>> import numpy as np >>> A = np.array([ ... [1, 2, 4], ... [2, 3, -1], ... [4, -1, 1] ... ]) >>> v = np.array([ ... [1], ... [2], ... [3] ... ]) >>> rayleigh_quotient(A, v) array([[3.]]) """ v_star = v.conjugate().T v_star_dot = v_star.dot(a) assert isinstance(v_star_dot, np.ndarray) return (v_star_dot.dot(v)) / (v_star.dot(v)) def tests() -> None: a = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]) v = np.array([[1], [2], [3]]) assert is_hermitian(a), f"{a} is not hermitian." print(rayleigh_quotient(a, v)) a = np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]) assert is_hermitian(a), f"{a} is not hermitian." assert rayleigh_quotient(a, v) == float(3) if __name__ == "__main__": import doctest doctest.testmod() tests()

""" https://en.wikipedia.org/wiki/Rayleigh_quotient """ from typing import Any import numpy as np def is_hermitian(matrix: np.ndarray) -> bool: """ Checks if a matrix is Hermitian. >>> import numpy as np >>> A = np.array([ ... [2, 2+1j, 4], ... [2-1j, 3, 1j], ... [4, -1j, 1]]) >>> is_hermitian(A) True >>> A = np.array([ ... [2, 2+1j, 4+1j], ... [2-1j, 3, 1j], ... [4, -1j, 1]]) >>> is_hermitian(A) False """ return np.array_equal(matrix, matrix.conjugate().T) def rayleigh_quotient(a: np.ndarray, v: np.ndarray) -> Any: """ Returns the Rayleigh quotient of a Hermitian matrix A and vector v. >>> import numpy as np >>> A = np.array([ ... [1, 2, 4], ... [2, 3, -1], ... [4, -1, 1] ... ]) >>> v = np.array([ ... [1], ... [2], ... [3] ... ]) >>> rayleigh_quotient(A, v) array([[3.]]) """ v_star = v.conjugate().T v_star_dot = v_star.dot(a) assert isinstance(v_star_dot, np.ndarray) return (v_star_dot.dot(v)) / (v_star.dot(v)) def tests() -> None: a = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]) v = np.array([[1], [2], [3]]) assert is_hermitian(a), f"{a} is not hermitian." print(rayleigh_quotient(a, v)) a = np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]) assert is_hermitian(a), f"{a} is not hermitian." assert rayleigh_quotient(a, v) == float(3) if __name__ == "__main__": import doctest doctest.testmod() tests()

TheAlgorithms/Python

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""" Implementation of finding nth fibonacci number using matrix exponentiation. Time Complexity is about O(log(n)*8), where 8 is the complexity of matrix multiplication of size 2 by 2. And on the other hand complexity of bruteforce solution is O(n). As we know f[n] = f[n-1] + f[n-1] Converting to matrix, [f(n),f(n-1)] = [[1,1],[1,0]] * [f(n-1),f(n-2)] -> [f(n),f(n-1)] = [[1,1],[1,0]]^2 * [f(n-2),f(n-3)] ... ... -> [f(n),f(n-1)] = [[1,1],[1,0]]^(n-1) * [f(1),f(0)] So we just need the n times multiplication of the matrix [1,1],[1,0]]. We can decrease the n times multiplication by following the divide and conquer approach. """ def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]: matrix_c = [] n = len(matrix_a) for i in range(n): list_1 = [] for j in range(n): val = 0 for k in range(n): val = val + matrix_a[i][k] * matrix_b[k][j] list_1.append(val) matrix_c.append(list_1) return matrix_c def identity(n: int) -> list[list[int]]: return [[int(row == column) for column in range(n)] for row in range(n)] def nth_fibonacci_matrix(n: int) -> int: """ >>> nth_fibonacci_matrix(100) 354224848179261915075 >>> nth_fibonacci_matrix(-100) -100 """ if n <= 1: return n res_matrix = identity(2) fibonacci_matrix = [[1, 1], [1, 0]] n = n - 1 while n > 0: if n % 2 == 1: res_matrix = multiply(res_matrix, fibonacci_matrix) fibonacci_matrix = multiply(fibonacci_matrix, fibonacci_matrix) n = int(n / 2) return res_matrix[0][0] def nth_fibonacci_bruteforce(n: int) -> int: """ >>> nth_fibonacci_bruteforce(100) 354224848179261915075 >>> nth_fibonacci_bruteforce(-100) -100 """ if n <= 1: return n fib0 = 0 fib1 = 1 for _ in range(2, n + 1): fib0, fib1 = fib1, fib0 + fib1 return fib1 def main() -> None: for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split(): n = int("".join(c for c in ordinal if c in "0123456789")) # 1000th --> 1000 print( f"{ordinal} fibonacci number using matrix exponentiation is " f"{nth_fibonacci_matrix(n)} and using bruteforce is " f"{nth_fibonacci_bruteforce(n)}\n" ) # from timeit import timeit # print(timeit("nth_fibonacci_matrix(1000000)", # "from main import nth_fibonacci_matrix", number=5)) # print(timeit("nth_fibonacci_bruteforce(1000000)", # "from main import nth_fibonacci_bruteforce", number=5)) # 2.3342058970001744 # 57.256506615000035 if __name__ == "__main__": import doctest doctest.testmod() main()

""" Implementation of finding nth fibonacci number using matrix exponentiation. Time Complexity is about O(log(n)*8), where 8 is the complexity of matrix multiplication of size 2 by 2. And on the other hand complexity of bruteforce solution is O(n). As we know f[n] = f[n-1] + f[n-1] Converting to matrix, [f(n),f(n-1)] = [[1,1],[1,0]] * [f(n-1),f(n-2)] -> [f(n),f(n-1)] = [[1,1],[1,0]]^2 * [f(n-2),f(n-3)] ... ... -> [f(n),f(n-1)] = [[1,1],[1,0]]^(n-1) * [f(1),f(0)] So we just need the n times multiplication of the matrix [1,1],[1,0]]. We can decrease the n times multiplication by following the divide and conquer approach. """ def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]: matrix_c = [] n = len(matrix_a) for i in range(n): list_1 = [] for j in range(n): val = 0 for k in range(n): val = val + matrix_a[i][k] * matrix_b[k][j] list_1.append(val) matrix_c.append(list_1) return matrix_c def identity(n: int) -> list[list[int]]: return [[int(row == column) for column in range(n)] for row in range(n)] def nth_fibonacci_matrix(n: int) -> int: """ >>> nth_fibonacci_matrix(100) 354224848179261915075 >>> nth_fibonacci_matrix(-100) -100 """ if n <= 1: return n res_matrix = identity(2) fibonacci_matrix = [[1, 1], [1, 0]] n = n - 1 while n > 0: if n % 2 == 1: res_matrix = multiply(res_matrix, fibonacci_matrix) fibonacci_matrix = multiply(fibonacci_matrix, fibonacci_matrix) n = int(n / 2) return res_matrix[0][0] def nth_fibonacci_bruteforce(n: int) -> int: """ >>> nth_fibonacci_bruteforce(100) 354224848179261915075 >>> nth_fibonacci_bruteforce(-100) -100 """ if n <= 1: return n fib0 = 0 fib1 = 1 for _ in range(2, n + 1): fib0, fib1 = fib1, fib0 + fib1 return fib1 def main() -> None: for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split(): n = int("".join(c for c in ordinal if c in "0123456789")) # 1000th --> 1000 print( f"{ordinal} fibonacci number using matrix exponentiation is " f"{nth_fibonacci_matrix(n)} and using bruteforce is " f"{nth_fibonacci_bruteforce(n)}\n" ) # from timeit import timeit # print(timeit("nth_fibonacci_matrix(1000000)", # "from main import nth_fibonacci_matrix", number=5)) # print(timeit("nth_fibonacci_bruteforce(1000000)", # "from main import nth_fibonacci_bruteforce", number=5)) # 2.3342058970001744 # 57.256506615000035 if __name__ == "__main__": import doctest doctest.testmod() main()

TheAlgorithms/Python

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"""Created by Nathan Damon, @bizzfitch on github >>> test_miller_rabin() """ def miller_rabin(n: int, allow_probable: bool = False) -> bool: """Deterministic Miller-Rabin algorithm for primes ~< 3.32e24. Uses numerical analysis results to return whether or not the passed number is prime. If the passed number is above the upper limit, and allow_probable is True, then a return value of True indicates that n is probably prime. This test does not allow False negatives- a return value of False is ALWAYS composite. Parameters ---------- n : int The integer to be tested. Since we usually care if a number is prime, n < 2 returns False instead of raising a ValueError. allow_probable: bool, default False Whether or not to test n above the upper bound of the deterministic test. Raises ------ ValueError Reference --------- https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test """ if n == 2: return True if not n % 2 or n < 2: return False if n > 5 and n % 10 not in (1, 3, 7, 9): # can quickly check last digit return False if n > 3_317_044_064_679_887_385_961_981 and not allow_probable: raise ValueError( "Warning: upper bound of deterministic test is exceeded. " "Pass allow_probable=True to allow probabilistic test. " "A return value of True indicates a probable prime." ) # array bounds provided by analysis bounds = [ 2_047, 1_373_653, 25_326_001, 3_215_031_751, 2_152_302_898_747, 3_474_749_660_383, 341_550_071_728_321, 1, 3_825_123_056_546_413_051, 1, 1, 318_665_857_834_031_151_167_461, 3_317_044_064_679_887_385_961_981, ] primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41] for idx, _p in enumerate(bounds, 1): if n < _p: # then we have our last prime to check plist = primes[:idx] break d, s = n - 1, 0 # break up n -1 into a power of 2 (s) and # remaining odd component # essentially, solve for d * 2 ** s == n - 1 while d % 2 == 0: d //= 2 s += 1 for prime in plist: pr = False for r in range(s): m = pow(prime, d * 2**r, n) # see article for analysis explanation for m if (r == 0 and m == 1) or ((m + 1) % n == 0): pr = True # this loop will not determine compositeness break if pr: continue # if pr is False, then the above loop never evaluated to true, # and the n MUST be composite return False return True def test_miller_rabin() -> None: """Testing a nontrivial (ends in 1, 3, 7, 9) composite and a prime in each range. """ assert not miller_rabin(561) assert miller_rabin(563) # 2047 assert not miller_rabin(838_201) assert miller_rabin(838_207) # 1_373_653 assert not miller_rabin(17_316_001) assert miller_rabin(17_316_017) # 25_326_001 assert not miller_rabin(3_078_386_641) assert miller_rabin(3_078_386_653) # 3_215_031_751 assert not miller_rabin(1_713_045_574_801) assert miller_rabin(1_713_045_574_819) # 2_152_302_898_747 assert not miller_rabin(2_779_799_728_307) assert miller_rabin(2_779_799_728_327) # 3_474_749_660_383 assert not miller_rabin(113_850_023_909_441) assert miller_rabin(113_850_023_909_527) # 341_550_071_728_321 assert not miller_rabin(1_275_041_018_848_804_351) assert miller_rabin(1_275_041_018_848_804_391) # 3_825_123_056_546_413_051 assert not miller_rabin(79_666_464_458_507_787_791_867) assert miller_rabin(79_666_464_458_507_787_791_951) # 318_665_857_834_031_151_167_461 assert not miller_rabin(552_840_677_446_647_897_660_333) assert miller_rabin(552_840_677_446_647_897_660_359) # 3_317_044_064_679_887_385_961_981 # upper limit for probabilistic test if __name__ == "__main__": test_miller_rabin()

"""Created by Nathan Damon, @bizzfitch on github >>> test_miller_rabin() """ def miller_rabin(n: int, allow_probable: bool = False) -> bool: """Deterministic Miller-Rabin algorithm for primes ~< 3.32e24. Uses numerical analysis results to return whether or not the passed number is prime. If the passed number is above the upper limit, and allow_probable is True, then a return value of True indicates that n is probably prime. This test does not allow False negatives- a return value of False is ALWAYS composite. Parameters ---------- n : int The integer to be tested. Since we usually care if a number is prime, n < 2 returns False instead of raising a ValueError. allow_probable: bool, default False Whether or not to test n above the upper bound of the deterministic test. Raises ------ ValueError Reference --------- https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test """ if n == 2: return True if not n % 2 or n < 2: return False if n > 5 and n % 10 not in (1, 3, 7, 9): # can quickly check last digit return False if n > 3_317_044_064_679_887_385_961_981 and not allow_probable: raise ValueError( "Warning: upper bound of deterministic test is exceeded. " "Pass allow_probable=True to allow probabilistic test. " "A return value of True indicates a probable prime." ) # array bounds provided by analysis bounds = [ 2_047, 1_373_653, 25_326_001, 3_215_031_751, 2_152_302_898_747, 3_474_749_660_383, 341_550_071_728_321, 1, 3_825_123_056_546_413_051, 1, 1, 318_665_857_834_031_151_167_461, 3_317_044_064_679_887_385_961_981, ] primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41] for idx, _p in enumerate(bounds, 1): if n < _p: # then we have our last prime to check plist = primes[:idx] break d, s = n - 1, 0 # break up n -1 into a power of 2 (s) and # remaining odd component # essentially, solve for d * 2 ** s == n - 1 while d % 2 == 0: d //= 2 s += 1 for prime in plist: pr = False for r in range(s): m = pow(prime, d * 2**r, n) # see article for analysis explanation for m if (r == 0 and m == 1) or ((m + 1) % n == 0): pr = True # this loop will not determine compositeness break if pr: continue # if pr is False, then the above loop never evaluated to true, # and the n MUST be composite return False return True def test_miller_rabin() -> None: """Testing a nontrivial (ends in 1, 3, 7, 9) composite and a prime in each range. """ assert not miller_rabin(561) assert miller_rabin(563) # 2047 assert not miller_rabin(838_201) assert miller_rabin(838_207) # 1_373_653 assert not miller_rabin(17_316_001) assert miller_rabin(17_316_017) # 25_326_001 assert not miller_rabin(3_078_386_641) assert miller_rabin(3_078_386_653) # 3_215_031_751 assert not miller_rabin(1_713_045_574_801) assert miller_rabin(1_713_045_574_819) # 2_152_302_898_747 assert not miller_rabin(2_779_799_728_307) assert miller_rabin(2_779_799_728_327) # 3_474_749_660_383 assert not miller_rabin(113_850_023_909_441) assert miller_rabin(113_850_023_909_527) # 341_550_071_728_321 assert not miller_rabin(1_275_041_018_848_804_351) assert miller_rabin(1_275_041_018_848_804_391) # 3_825_123_056_546_413_051 assert not miller_rabin(79_666_464_458_507_787_791_867) assert miller_rabin(79_666_464_458_507_787_791_951) # 318_665_857_834_031_151_167_461 assert not miller_rabin(552_840_677_446_647_897_660_333) assert miller_rabin(552_840_677_446_647_897_660_359) # 3_317_044_064_679_887_385_961_981 # upper limit for probabilistic test if __name__ == "__main__": test_miller_rabin()

TheAlgorithms/Python

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""" This module contains the functions to calculate the focal length, object distance and image distance of a mirror. The mirror formula is an equation that relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror. It is commonly used in optics to determine the position and characteristics of an image formed by a mirror. It is expressed using the formulae : ------------------- | 1/f = 1/v + 1/u | ------------------- Where, f = Focal length of the spherical mirror (metre) v = Image distance from the mirror (metre) u = Object distance from the mirror (metre) The signs of the distances are taken with respect to the sign convention. The sign convention is as follows: 1) Object is always placed to the left of mirror 2) Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative. 3) All distances are measured from the pole of the mirror. There are a few assumptions that are made while using the mirror formulae. They are as follows: 1) Thin Mirror: The mirror is assumed to be thin, meaning its thickness is negligible compared to its radius of curvature. This assumption allows us to treat the mirror as a two-dimensional surface. 2) Spherical Mirror: The mirror is assumed to have a spherical shape. While this assumption may not hold exactly for all mirrors, it is a reasonable approximation for most practical purposes. 3) Small Angles: The angles involved in the derivation are assumed to be small. This assumption allows us to use the small-angle approximation, where the tangent of a small angle is approximately equal to the angle itself. It simplifies the calculations and makes the derivation more manageable. 4) Paraxial Rays: The mirror formula is derived using paraxial rays, which are rays that are close to the principal axis and make small angles with it. This assumption ensures that the rays are close enough to the principal axis, making the calculations more accurate. 5) Reflection and Refraction Laws: The derivation assumes that the laws of reflection and refraction hold. These laws state that the angle of incidence is equal to the angle of reflection for reflection, and the incident and refracted rays lie in the same plane and obey Snell's law for refraction. (Description and Assumptions adapted from https://www.collegesearch.in/articles/mirror-formula-derivation) (Sign Convention adapted from https://www.toppr.com/ask/content/concept/sign-convention-for-mirrors-210189/) """ def focal_length(distance_of_object: float, distance_of_image: float) -> float: """ >>> from math import isclose >>> isclose(focal_length(10, 20), 6.66666666666666) True >>> from math import isclose >>> isclose(focal_length(9.5, 6.7), 3.929012346) True >>> focal_length(0, 20) # doctest: +NORMALIZE_WHITESPACE Traceback (most recent call last): ... ValueError: Invalid inputs. Enter non zero values with respect to the sign convention. """ if distance_of_object == 0 or distance_of_image == 0: raise ValueError( "Invalid inputs. Enter non zero values with respect to the sign convention." ) focal_length = 1 / ((1 / distance_of_object) + (1 / distance_of_image)) return focal_length def object_distance(focal_length: float, distance_of_image: float) -> float: """ >>> from math import isclose >>> isclose(object_distance(30, 20), -60.0) True >>> from math import isclose >>> isclose(object_distance(10.5, 11.7), 102.375) True >>> object_distance(90, 0) # doctest: +NORMALIZE_WHITESPACE Traceback (most recent call last): ... ValueError: Invalid inputs. Enter non zero values with respect to the sign convention. """ if distance_of_image == 0 or focal_length == 0: raise ValueError( "Invalid inputs. Enter non zero values with respect to the sign convention." ) object_distance = 1 / ((1 / focal_length) - (1 / distance_of_image)) return object_distance def image_distance(focal_length: float, distance_of_object: float) -> float: """ >>> from math import isclose >>> isclose(image_distance(10, 40), 13.33333333) True >>> from math import isclose >>> isclose(image_distance(1.5, 6.7), 1.932692308) True >>> image_distance(0, 0) # doctest: +NORMALIZE_WHITESPACE Traceback (most recent call last): ... ValueError: Invalid inputs. Enter non zero values with respect to the sign convention. """ if distance_of_object == 0 or focal_length == 0: raise ValueError( "Invalid inputs. Enter non zero values with respect to the sign convention." ) image_distance = 1 / ((1 / focal_length) - (1 / distance_of_object)) return image_distance

""" This module contains the functions to calculate the focal length, object distance and image distance of a mirror. The mirror formula is an equation that relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror. It is commonly used in optics to determine the position and characteristics of an image formed by a mirror. It is expressed using the formulae : ------------------- | 1/f = 1/v + 1/u | ------------------- Where, f = Focal length of the spherical mirror (metre) v = Image distance from the mirror (metre) u = Object distance from the mirror (metre) The signs of the distances are taken with respect to the sign convention. The sign convention is as follows: 1) Object is always placed to the left of mirror 2) Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative. 3) All distances are measured from the pole of the mirror. There are a few assumptions that are made while using the mirror formulae. They are as follows: 1) Thin Mirror: The mirror is assumed to be thin, meaning its thickness is negligible compared to its radius of curvature. This assumption allows us to treat the mirror as a two-dimensional surface. 2) Spherical Mirror: The mirror is assumed to have a spherical shape. While this assumption may not hold exactly for all mirrors, it is a reasonable approximation for most practical purposes. 3) Small Angles: The angles involved in the derivation are assumed to be small. This assumption allows us to use the small-angle approximation, where the tangent of a small angle is approximately equal to the angle itself. It simplifies the calculations and makes the derivation more manageable. 4) Paraxial Rays: The mirror formula is derived using paraxial rays, which are rays that are close to the principal axis and make small angles with it. This assumption ensures that the rays are close enough to the principal axis, making the calculations more accurate. 5) Reflection and Refraction Laws: The derivation assumes that the laws of reflection and refraction hold. These laws state that the angle of incidence is equal to the angle of reflection for reflection, and the incident and refracted rays lie in the same plane and obey Snell's law for refraction. (Description and Assumptions adapted from https://www.collegesearch.in/articles/mirror-formula-derivation) (Sign Convention adapted from https://www.toppr.com/ask/content/concept/sign-convention-for-mirrors-210189/) """ def focal_length(distance_of_object: float, distance_of_image: float) -> float: """ >>> from math import isclose >>> isclose(focal_length(10, 20), 6.66666666666666) True >>> from math import isclose >>> isclose(focal_length(9.5, 6.7), 3.929012346) True >>> focal_length(0, 20) # doctest: +NORMALIZE_WHITESPACE Traceback (most recent call last): ... ValueError: Invalid inputs. Enter non zero values with respect to the sign convention. """ if distance_of_object == 0 or distance_of_image == 0: raise ValueError( "Invalid inputs. Enter non zero values with respect to the sign convention." ) focal_length = 1 / ((1 / distance_of_object) + (1 / distance_of_image)) return focal_length def object_distance(focal_length: float, distance_of_image: float) -> float: """ >>> from math import isclose >>> isclose(object_distance(30, 20), -60.0) True >>> from math import isclose >>> isclose(object_distance(10.5, 11.7), 102.375) True >>> object_distance(90, 0) # doctest: +NORMALIZE_WHITESPACE Traceback (most recent call last): ... ValueError: Invalid inputs. Enter non zero values with respect to the sign convention. """ if distance_of_image == 0 or focal_length == 0: raise ValueError( "Invalid inputs. Enter non zero values with respect to the sign convention." ) object_distance = 1 / ((1 / focal_length) - (1 / distance_of_image)) return object_distance def image_distance(focal_length: float, distance_of_object: float) -> float: """ >>> from math import isclose >>> isclose(image_distance(10, 40), 13.33333333) True >>> from math import isclose >>> isclose(image_distance(1.5, 6.7), 1.932692308) True >>> image_distance(0, 0) # doctest: +NORMALIZE_WHITESPACE Traceback (most recent call last): ... ValueError: Invalid inputs. Enter non zero values with respect to the sign convention. """ if distance_of_object == 0 or focal_length == 0: raise ValueError( "Invalid inputs. Enter non zero values with respect to the sign convention." ) image_distance = 1 / ((1 / focal_length) - (1 / distance_of_object)) return image_distance

TheAlgorithms/Python

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""" A Radix Tree is a data structure that represents a space-optimized trie (prefix tree) in whicheach node that is the only child is merged with its parent [https://en.wikipedia.org/wiki/Radix_tree] """ class RadixNode: def __init__(self, prefix: str = "", is_leaf: bool = False) -> None: # Mapping from the first character of the prefix of the node self.nodes: dict[str, RadixNode] = {} # A node will be a leaf if the tree contains its word self.is_leaf = is_leaf self.prefix = prefix def match(self, word: str) -> tuple[str, str, str]: """Compute the common substring of the prefix of the node and a word Args: word (str): word to compare Returns: (str, str, str): common substring, remaining prefix, remaining word >>> RadixNode("myprefix").match("mystring") ('my', 'prefix', 'string') """ x = 0 for q, w in zip(self.prefix, word): if q != w: break x += 1 return self.prefix[:x], self.prefix[x:], word[x:] def insert_many(self, words: list[str]) -> None: """Insert many words in the tree Args: words (list[str]): list of words >>> RadixNode("myprefix").insert_many(["mystring", "hello"]) """ for word in words: self.insert(word) def insert(self, word: str) -> None: """Insert a word into the tree Args: word (str): word to insert >>> RadixNode("myprefix").insert("mystring") >>> root = RadixNode() >>> root.insert_many(['myprefix', 'myprefixA', 'myprefixAA']) >>> root.print_tree() - myprefix (leaf) -- A (leaf) --- A (leaf) """ # Case 1: If the word is the prefix of the node # Solution: We set the current node as leaf if self.prefix == word and not self.is_leaf: self.is_leaf = True # Case 2: The node has no edges that have a prefix to the word # Solution: We create an edge from the current node to a new one # containing the word elif word[0] not in self.nodes: self.nodes[word[0]] = RadixNode(prefix=word, is_leaf=True) else: incoming_node = self.nodes[word[0]] matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # Case 3: The node prefix is equal to the matching # Solution: We insert remaining word on the next node if remaining_prefix == "": self.nodes[matching_string[0]].insert(remaining_word) # Case 4: The word is greater equal to the matching # Solution: Create a node in between both nodes, change # prefixes and add the new node for the remaining word else: incoming_node.prefix = remaining_prefix aux_node = self.nodes[matching_string[0]] self.nodes[matching_string[0]] = RadixNode(matching_string, False) self.nodes[matching_string[0]].nodes[remaining_prefix[0]] = aux_node if remaining_word == "": self.nodes[matching_string[0]].is_leaf = True else: self.nodes[matching_string[0]].insert(remaining_word) def find(self, word: str) -> bool: """Returns if the word is on the tree Args: word (str): word to check Returns: bool: True if the word appears on the tree >>> RadixNode("myprefix").find("mystring") False """ incoming_node = self.nodes.get(word[0], None) if not incoming_node: return False else: matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # If there is remaining prefix, the word can't be on the tree if remaining_prefix != "": return False # This applies when the word and the prefix are equal elif remaining_word == "": return incoming_node.is_leaf # We have word remaining so we check the next node else: return incoming_node.find(remaining_word) def delete(self, word: str) -> bool: """Deletes a word from the tree if it exists Args: word (str): word to be deleted Returns: bool: True if the word was found and deleted. False if word is not found >>> RadixNode("myprefix").delete("mystring") False """ incoming_node = self.nodes.get(word[0], None) if not incoming_node: return False else: matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # If there is remaining prefix, the word can't be on the tree if remaining_prefix != "": return False # We have word remaining so we check the next node elif remaining_word != "": return incoming_node.delete(remaining_word) else: # If it is not a leaf, we don't have to delete if not incoming_node.is_leaf: return False else: # We delete the nodes if no edges go from it if len(incoming_node.nodes) == 0: del self.nodes[word[0]] # We merge the current node with its only child if len(self.nodes) == 1 and not self.is_leaf: merging_node = next(iter(self.nodes.values())) self.is_leaf = merging_node.is_leaf self.prefix += merging_node.prefix self.nodes = merging_node.nodes # If there is more than 1 edge, we just mark it as non-leaf elif len(incoming_node.nodes) > 1: incoming_node.is_leaf = False # If there is 1 edge, we merge it with its child else: merging_node = next(iter(incoming_node.nodes.values())) incoming_node.is_leaf = merging_node.is_leaf incoming_node.prefix += merging_node.prefix incoming_node.nodes = merging_node.nodes return True def print_tree(self, height: int = 0) -> None: """Print the tree Args: height (int, optional): Height of the printed node """ if self.prefix != "": print("-" * height, self.prefix, " (leaf)" if self.is_leaf else "") for value in self.nodes.values(): value.print_tree(height + 1) def test_trie() -> bool: words = "banana bananas bandana band apple all beast".split() root = RadixNode() root.insert_many(words) assert all(root.find(word) for word in words) assert not root.find("bandanas") assert not root.find("apps") root.delete("all") assert not root.find("all") root.delete("banana") assert not root.find("banana") assert root.find("bananas") return True def pytests() -> None: assert test_trie() def main() -> None: """ >>> pytests() """ root = RadixNode() words = "banana bananas bandanas bandana band apple all beast".split() root.insert_many(words) print("Words:", words) print("Tree:") root.print_tree() if __name__ == "__main__": main()

""" A Radix Tree is a data structure that represents a space-optimized trie (prefix tree) in whicheach node that is the only child is merged with its parent [https://en.wikipedia.org/wiki/Radix_tree] """ class RadixNode: def __init__(self, prefix: str = "", is_leaf: bool = False) -> None: # Mapping from the first character of the prefix of the node self.nodes: dict[str, RadixNode] = {} # A node will be a leaf if the tree contains its word self.is_leaf = is_leaf self.prefix = prefix def match(self, word: str) -> tuple[str, str, str]: """Compute the common substring of the prefix of the node and a word Args: word (str): word to compare Returns: (str, str, str): common substring, remaining prefix, remaining word >>> RadixNode("myprefix").match("mystring") ('my', 'prefix', 'string') """ x = 0 for q, w in zip(self.prefix, word): if q != w: break x += 1 return self.prefix[:x], self.prefix[x:], word[x:] def insert_many(self, words: list[str]) -> None: """Insert many words in the tree Args: words (list[str]): list of words >>> RadixNode("myprefix").insert_many(["mystring", "hello"]) """ for word in words: self.insert(word) def insert(self, word: str) -> None: """Insert a word into the tree Args: word (str): word to insert >>> RadixNode("myprefix").insert("mystring") >>> root = RadixNode() >>> root.insert_many(['myprefix', 'myprefixA', 'myprefixAA']) >>> root.print_tree() - myprefix (leaf) -- A (leaf) --- A (leaf) """ # Case 1: If the word is the prefix of the node # Solution: We set the current node as leaf if self.prefix == word and not self.is_leaf: self.is_leaf = True # Case 2: The node has no edges that have a prefix to the word # Solution: We create an edge from the current node to a new one # containing the word elif word[0] not in self.nodes: self.nodes[word[0]] = RadixNode(prefix=word, is_leaf=True) else: incoming_node = self.nodes[word[0]] matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # Case 3: The node prefix is equal to the matching # Solution: We insert remaining word on the next node if remaining_prefix == "": self.nodes[matching_string[0]].insert(remaining_word) # Case 4: The word is greater equal to the matching # Solution: Create a node in between both nodes, change # prefixes and add the new node for the remaining word else: incoming_node.prefix = remaining_prefix aux_node = self.nodes[matching_string[0]] self.nodes[matching_string[0]] = RadixNode(matching_string, False) self.nodes[matching_string[0]].nodes[remaining_prefix[0]] = aux_node if remaining_word == "": self.nodes[matching_string[0]].is_leaf = True else: self.nodes[matching_string[0]].insert(remaining_word) def find(self, word: str) -> bool: """Returns if the word is on the tree Args: word (str): word to check Returns: bool: True if the word appears on the tree >>> RadixNode("myprefix").find("mystring") False """ incoming_node = self.nodes.get(word[0], None) if not incoming_node: return False else: matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # If there is remaining prefix, the word can't be on the tree if remaining_prefix != "": return False # This applies when the word and the prefix are equal elif remaining_word == "": return incoming_node.is_leaf # We have word remaining so we check the next node else: return incoming_node.find(remaining_word) def delete(self, word: str) -> bool: """Deletes a word from the tree if it exists Args: word (str): word to be deleted Returns: bool: True if the word was found and deleted. False if word is not found >>> RadixNode("myprefix").delete("mystring") False """ incoming_node = self.nodes.get(word[0], None) if not incoming_node: return False else: matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # If there is remaining prefix, the word can't be on the tree if remaining_prefix != "": return False # We have word remaining so we check the next node elif remaining_word != "": return incoming_node.delete(remaining_word) else: # If it is not a leaf, we don't have to delete if not incoming_node.is_leaf: return False else: # We delete the nodes if no edges go from it if len(incoming_node.nodes) == 0: del self.nodes[word[0]] # We merge the current node with its only child if len(self.nodes) == 1 and not self.is_leaf: merging_node = next(iter(self.nodes.values())) self.is_leaf = merging_node.is_leaf self.prefix += merging_node.prefix self.nodes = merging_node.nodes # If there is more than 1 edge, we just mark it as non-leaf elif len(incoming_node.nodes) > 1: incoming_node.is_leaf = False # If there is 1 edge, we merge it with its child else: merging_node = next(iter(incoming_node.nodes.values())) incoming_node.is_leaf = merging_node.is_leaf incoming_node.prefix += merging_node.prefix incoming_node.nodes = merging_node.nodes return True def print_tree(self, height: int = 0) -> None: """Print the tree Args: height (int, optional): Height of the printed node """ if self.prefix != "": print("-" * height, self.prefix, " (leaf)" if self.is_leaf else "") for value in self.nodes.values(): value.print_tree(height + 1) def test_trie() -> bool: words = "banana bananas bandana band apple all beast".split() root = RadixNode() root.insert_many(words) assert all(root.find(word) for word in words) assert not root.find("bandanas") assert not root.find("apps") root.delete("all") assert not root.find("all") root.delete("banana") assert not root.find("banana") assert root.find("bananas") return True def pytests() -> None: assert test_trie() def main() -> None: """ >>> pytests() """ root = RadixNode() words = "banana bananas bandanas bandana band apple all beast".split() root.insert_many(words) print("Words:", words) print("Tree:") root.print_tree() if __name__ == "__main__": main()

TheAlgorithms/Python

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#!/usr/bin/env python3 import os try: from .build_directory_md import good_file_paths except ImportError: from build_directory_md import good_file_paths # type: ignore filepaths = list(good_file_paths()) assert filepaths, "good_file_paths() failed!" upper_files = [file for file in filepaths if file != file.lower()] if upper_files: print(f"{len(upper_files)} files contain uppercase characters:") print("\n".join(upper_files) + "\n") space_files = [file for file in filepaths if " " in file] if space_files: print(f"{len(space_files)} files contain space characters:") print("\n".join(space_files) + "\n") hyphen_files = [file for file in filepaths if "-" in file] if hyphen_files: print(f"{len(hyphen_files)} files contain hyphen characters:") print("\n".join(hyphen_files) + "\n") nodir_files = [file for file in filepaths if os.sep not in file] if nodir_files: print(f"{len(nodir_files)} files are not in a directory:") print("\n".join(nodir_files) + "\n") bad_files = len(upper_files + space_files + hyphen_files + nodir_files) if bad_files: import sys sys.exit(bad_files)

#!/usr/bin/env python3 import os try: from .build_directory_md import good_file_paths except ImportError: from build_directory_md import good_file_paths # type: ignore filepaths = list(good_file_paths()) assert filepaths, "good_file_paths() failed!" upper_files = [file for file in filepaths if file != file.lower()] if upper_files: print(f"{len(upper_files)} files contain uppercase characters:") print("\n".join(upper_files) + "\n") space_files = [file for file in filepaths if " " in file] if space_files: print(f"{len(space_files)} files contain space characters:") print("\n".join(space_files) + "\n") hyphen_files = [file for file in filepaths if "-" in file] if hyphen_files: print(f"{len(hyphen_files)} files contain hyphen characters:") print("\n".join(hyphen_files) + "\n") nodir_files = [file for file in filepaths if os.sep not in file] if nodir_files: print(f"{len(nodir_files)} files are not in a directory:") print("\n".join(nodir_files) + "\n") bad_files = len(upper_files + space_files + hyphen_files + nodir_files) if bad_files: import sys sys.exit(bad_files)

TheAlgorithms/Python

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""" README, Author - Jigyasa Gandhi(mailto:[email protected]) Requirements: - scikit-fuzzy - numpy - matplotlib Python: - 3.5 """ import numpy as np import skfuzzy as fuzz if __name__ == "__main__": # Create universe of discourse in Python using linspace () X = np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False) # Create two fuzzy sets by defining any membership function # (trapmf(), gbellmf(), gaussmf(), etc). abc1 = [0, 25, 50] abc2 = [25, 50, 75] young = fuzz.membership.trimf(X, abc1) middle_aged = fuzz.membership.trimf(X, abc2) # Compute the different operations using inbuilt functions. one = np.ones(75) zero = np.zeros((75,)) # 1. Union = max(µA(x), µB(x)) union = fuzz.fuzzy_or(X, young, X, middle_aged)[1] # 2. Intersection = min(µA(x), µB(x)) intersection = fuzz.fuzzy_and(X, young, X, middle_aged)[1] # 3. Complement (A) = (1- min(µA(x)) complement_a = fuzz.fuzzy_not(young) # 4. Difference (A/B) = min(µA(x),(1- µB(x))) difference = fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1] # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))] alg_sum = young + middle_aged - (young * middle_aged) # 6. Algebraic Product = (µA(x) * µB(x)) alg_product = young * middle_aged # 7. Bounded Sum = min[1,(µA(x), µB(x))] bdd_sum = fuzz.fuzzy_and(X, one, X, young + middle_aged)[1] # 8. Bounded difference = min[0,(µA(x), µB(x))] bdd_difference = fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1] # max-min composition # max-product composition # Plot each set A, set B and each operation result using plot() and subplot(). from matplotlib import pyplot as plt plt.figure() plt.subplot(4, 3, 1) plt.plot(X, young) plt.title("Young") plt.grid(True) plt.subplot(4, 3, 2) plt.plot(X, middle_aged) plt.title("Middle aged") plt.grid(True) plt.subplot(4, 3, 3) plt.plot(X, union) plt.title("union") plt.grid(True) plt.subplot(4, 3, 4) plt.plot(X, intersection) plt.title("intersection") plt.grid(True) plt.subplot(4, 3, 5) plt.plot(X, complement_a) plt.title("complement_a") plt.grid(True) plt.subplot(4, 3, 6) plt.plot(X, difference) plt.title("difference a/b") plt.grid(True) plt.subplot(4, 3, 7) plt.plot(X, alg_sum) plt.title("alg_sum") plt.grid(True) plt.subplot(4, 3, 8) plt.plot(X, alg_product) plt.title("alg_product") plt.grid(True) plt.subplot(4, 3, 9) plt.plot(X, bdd_sum) plt.title("bdd_sum") plt.grid(True) plt.subplot(4, 3, 10) plt.plot(X, bdd_difference) plt.title("bdd_difference") plt.grid(True) plt.subplots_adjust(hspace=0.5) plt.show()

""" README, Author - Jigyasa Gandhi(mailto:[email protected]) Requirements: - scikit-fuzzy - numpy - matplotlib Python: - 3.5 """ import numpy as np import skfuzzy as fuzz if __name__ == "__main__": # Create universe of discourse in Python using linspace () X = np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False) # Create two fuzzy sets by defining any membership function # (trapmf(), gbellmf(), gaussmf(), etc). abc1 = [0, 25, 50] abc2 = [25, 50, 75] young = fuzz.membership.trimf(X, abc1) middle_aged = fuzz.membership.trimf(X, abc2) # Compute the different operations using inbuilt functions. one = np.ones(75) zero = np.zeros((75,)) # 1. Union = max(µA(x), µB(x)) union = fuzz.fuzzy_or(X, young, X, middle_aged)[1] # 2. Intersection = min(µA(x), µB(x)) intersection = fuzz.fuzzy_and(X, young, X, middle_aged)[1] # 3. Complement (A) = (1- min(µA(x)) complement_a = fuzz.fuzzy_not(young) # 4. Difference (A/B) = min(µA(x),(1- µB(x))) difference = fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1] # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))] alg_sum = young + middle_aged - (young * middle_aged) # 6. Algebraic Product = (µA(x) * µB(x)) alg_product = young * middle_aged # 7. Bounded Sum = min[1,(µA(x), µB(x))] bdd_sum = fuzz.fuzzy_and(X, one, X, young + middle_aged)[1] # 8. Bounded difference = min[0,(µA(x), µB(x))] bdd_difference = fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1] # max-min composition # max-product composition # Plot each set A, set B and each operation result using plot() and subplot(). from matplotlib import pyplot as plt plt.figure() plt.subplot(4, 3, 1) plt.plot(X, young) plt.title("Young") plt.grid(True) plt.subplot(4, 3, 2) plt.plot(X, middle_aged) plt.title("Middle aged") plt.grid(True) plt.subplot(4, 3, 3) plt.plot(X, union) plt.title("union") plt.grid(True) plt.subplot(4, 3, 4) plt.plot(X, intersection) plt.title("intersection") plt.grid(True) plt.subplot(4, 3, 5) plt.plot(X, complement_a) plt.title("complement_a") plt.grid(True) plt.subplot(4, 3, 6) plt.plot(X, difference) plt.title("difference a/b") plt.grid(True) plt.subplot(4, 3, 7) plt.plot(X, alg_sum) plt.title("alg_sum") plt.grid(True) plt.subplot(4, 3, 8) plt.plot(X, alg_product) plt.title("alg_product") plt.grid(True) plt.subplot(4, 3, 9) plt.plot(X, bdd_sum) plt.title("bdd_sum") plt.grid(True) plt.subplot(4, 3, 10) plt.plot(X, bdd_difference) plt.title("bdd_difference") plt.grid(True) plt.subplots_adjust(hspace=0.5) plt.show()

TheAlgorithms/Python

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""" Project Euler Problem 72: https://projecteuler.net/problem=72 Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8 It can be seen that there are 21 elements in this set. How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000? """ def solution(limit: int = 1000000) -> int: """ Return the number of reduced proper fractions with denominator less than limit. >>> solution(8) 21 >>> solution(1000) 304191 """ primes = set(range(3, limit, 2)) primes.add(2) for p in range(3, limit, 2): if p not in primes: continue primes.difference_update(set(range(p * p, limit, p))) phi = [float(n) for n in range(limit + 1)] for p in primes: for n in range(p, limit + 1, p): phi[n] *= 1 - 1 / p return int(sum(phi[2:])) if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 72: https://projecteuler.net/problem=72 Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8 It can be seen that there are 21 elements in this set. How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000? """ def solution(limit: int = 1000000) -> int: """ Return the number of reduced proper fractions with denominator less than limit. >>> solution(8) 21 >>> solution(1000) 304191 """ primes = set(range(3, limit, 2)) primes.add(2) for p in range(3, limit, 2): if p not in primes: continue primes.difference_update(set(range(p * p, limit, p))) phi = [float(n) for n in range(limit + 1)] for p in primes: for n in range(p, limit + 1, p): phi[n] *= 1 - 1 / p return int(sum(phi[2:])) if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

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""" Project Euler Problem 131: https://projecteuler.net/problem=131 There are some prime values, p, for which there exists a positive integer, n, such that the expression n^3 + n^2p is a perfect cube. For example, when p = 19, 8^3 + 8^2 x 19 = 12^3. What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred. How many primes below one million have this remarkable property? """ from math import isqrt def is_prime(number: int) -> bool: """ Determines whether number is prime >>> is_prime(3) True >>> is_prime(4) False """ return all(number % divisor != 0 for divisor in range(2, isqrt(number) + 1)) def solution(max_prime: int = 10**6) -> int: """ Returns number of primes below max_prime with the property >>> solution(100) 4 """ primes_count = 0 cube_index = 1 prime_candidate = 7 while prime_candidate < max_prime: primes_count += is_prime(prime_candidate) cube_index += 1 prime_candidate += 6 * cube_index return primes_count if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 131: https://projecteuler.net/problem=131 There are some prime values, p, for which there exists a positive integer, n, such that the expression n^3 + n^2p is a perfect cube. For example, when p = 19, 8^3 + 8^2 x 19 = 12^3. What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred. How many primes below one million have this remarkable property? """ from math import isqrt def is_prime(number: int) -> bool: """ Determines whether number is prime >>> is_prime(3) True >>> is_prime(4) False """ return all(number % divisor != 0 for divisor in range(2, isqrt(number) + 1)) def solution(max_prime: int = 10**6) -> int: """ Returns number of primes below max_prime with the property >>> solution(100) 4 """ primes_count = 0 cube_index = 1 prime_candidate = 7 while prime_candidate < max_prime: primes_count += is_prime(prime_candidate) cube_index += 1 prime_candidate += 6 * cube_index return primes_count if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

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def binary_search(lst, item, start, end): if start == end: return start if lst[start] > item else start + 1 if start > end: return start mid = (start + end) // 2 if lst[mid] < item: return binary_search(lst, item, mid + 1, end) elif lst[mid] > item: return binary_search(lst, item, start, mid - 1) else: return mid def insertion_sort(lst): length = len(lst) for index in range(1, length): value = lst[index] pos = binary_search(lst, value, 0, index - 1) lst = lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :] return lst def merge(left, right): if not left: return right if not right: return left if left[0] < right[0]: return [left[0], *merge(left[1:], right)] return [right[0], *merge(left, right[1:])] def tim_sort(lst): """ >>> tim_sort("Python") ['P', 'h', 'n', 'o', 't', 'y'] >>> tim_sort((1.1, 1, 0, -1, -1.1)) [-1.1, -1, 0, 1, 1.1] >>> tim_sort(list(reversed(list(range(7))))) [0, 1, 2, 3, 4, 5, 6] >>> tim_sort([3, 2, 1]) == insertion_sort([3, 2, 1]) True >>> tim_sort([3, 2, 1]) == sorted([3, 2, 1]) True """ length = len(lst) runs, sorted_runs = [], [] new_run = [lst[0]] sorted_array = [] i = 1 while i < length: if lst[i] < lst[i - 1]: runs.append(new_run) new_run = [lst[i]] else: new_run.append(lst[i]) i += 1 runs.append(new_run) for run in runs: sorted_runs.append(insertion_sort(run)) for run in sorted_runs: sorted_array = merge(sorted_array, run) return sorted_array def main(): lst = [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7] sorted_lst = tim_sort(lst) print(sorted_lst) if __name__ == "__main__": main()

def binary_search(lst, item, start, end): if start == end: return start if lst[start] > item else start + 1 if start > end: return start mid = (start + end) // 2 if lst[mid] < item: return binary_search(lst, item, mid + 1, end) elif lst[mid] > item: return binary_search(lst, item, start, mid - 1) else: return mid def insertion_sort(lst): length = len(lst) for index in range(1, length): value = lst[index] pos = binary_search(lst, value, 0, index - 1) lst = lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :] return lst def merge(left, right): if not left: return right if not right: return left if left[0] < right[0]: return [left[0], *merge(left[1:], right)] return [right[0], *merge(left, right[1:])] def tim_sort(lst): """ >>> tim_sort("Python") ['P', 'h', 'n', 'o', 't', 'y'] >>> tim_sort((1.1, 1, 0, -1, -1.1)) [-1.1, -1, 0, 1, 1.1] >>> tim_sort(list(reversed(list(range(7))))) [0, 1, 2, 3, 4, 5, 6] >>> tim_sort([3, 2, 1]) == insertion_sort([3, 2, 1]) True >>> tim_sort([3, 2, 1]) == sorted([3, 2, 1]) True """ length = len(lst) runs, sorted_runs = [], [] new_run = [lst[0]] sorted_array = [] i = 1 while i < length: if lst[i] < lst[i - 1]: runs.append(new_run) new_run = [lst[i]] else: new_run.append(lst[i]) i += 1 runs.append(new_run) for run in runs: sorted_runs.append(insertion_sort(run)) for run in sorted_runs: sorted_array = merge(sorted_array, run) return sorted_array def main(): lst = [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7] sorted_lst = tim_sort(lst) print(sorted_lst) if __name__ == "__main__": main()

TheAlgorithms/Python

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""" Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that f(a) * f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents algebraic or transcendental equation. Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0) https://en.wikipedia.org/wiki/Bisection_method """ def equation(x: float) -> float: """ >>> equation(5) -15 >>> equation(0) 10 >>> equation(-5) -15 >>> equation(0.1) 9.99 >>> equation(-0.1) 9.99 """ return 10 - x * x def bisection(a: float, b: float) -> float: """ >>> bisection(-2, 5) 3.1611328125 >>> bisection(0, 6) 3.158203125 >>> bisection(2, 3) Traceback (most recent call last): ... ValueError: Wrong space! """ # Bolzano theory in order to find if there is a root between a and b if equation(a) * equation(b) >= 0: raise ValueError("Wrong space!") c = a while (b - a) >= 0.01: # Find middle point c = (a + b) / 2 # Check if middle point is root if equation(c) == 0.0: break # Decide the side to repeat the steps if equation(c) * equation(a) < 0: b = c else: a = c return c if __name__ == "__main__": import doctest doctest.testmod() print(bisection(-2, 5)) print(bisection(0, 6))

""" Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that f(a) * f(b) < 0 and f(x) is continuous in [a, b]. Here f(x) represents algebraic or transcendental equation. Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0) https://en.wikipedia.org/wiki/Bisection_method """ def equation(x: float) -> float: """ >>> equation(5) -15 >>> equation(0) 10 >>> equation(-5) -15 >>> equation(0.1) 9.99 >>> equation(-0.1) 9.99 """ return 10 - x * x def bisection(a: float, b: float) -> float: """ >>> bisection(-2, 5) 3.1611328125 >>> bisection(0, 6) 3.158203125 >>> bisection(2, 3) Traceback (most recent call last): ... ValueError: Wrong space! """ # Bolzano theory in order to find if there is a root between a and b if equation(a) * equation(b) >= 0: raise ValueError("Wrong space!") c = a while (b - a) >= 0.01: # Find middle point c = (a + b) / 2 # Check if middle point is root if equation(c) == 0.0: break # Decide the side to repeat the steps if equation(c) * equation(a) < 0: b = c else: a = c return c if __name__ == "__main__": import doctest doctest.testmod() print(bisection(-2, 5)) print(bisection(0, 6))

TheAlgorithms/Python

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TheAlgorithms/Python

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## Audio Filters * [Butterworth Filter](audio_filters/butterworth_filter.py) * [Iir Filter](audio_filters/iir_filter.py) * [Show Response](audio_filters/show_response.py) ## Backtracking * [All Combinations](backtracking/all_combinations.py) * [All Permutations](backtracking/all_permutations.py) * [All Subsequences](backtracking/all_subsequences.py) * [Coloring](backtracking/coloring.py) * [Combination Sum](backtracking/combination_sum.py) * [Crossword Puzzle Solver](backtracking/crossword_puzzle_solver.py) * [Generate Parentheses](backtracking/generate_parentheses.py) * [Hamiltonian Cycle](backtracking/hamiltonian_cycle.py) * [Knight Tour](backtracking/knight_tour.py) * [Match Word Pattern](backtracking/match_word_pattern.py) * [Minimax](backtracking/minimax.py) * [N Queens](backtracking/n_queens.py) * [N Queens Math](backtracking/n_queens_math.py) * [Power Sum](backtracking/power_sum.py) * [Rat In Maze](backtracking/rat_in_maze.py) * [Sudoku](backtracking/sudoku.py) * [Sum Of Subsets](backtracking/sum_of_subsets.py) * [Word Search](backtracking/word_search.py) ## Bit Manipulation * [Binary And Operator](bit_manipulation/binary_and_operator.py) * [Binary Coded Decimal](bit_manipulation/binary_coded_decimal.py) * [Binary Count Setbits](bit_manipulation/binary_count_setbits.py) * [Binary Count Trailing Zeros](bit_manipulation/binary_count_trailing_zeros.py) * [Binary Or Operator](bit_manipulation/binary_or_operator.py) * [Binary Shifts](bit_manipulation/binary_shifts.py) * [Binary Twos Complement](bit_manipulation/binary_twos_complement.py) * [Binary Xor Operator](bit_manipulation/binary_xor_operator.py) * [Bitwise Addition Recursive](bit_manipulation/bitwise_addition_recursive.py) * [Count 1S Brian Kernighan Method](bit_manipulation/count_1s_brian_kernighan_method.py) * [Count Number Of One Bits](bit_manipulation/count_number_of_one_bits.py) * [Excess 3 Code](bit_manipulation/excess_3_code.py) * [Find Previous Power Of Two](bit_manipulation/find_previous_power_of_two.py) * [Gray Code Sequence](bit_manipulation/gray_code_sequence.py) * [Highest Set Bit](bit_manipulation/highest_set_bit.py) * [Index Of Rightmost Set Bit](bit_manipulation/index_of_rightmost_set_bit.py) * [Is Even](bit_manipulation/is_even.py) * [Is Power Of Two](bit_manipulation/is_power_of_two.py) * [Largest Pow Of Two Le Num](bit_manipulation/largest_pow_of_two_le_num.py) * [Missing Number](bit_manipulation/missing_number.py) * [Numbers Different Signs](bit_manipulation/numbers_different_signs.py) * [Power Of 4](bit_manipulation/power_of_4.py) * [Reverse Bits](bit_manipulation/reverse_bits.py) * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py) * [Swap All Odd And Even Bits](bit_manipulation/swap_all_odd_and_even_bits.py) ## Blockchain * [Diophantine Equation](blockchain/diophantine_equation.py) ## Boolean Algebra * [And Gate](boolean_algebra/and_gate.py) * [Imply Gate](boolean_algebra/imply_gate.py) * [Karnaugh Map Simplification](boolean_algebra/karnaugh_map_simplification.py) * [Multiplexer](boolean_algebra/multiplexer.py) * [Nand Gate](boolean_algebra/nand_gate.py) * [Nimply Gate](boolean_algebra/nimply_gate.py) * [Nor Gate](boolean_algebra/nor_gate.py) * [Not Gate](boolean_algebra/not_gate.py) * [Or Gate](boolean_algebra/or_gate.py) * [Quine Mc Cluskey](boolean_algebra/quine_mc_cluskey.py) * [Xnor Gate](boolean_algebra/xnor_gate.py) * [Xor Gate](boolean_algebra/xor_gate.py) ## Cellular Automata * [Conways Game Of Life](cellular_automata/conways_game_of_life.py) * [Game Of Life](cellular_automata/game_of_life.py) * [Langtons Ant](cellular_automata/langtons_ant.py) * [Nagel Schrekenberg](cellular_automata/nagel_schrekenberg.py) * [One Dimensional](cellular_automata/one_dimensional.py) * [Wa Tor](cellular_automata/wa_tor.py) ## Ciphers * [A1Z26](ciphers/a1z26.py) * [Affine Cipher](ciphers/affine_cipher.py) * [Atbash](ciphers/atbash.py) * [Autokey](ciphers/autokey.py) * [Baconian Cipher](ciphers/baconian_cipher.py) * [Base16](ciphers/base16.py) * [Base32](ciphers/base32.py) * [Base64](ciphers/base64.py) * [Base85](ciphers/base85.py) * [Beaufort Cipher](ciphers/beaufort_cipher.py) * [Bifid](ciphers/bifid.py) * [Brute Force Caesar Cipher](ciphers/brute_force_caesar_cipher.py) * [Caesar Cipher](ciphers/caesar_cipher.py) * [Cryptomath Module](ciphers/cryptomath_module.py) * [Decrypt Caesar With Chi Squared](ciphers/decrypt_caesar_with_chi_squared.py) * [Deterministic Miller Rabin](ciphers/deterministic_miller_rabin.py) * [Diffie](ciphers/diffie.py) * [Diffie Hellman](ciphers/diffie_hellman.py) * [Elgamal Key Generator](ciphers/elgamal_key_generator.py) * [Enigma Machine2](ciphers/enigma_machine2.py) * [Fractionated Morse Cipher](ciphers/fractionated_morse_cipher.py) * [Hill Cipher](ciphers/hill_cipher.py) * [Mixed Keyword Cypher](ciphers/mixed_keyword_cypher.py) * [Mono Alphabetic Ciphers](ciphers/mono_alphabetic_ciphers.py) * [Morse Code](ciphers/morse_code.py) * [Onepad Cipher](ciphers/onepad_cipher.py) * [Permutation Cipher](ciphers/permutation_cipher.py) * [Playfair Cipher](ciphers/playfair_cipher.py) * [Polybius](ciphers/polybius.py) * [Porta Cipher](ciphers/porta_cipher.py) * [Rabin Miller](ciphers/rabin_miller.py) * [Rail Fence Cipher](ciphers/rail_fence_cipher.py) * [Rot13](ciphers/rot13.py) * [Rsa Cipher](ciphers/rsa_cipher.py) * [Rsa Factorization](ciphers/rsa_factorization.py) * [Rsa Key Generator](ciphers/rsa_key_generator.py) * [Running Key Cipher](ciphers/running_key_cipher.py) * [Shuffled Shift Cipher](ciphers/shuffled_shift_cipher.py) * [Simple Keyword Cypher](ciphers/simple_keyword_cypher.py) * [Simple Substitution Cipher](ciphers/simple_substitution_cipher.py) * [Transposition Cipher](ciphers/transposition_cipher.py) * [Transposition Cipher Encrypt Decrypt File](ciphers/transposition_cipher_encrypt_decrypt_file.py) * [Trifid Cipher](ciphers/trifid_cipher.py) * [Vernam Cipher](ciphers/vernam_cipher.py) * [Vigenere Cipher](ciphers/vigenere_cipher.py) * [Xor Cipher](ciphers/xor_cipher.py) ## Compression * [Burrows Wheeler](compression/burrows_wheeler.py) * [Huffman](compression/huffman.py) * [Lempel Ziv](compression/lempel_ziv.py) * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py) * [Lz77](compression/lz77.py) * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py) * [Run Length Encoding](compression/run_length_encoding.py) ## Computer Vision * [Flip Augmentation](computer_vision/flip_augmentation.py) * [Haralick Descriptors](computer_vision/haralick_descriptors.py) * [Harris Corner](computer_vision/harris_corner.py) * [Horn Schunck](computer_vision/horn_schunck.py) * [Mean Threshold](computer_vision/mean_threshold.py) * [Mosaic Augmentation](computer_vision/mosaic_augmentation.py) * [Pooling Functions](computer_vision/pooling_functions.py) ## Conversions * [Astronomical Length Scale Conversion](conversions/astronomical_length_scale_conversion.py) * [Binary To Decimal](conversions/binary_to_decimal.py) * [Binary To Hexadecimal](conversions/binary_to_hexadecimal.py) * [Binary To Octal](conversions/binary_to_octal.py) * [Convert Number To Words](conversions/convert_number_to_words.py) * [Decimal To Any](conversions/decimal_to_any.py) * [Decimal To Binary](conversions/decimal_to_binary.py) * [Decimal To Hexadecimal](conversions/decimal_to_hexadecimal.py) * [Decimal To Octal](conversions/decimal_to_octal.py) * [Energy Conversions](conversions/energy_conversions.py) * [Excel Title To Column](conversions/excel_title_to_column.py) * [Hex To Bin](conversions/hex_to_bin.py) * [Hexadecimal To Decimal](conversions/hexadecimal_to_decimal.py) * [Ipv4 Conversion](conversions/ipv4_conversion.py) * [Length Conversion](conversions/length_conversion.py) * [Molecular Chemistry](conversions/molecular_chemistry.py) * [Octal To Binary](conversions/octal_to_binary.py) * [Octal To Decimal](conversions/octal_to_decimal.py) * [Octal To Hexadecimal](conversions/octal_to_hexadecimal.py) * [Prefix Conversions](conversions/prefix_conversions.py) * [Prefix Conversions String](conversions/prefix_conversions_string.py) * [Pressure Conversions](conversions/pressure_conversions.py) * [Rgb Cmyk Conversion](conversions/rgb_cmyk_conversion.py) * [Rgb Hsv Conversion](conversions/rgb_hsv_conversion.py) * [Roman Numerals](conversions/roman_numerals.py) * [Speed Conversions](conversions/speed_conversions.py) * [Temperature Conversions](conversions/temperature_conversions.py) * [Time Conversions](conversions/time_conversions.py) * [Volume Conversions](conversions/volume_conversions.py) * [Weight Conversion](conversions/weight_conversion.py) ## Data Structures * Arrays * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py) * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py) * [Index 2D Array In 1D](data_structures/arrays/index_2d_array_in_1d.py) * [Kth Largest Element](data_structures/arrays/kth_largest_element.py) * [Median Two Array](data_structures/arrays/median_two_array.py) * [Monotonic Array](data_structures/arrays/monotonic_array.py) * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py) * [Permutations](data_structures/arrays/permutations.py) * [Prefix Sum](data_structures/arrays/prefix_sum.py) * [Product Sum](data_structures/arrays/product_sum.py) * [Sparse Table](data_structures/arrays/sparse_table.py) * [Sudoku Solver](data_structures/arrays/sudoku_solver.py) * Binary Tree * [Avl Tree](data_structures/binary_tree/avl_tree.py) * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py) * [Binary Search Tree](data_structures/binary_tree/binary_search_tree.py) * [Binary Search Tree Recursive](data_structures/binary_tree/binary_search_tree_recursive.py) * [Binary Tree Mirror](data_structures/binary_tree/binary_tree_mirror.py) * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py) * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py) * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py) * [Diameter Of Binary Tree](data_structures/binary_tree/diameter_of_binary_tree.py) * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py) * [Distribute Coins](data_structures/binary_tree/distribute_coins.py) * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py) * [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py) * [Floor And Ceiling](data_structures/binary_tree/floor_and_ceiling.py) * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py) * [Is Sorted](data_structures/binary_tree/is_sorted.py) * [Is Sum Tree](data_structures/binary_tree/is_sum_tree.py) * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py) * [Lowest Common Ancestor](data_structures/binary_tree/lowest_common_ancestor.py) * [Maximum Fenwick Tree](data_structures/binary_tree/maximum_fenwick_tree.py) * [Merge Two Binary Trees](data_structures/binary_tree/merge_two_binary_trees.py) * [Mirror Binary Tree](data_structures/binary_tree/mirror_binary_tree.py) * [Non Recursive Segment Tree](data_structures/binary_tree/non_recursive_segment_tree.py) * [Number Of Possible Binary Trees](data_structures/binary_tree/number_of_possible_binary_trees.py) * [Red Black Tree](data_structures/binary_tree/red_black_tree.py) * [Segment Tree](data_structures/binary_tree/segment_tree.py) * [Segment Tree Other](data_structures/binary_tree/segment_tree_other.py) * [Serialize Deserialize Binary Tree](data_structures/binary_tree/serialize_deserialize_binary_tree.py) * [Symmetric Tree](data_structures/binary_tree/symmetric_tree.py) * [Treap](data_structures/binary_tree/treap.py) * [Wavelet Tree](data_structures/binary_tree/wavelet_tree.py) * Disjoint Set * [Alternate Disjoint Set](data_structures/disjoint_set/alternate_disjoint_set.py) * [Disjoint Set](data_structures/disjoint_set/disjoint_set.py) * Hashing * [Bloom Filter](data_structures/hashing/bloom_filter.py) * [Double Hash](data_structures/hashing/double_hash.py) * [Hash Map](data_structures/hashing/hash_map.py) * [Hash Table](data_structures/hashing/hash_table.py) * [Hash Table With Linked List](data_structures/hashing/hash_table_with_linked_list.py) * Number Theory * [Prime Numbers](data_structures/hashing/number_theory/prime_numbers.py) * [Quadratic Probing](data_structures/hashing/quadratic_probing.py) * Tests * [Test Hash Map](data_structures/hashing/tests/test_hash_map.py) * Heap * [Binomial Heap](data_structures/heap/binomial_heap.py) * [Heap](data_structures/heap/heap.py) * [Heap Generic](data_structures/heap/heap_generic.py) * [Max Heap](data_structures/heap/max_heap.py) * [Min Heap](data_structures/heap/min_heap.py) * [Randomized Heap](data_structures/heap/randomized_heap.py) * [Skew Heap](data_structures/heap/skew_heap.py) * Linked List * [Circular Linked List](data_structures/linked_list/circular_linked_list.py) * [Deque Doubly](data_structures/linked_list/deque_doubly.py) * [Doubly Linked List](data_structures/linked_list/doubly_linked_list.py) * [Doubly Linked List Two](data_structures/linked_list/doubly_linked_list_two.py) * [Floyds Cycle Detection](data_structures/linked_list/floyds_cycle_detection.py) * [From Sequence](data_structures/linked_list/from_sequence.py) * [Has Loop](data_structures/linked_list/has_loop.py) * [Is Palindrome](data_structures/linked_list/is_palindrome.py) * [Merge Two Lists](data_structures/linked_list/merge_two_lists.py) * [Middle Element Of Linked List](data_structures/linked_list/middle_element_of_linked_list.py) * [Print Reverse](data_structures/linked_list/print_reverse.py) * [Reverse K Group](data_structures/linked_list/reverse_k_group.py) * [Rotate To The Right](data_structures/linked_list/rotate_to_the_right.py) * [Singly Linked List](data_structures/linked_list/singly_linked_list.py) * [Skip List](data_structures/linked_list/skip_list.py) * [Swap Nodes](data_structures/linked_list/swap_nodes.py) * Queue * [Circular Queue](data_structures/queue/circular_queue.py) * [Circular Queue Linked List](data_structures/queue/circular_queue_linked_list.py) * [Double Ended Queue](data_structures/queue/double_ended_queue.py) * [Linked Queue](data_structures/queue/linked_queue.py) * [Priority Queue Using List](data_structures/queue/priority_queue_using_list.py) * [Queue By List](data_structures/queue/queue_by_list.py) * [Queue By Two Stacks](data_structures/queue/queue_by_two_stacks.py) * [Queue On Pseudo Stack](data_structures/queue/queue_on_pseudo_stack.py) * Stacks * [Balanced Parentheses](data_structures/stacks/balanced_parentheses.py) * [Dijkstras Two Stack Algorithm](data_structures/stacks/dijkstras_two_stack_algorithm.py) * [Infix To Postfix Conversion](data_structures/stacks/infix_to_postfix_conversion.py) * [Infix To Prefix Conversion](data_structures/stacks/infix_to_prefix_conversion.py) * [Next Greater Element](data_structures/stacks/next_greater_element.py) * [Postfix Evaluation](data_structures/stacks/postfix_evaluation.py) * [Prefix Evaluation](data_structures/stacks/prefix_evaluation.py) * [Stack](data_structures/stacks/stack.py) * [Stack Using Two Queues](data_structures/stacks/stack_using_two_queues.py) * [Stack With Doubly Linked List](data_structures/stacks/stack_with_doubly_linked_list.py) * [Stack With Singly Linked List](data_structures/stacks/stack_with_singly_linked_list.py) * [Stock Span Problem](data_structures/stacks/stock_span_problem.py) * Trie * [Radix Tree](data_structures/trie/radix_tree.py) * [Trie](data_structures/trie/trie.py) ## Digital Image Processing * [Change Brightness](digital_image_processing/change_brightness.py) * [Change Contrast](digital_image_processing/change_contrast.py) * [Convert To Negative](digital_image_processing/convert_to_negative.py) * Dithering * [Burkes](digital_image_processing/dithering/burkes.py) * Edge Detection * [Canny](digital_image_processing/edge_detection/canny.py) * Filters * [Bilateral Filter](digital_image_processing/filters/bilateral_filter.py) * [Convolve](digital_image_processing/filters/convolve.py) * [Gabor Filter](digital_image_processing/filters/gabor_filter.py) * [Gaussian Filter](digital_image_processing/filters/gaussian_filter.py) * [Laplacian Filter](digital_image_processing/filters/laplacian_filter.py) * [Local Binary Pattern](digital_image_processing/filters/local_binary_pattern.py) * [Median Filter](digital_image_processing/filters/median_filter.py) * [Sobel Filter](digital_image_processing/filters/sobel_filter.py) * Histogram Equalization * [Histogram Stretch](digital_image_processing/histogram_equalization/histogram_stretch.py) * [Index Calculation](digital_image_processing/index_calculation.py) * Morphological Operations * [Dilation Operation](digital_image_processing/morphological_operations/dilation_operation.py) * [Erosion Operation](digital_image_processing/morphological_operations/erosion_operation.py) * Resize * [Resize](digital_image_processing/resize/resize.py) * Rotation * [Rotation](digital_image_processing/rotation/rotation.py) * [Sepia](digital_image_processing/sepia.py) * [Test Digital Image Processing](digital_image_processing/test_digital_image_processing.py) ## Divide And Conquer * [Closest Pair Of Points](divide_and_conquer/closest_pair_of_points.py) * [Convex Hull](divide_and_conquer/convex_hull.py) * [Heaps Algorithm](divide_and_conquer/heaps_algorithm.py) * [Heaps Algorithm Iterative](divide_and_conquer/heaps_algorithm_iterative.py) * [Inversions](divide_and_conquer/inversions.py) * [Kth Order Statistic](divide_and_conquer/kth_order_statistic.py) * [Max Difference Pair](divide_and_conquer/max_difference_pair.py) * [Max Subarray](divide_and_conquer/max_subarray.py) * [Mergesort](divide_and_conquer/mergesort.py) * [Peak](divide_and_conquer/peak.py) * [Power](divide_and_conquer/power.py) * [Strassen Matrix Multiplication](divide_and_conquer/strassen_matrix_multiplication.py) ## Dynamic Programming * [Abbreviation](dynamic_programming/abbreviation.py) * [All Construct](dynamic_programming/all_construct.py) * [Bitmask](dynamic_programming/bitmask.py) * [Catalan Numbers](dynamic_programming/catalan_numbers.py) * [Climbing Stairs](dynamic_programming/climbing_stairs.py) * [Combination Sum Iv](dynamic_programming/combination_sum_iv.py) * [Edit Distance](dynamic_programming/edit_distance.py) * [Factorial](dynamic_programming/factorial.py) * [Fast Fibonacci](dynamic_programming/fast_fibonacci.py) * [Fibonacci](dynamic_programming/fibonacci.py) * [Fizz Buzz](dynamic_programming/fizz_buzz.py) * [Floyd Warshall](dynamic_programming/floyd_warshall.py) * [Integer Partition](dynamic_programming/integer_partition.py) * [Iterating Through Submasks](dynamic_programming/iterating_through_submasks.py) * [Knapsack](dynamic_programming/knapsack.py) * [Largest Divisible Subset](dynamic_programming/largest_divisible_subset.py) * [Longest Common Subsequence](dynamic_programming/longest_common_subsequence.py) * [Longest Common Substring](dynamic_programming/longest_common_substring.py) * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py) * [Longest Increasing Subsequence O(Nlogn)](dynamic_programming/longest_increasing_subsequence_o(nlogn).py) * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py) * [Matrix Chain Multiplication](dynamic_programming/matrix_chain_multiplication.py) * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py) * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py) * [Max Product Subarray](dynamic_programming/max_product_subarray.py) * [Max Subarray Sum](dynamic_programming/max_subarray_sum.py) * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py) * [Minimum Coin Change](dynamic_programming/minimum_coin_change.py) * [Minimum Cost Path](dynamic_programming/minimum_cost_path.py) * [Minimum Partition](dynamic_programming/minimum_partition.py) * [Minimum Size Subarray Sum](dynamic_programming/minimum_size_subarray_sum.py) * [Minimum Squares To Represent A Number](dynamic_programming/minimum_squares_to_represent_a_number.py) * [Minimum Steps To One](dynamic_programming/minimum_steps_to_one.py) * [Minimum Tickets Cost](dynamic_programming/minimum_tickets_cost.py) * [Optimal Binary Search Tree](dynamic_programming/optimal_binary_search_tree.py) * [Palindrome Partitioning](dynamic_programming/palindrome_partitioning.py) * [Regex Match](dynamic_programming/regex_match.py) * [Rod Cutting](dynamic_programming/rod_cutting.py) * [Smith Waterman](dynamic_programming/smith_waterman.py) * [Subset Generation](dynamic_programming/subset_generation.py) * [Sum Of Subset](dynamic_programming/sum_of_subset.py) * [Trapped Water](dynamic_programming/trapped_water.py) * [Tribonacci](dynamic_programming/tribonacci.py) * [Viterbi](dynamic_programming/viterbi.py) * [Wildcard Matching](dynamic_programming/wildcard_matching.py) * [Word Break](dynamic_programming/word_break.py) ## Electronics * [Apparent Power](electronics/apparent_power.py) * [Builtin Voltage](electronics/builtin_voltage.py) * [Capacitor Equivalence](electronics/capacitor_equivalence.py) * [Carrier Concentration](electronics/carrier_concentration.py) * [Charging Capacitor](electronics/charging_capacitor.py) * [Charging Inductor](electronics/charging_inductor.py) * [Circular Convolution](electronics/circular_convolution.py) * [Coulombs Law](electronics/coulombs_law.py) * [Electric Conductivity](electronics/electric_conductivity.py) * [Electric Power](electronics/electric_power.py) * [Electrical Impedance](electronics/electrical_impedance.py) * [Ic 555 Timer](electronics/ic_555_timer.py) * [Ind Reactance](electronics/ind_reactance.py) * [Ohms Law](electronics/ohms_law.py) * [Real And Reactive Power](electronics/real_and_reactive_power.py) * [Resistor Color Code](electronics/resistor_color_code.py) * [Resistor Equivalence](electronics/resistor_equivalence.py) * [Resonant Frequency](electronics/resonant_frequency.py) * [Wheatstone Bridge](electronics/wheatstone_bridge.py) ## File Transfer * [Receive File](file_transfer/receive_file.py) * [Send File](file_transfer/send_file.py) * Tests * [Test Send File](file_transfer/tests/test_send_file.py) ## Financial * [Equated Monthly Installments](financial/equated_monthly_installments.py) * [Exponential Moving Average](financial/exponential_moving_average.py) * [Interest](financial/interest.py) * [Present Value](financial/present_value.py) * [Price Plus Tax](financial/price_plus_tax.py) * [Simple Moving Average](financial/simple_moving_average.py) ## Fractals * [Julia Sets](fractals/julia_sets.py) * [Koch Snowflake](fractals/koch_snowflake.py) * [Mandelbrot](fractals/mandelbrot.py) * [Sierpinski Triangle](fractals/sierpinski_triangle.py) ## Fuzzy Logic * [Fuzzy Operations](fuzzy_logic/fuzzy_operations.py) ## Genetic Algorithm * [Basic String](genetic_algorithm/basic_string.py) ## Geodesy * [Haversine Distance](geodesy/haversine_distance.py) * [Lamberts Ellipsoidal Distance](geodesy/lamberts_ellipsoidal_distance.py) ## Graphics * [Bezier Curve](graphics/bezier_curve.py) * [Vector3 For 2D Rendering](graphics/vector3_for_2d_rendering.py) ## Graphs * [A Star](graphs/a_star.py) * [Articulation Points](graphs/articulation_points.py) * [Basic Graphs](graphs/basic_graphs.py) * [Bellman Ford](graphs/bellman_ford.py) * [Bi Directional Dijkstra](graphs/bi_directional_dijkstra.py) * [Bidirectional A Star](graphs/bidirectional_a_star.py) * [Bidirectional Breadth First Search](graphs/bidirectional_breadth_first_search.py) * [Boruvka](graphs/boruvka.py) * [Breadth First Search](graphs/breadth_first_search.py) * [Breadth First Search 2](graphs/breadth_first_search_2.py) * [Breadth First Search Shortest Path](graphs/breadth_first_search_shortest_path.py) * [Breadth First Search Shortest Path 2](graphs/breadth_first_search_shortest_path_2.py) * [Breadth First Search Zero One Shortest Path](graphs/breadth_first_search_zero_one_shortest_path.py) * [Check Bipatrite](graphs/check_bipatrite.py) * [Check Cycle](graphs/check_cycle.py) * [Connected Components](graphs/connected_components.py) * [Deep Clone Graph](graphs/deep_clone_graph.py) * [Depth First Search](graphs/depth_first_search.py) * [Depth First Search 2](graphs/depth_first_search_2.py) * [Dijkstra](graphs/dijkstra.py) * [Dijkstra 2](graphs/dijkstra_2.py) * [Dijkstra Algorithm](graphs/dijkstra_algorithm.py) * [Dijkstra Alternate](graphs/dijkstra_alternate.py) * [Dijkstra Binary Grid](graphs/dijkstra_binary_grid.py) * [Dinic](graphs/dinic.py) * [Directed And Undirected (Weighted) Graph](graphs/directed_and_undirected_(weighted)_graph.py) * [Edmonds Karp Multiple Source And Sink](graphs/edmonds_karp_multiple_source_and_sink.py) * [Eulerian Path And Circuit For Undirected Graph](graphs/eulerian_path_and_circuit_for_undirected_graph.py) * [Even Tree](graphs/even_tree.py) * [Finding Bridges](graphs/finding_bridges.py) * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py) * [G Topological Sort](graphs/g_topological_sort.py) * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py) * [Graph Adjacency List](graphs/graph_adjacency_list.py) * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py) * [Graph List](graphs/graph_list.py) * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py) * [Greedy Best First](graphs/greedy_best_first.py) * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py) * [Kahns Algorithm Long](graphs/kahns_algorithm_long.py) * [Kahns Algorithm Topo](graphs/kahns_algorithm_topo.py) * [Karger](graphs/karger.py) * [Markov Chain](graphs/markov_chain.py) * [Matching Min Vertex Cover](graphs/matching_min_vertex_cover.py) * [Minimum Path Sum](graphs/minimum_path_sum.py) * [Minimum Spanning Tree Boruvka](graphs/minimum_spanning_tree_boruvka.py) * [Minimum Spanning Tree Kruskal](graphs/minimum_spanning_tree_kruskal.py) * [Minimum Spanning Tree Kruskal2](graphs/minimum_spanning_tree_kruskal2.py) * [Minimum Spanning Tree Prims](graphs/minimum_spanning_tree_prims.py) * [Minimum Spanning Tree Prims2](graphs/minimum_spanning_tree_prims2.py) * [Multi Heuristic Astar](graphs/multi_heuristic_astar.py) * [Page Rank](graphs/page_rank.py) * [Prim](graphs/prim.py) * [Random Graph Generator](graphs/random_graph_generator.py) * [Scc Kosaraju](graphs/scc_kosaraju.py) * [Strongly Connected Components](graphs/strongly_connected_components.py) * [Tarjans Scc](graphs/tarjans_scc.py) * Tests * [Test Min Spanning Tree Kruskal](graphs/tests/test_min_spanning_tree_kruskal.py) * [Test Min Spanning Tree Prim](graphs/tests/test_min_spanning_tree_prim.py) ## Greedy Methods * [Best Time To Buy And Sell Stock](greedy_methods/best_time_to_buy_and_sell_stock.py) * [Fractional Cover Problem](greedy_methods/fractional_cover_problem.py) * [Fractional Knapsack](greedy_methods/fractional_knapsack.py) * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py) * [Gas Station](greedy_methods/gas_station.py) * [Minimum Coin Change](greedy_methods/minimum_coin_change.py) * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py) * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py) ## Hashes * [Adler32](hashes/adler32.py) * [Chaos Machine](hashes/chaos_machine.py) * [Djb2](hashes/djb2.py) * [Elf](hashes/elf.py) * [Enigma Machine](hashes/enigma_machine.py) * [Fletcher16](hashes/fletcher16.py) * [Hamming Code](hashes/hamming_code.py) * [Luhn](hashes/luhn.py) * [Md5](hashes/md5.py) * [Sdbm](hashes/sdbm.py) * [Sha1](hashes/sha1.py) * [Sha256](hashes/sha256.py) ## Knapsack * [Greedy Knapsack](knapsack/greedy_knapsack.py) * [Knapsack](knapsack/knapsack.py) * [Recursive Approach Knapsack](knapsack/recursive_approach_knapsack.py) * Tests * [Test Greedy Knapsack](knapsack/tests/test_greedy_knapsack.py) * [Test Knapsack](knapsack/tests/test_knapsack.py) ## Linear Algebra * [Gaussian Elimination](linear_algebra/gaussian_elimination.py) * [Jacobi Iteration Method](linear_algebra/jacobi_iteration_method.py) * [Lu Decomposition](linear_algebra/lu_decomposition.py) * Src * [Conjugate Gradient](linear_algebra/src/conjugate_gradient.py) * Gaussian Elimination Pivoting * [Gaussian Elimination Pivoting](linear_algebra/src/gaussian_elimination_pivoting/gaussian_elimination_pivoting.py) * [Lib](linear_algebra/src/lib.py) * [Polynom For Points](linear_algebra/src/polynom_for_points.py) * [Power Iteration](linear_algebra/src/power_iteration.py) * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py) * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py) * [Schur Complement](linear_algebra/src/schur_complement.py) * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py) * [Transformations 2D](linear_algebra/src/transformations_2d.py) ## Linear Programming * [Simplex](linear_programming/simplex.py) ## Machine Learning * [Apriori Algorithm](machine_learning/apriori_algorithm.py) * [Astar](machine_learning/astar.py) * [Automatic Differentiation](machine_learning/automatic_differentiation.py) * [Data Transformations](machine_learning/data_transformations.py) * [Decision Tree](machine_learning/decision_tree.py) * [Dimensionality Reduction](machine_learning/dimensionality_reduction.py) * Forecasting * [Run](machine_learning/forecasting/run.py) * [Frequent Pattern Growth](machine_learning/frequent_pattern_growth.py) * [Gradient Boosting Classifier](machine_learning/gradient_boosting_classifier.py) * [Gradient Descent](machine_learning/gradient_descent.py) * [K Means Clust](machine_learning/k_means_clust.py) * [K Nearest Neighbours](machine_learning/k_nearest_neighbours.py) * [Linear Discriminant Analysis](machine_learning/linear_discriminant_analysis.py) * [Linear Regression](machine_learning/linear_regression.py) * Local Weighted Learning * [Local Weighted Learning](machine_learning/local_weighted_learning/local_weighted_learning.py) * [Logistic Regression](machine_learning/logistic_regression.py) * [Loss Functions](machine_learning/loss_functions.py) * [Mfcc](machine_learning/mfcc.py) * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py) * [Polynomial Regression](machine_learning/polynomial_regression.py) * [Scoring Functions](machine_learning/scoring_functions.py) * [Self Organizing Map](machine_learning/self_organizing_map.py) * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py) * [Similarity Search](machine_learning/similarity_search.py) * [Support Vector Machines](machine_learning/support_vector_machines.py) * [Word Frequency Functions](machine_learning/word_frequency_functions.py) * [Xgboost Classifier](machine_learning/xgboost_classifier.py) * [Xgboost Regressor](machine_learning/xgboost_regressor.py) ## Maths * [Abs](maths/abs.py) * [Addition Without Arithmetic](maths/addition_without_arithmetic.py) * [Aliquot Sum](maths/aliquot_sum.py) * [Allocation Number](maths/allocation_number.py) * [Arc Length](maths/arc_length.py) * [Area](maths/area.py) * [Area Under Curve](maths/area_under_curve.py) * [Average Absolute Deviation](maths/average_absolute_deviation.py) * [Average Mean](maths/average_mean.py) * [Average Median](maths/average_median.py) * [Average Mode](maths/average_mode.py) * [Bailey Borwein Plouffe](maths/bailey_borwein_plouffe.py) * [Base Neg2 Conversion](maths/base_neg2_conversion.py) * [Basic Maths](maths/basic_maths.py) * [Binary Exponentiation](maths/binary_exponentiation.py) * [Binary Multiplication](maths/binary_multiplication.py) * [Binomial Coefficient](maths/binomial_coefficient.py) * [Binomial Distribution](maths/binomial_distribution.py) * [Ceil](maths/ceil.py) * [Chebyshev Distance](maths/chebyshev_distance.py) * [Check Polygon](maths/check_polygon.py) * [Chinese Remainder Theorem](maths/chinese_remainder_theorem.py) * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py) * [Collatz Sequence](maths/collatz_sequence.py) * [Combinations](maths/combinations.py) * [Continued Fraction](maths/continued_fraction.py) * [Decimal Isolate](maths/decimal_isolate.py) * [Decimal To Fraction](maths/decimal_to_fraction.py) * [Dodecahedron](maths/dodecahedron.py) * [Double Factorial](maths/double_factorial.py) * [Dual Number Automatic Differentiation](maths/dual_number_automatic_differentiation.py) * [Entropy](maths/entropy.py) * [Euclidean Distance](maths/euclidean_distance.py) * [Euler Method](maths/euler_method.py) * [Euler Modified](maths/euler_modified.py) * [Eulers Totient](maths/eulers_totient.py) * [Extended Euclidean Algorithm](maths/extended_euclidean_algorithm.py) * [Factorial](maths/factorial.py) * [Factors](maths/factors.py) * [Fast Inverse Sqrt](maths/fast_inverse_sqrt.py) * [Fermat Little Theorem](maths/fermat_little_theorem.py) * [Fibonacci](maths/fibonacci.py) * [Find Max](maths/find_max.py) * [Find Min](maths/find_min.py) * [Floor](maths/floor.py) * [Gamma](maths/gamma.py) * [Gaussian](maths/gaussian.py) * [Gaussian Error Linear Unit](maths/gaussian_error_linear_unit.py) * [Gcd Of N Numbers](maths/gcd_of_n_numbers.py) * [Germain Primes](maths/germain_primes.py) * [Greatest Common Divisor](maths/greatest_common_divisor.py) * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py) * [Integer Square Root](maths/integer_square_root.py) * [Interquartile Range](maths/interquartile_range.py) * [Is Int Palindrome](maths/is_int_palindrome.py) * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py) * [Is Square Free](maths/is_square_free.py) * [Jaccard Similarity](maths/jaccard_similarity.py) * [Joint Probability Distribution](maths/joint_probability_distribution.py) * [Josephus Problem](maths/josephus_problem.py) * [Juggler Sequence](maths/juggler_sequence.py) * [Karatsuba](maths/karatsuba.py) * [Kth Lexicographic Permutation](maths/kth_lexicographic_permutation.py) * [Largest Of Very Large Numbers](maths/largest_of_very_large_numbers.py) * [Least Common Multiple](maths/least_common_multiple.py) * [Line Length](maths/line_length.py) * [Liouville Lambda](maths/liouville_lambda.py) * [Lucas Lehmer Primality Test](maths/lucas_lehmer_primality_test.py) * [Lucas Series](maths/lucas_series.py) * [Maclaurin Series](maths/maclaurin_series.py) * [Manhattan Distance](maths/manhattan_distance.py) * [Matrix Exponentiation](maths/matrix_exponentiation.py) * [Max Sum Sliding Window](maths/max_sum_sliding_window.py) * [Median Of Two Arrays](maths/median_of_two_arrays.py) * [Minkowski Distance](maths/minkowski_distance.py) * [Mobius Function](maths/mobius_function.py) * [Modular Division](maths/modular_division.py) * [Modular Exponential](maths/modular_exponential.py) * [Monte Carlo](maths/monte_carlo.py) * [Monte Carlo Dice](maths/monte_carlo_dice.py) * [Number Of Digits](maths/number_of_digits.py) * Numerical Analysis * [Adams Bashforth](maths/numerical_analysis/adams_bashforth.py) * [Bisection](maths/numerical_analysis/bisection.py) * [Bisection 2](maths/numerical_analysis/bisection_2.py) * [Integration By Simpson Approx](maths/numerical_analysis/integration_by_simpson_approx.py) * [Intersection](maths/numerical_analysis/intersection.py) * [Nevilles Method](maths/numerical_analysis/nevilles_method.py) * [Newton Forward Interpolation](maths/numerical_analysis/newton_forward_interpolation.py) * [Newton Raphson](maths/numerical_analysis/newton_raphson.py) * [Numerical Integration](maths/numerical_analysis/numerical_integration.py) * [Runge Kutta](maths/numerical_analysis/runge_kutta.py) * [Runge Kutta Fehlberg 45](maths/numerical_analysis/runge_kutta_fehlberg_45.py) * [Runge Kutta Gills](maths/numerical_analysis/runge_kutta_gills.py) * [Secant Method](maths/numerical_analysis/secant_method.py) * [Simpson Rule](maths/numerical_analysis/simpson_rule.py) * [Square Root](maths/numerical_analysis/square_root.py) * [Odd Sieve](maths/odd_sieve.py) * [Perfect Cube](maths/perfect_cube.py) * [Perfect Number](maths/perfect_number.py) * [Perfect Square](maths/perfect_square.py) * [Persistence](maths/persistence.py) * [Pi Generator](maths/pi_generator.py) * [Pi Monte Carlo Estimation](maths/pi_monte_carlo_estimation.py) * [Points Are Collinear 3D](maths/points_are_collinear_3d.py) * [Pollard Rho](maths/pollard_rho.py) * [Polynomial Evaluation](maths/polynomial_evaluation.py) * Polynomials * [Single Indeterminate Operations](maths/polynomials/single_indeterminate_operations.py) * [Power Using Recursion](maths/power_using_recursion.py) * [Prime Check](maths/prime_check.py) * [Prime Factors](maths/prime_factors.py) * [Prime Numbers](maths/prime_numbers.py) * [Prime Sieve Eratosthenes](maths/prime_sieve_eratosthenes.py) * [Primelib](maths/primelib.py) * [Print Multiplication Table](maths/print_multiplication_table.py) * [Pythagoras](maths/pythagoras.py) * [Qr Decomposition](maths/qr_decomposition.py) * [Quadratic Equations Complex Numbers](maths/quadratic_equations_complex_numbers.py) * [Radians](maths/radians.py) * [Radix2 Fft](maths/radix2_fft.py) * [Remove Digit](maths/remove_digit.py) * [Segmented Sieve](maths/segmented_sieve.py) * Series * [Arithmetic](maths/series/arithmetic.py) * [Geometric](maths/series/geometric.py) * [Geometric Series](maths/series/geometric_series.py) * [Harmonic](maths/series/harmonic.py) * [Harmonic Series](maths/series/harmonic_series.py) * [Hexagonal Numbers](maths/series/hexagonal_numbers.py) * [P Series](maths/series/p_series.py) * [Sieve Of Eratosthenes](maths/sieve_of_eratosthenes.py) * [Sigmoid](maths/sigmoid.py) * [Signum](maths/signum.py) * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py) * [Sin](maths/sin.py) * [Sock Merchant](maths/sock_merchant.py) * [Softmax](maths/softmax.py) * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py) * Special Numbers * [Armstrong Numbers](maths/special_numbers/armstrong_numbers.py) * [Automorphic Number](maths/special_numbers/automorphic_number.py) * [Bell Numbers](maths/special_numbers/bell_numbers.py) * [Carmichael Number](maths/special_numbers/carmichael_number.py) * [Catalan Number](maths/special_numbers/catalan_number.py) * [Hamming Numbers](maths/special_numbers/hamming_numbers.py) * [Harshad Numbers](maths/special_numbers/harshad_numbers.py) * [Hexagonal Number](maths/special_numbers/hexagonal_number.py) * [Krishnamurthy Number](maths/special_numbers/krishnamurthy_number.py) * [Perfect Number](maths/special_numbers/perfect_number.py) * [Polygonal Numbers](maths/special_numbers/polygonal_numbers.py) * [Pronic Number](maths/special_numbers/pronic_number.py) * [Proth Number](maths/special_numbers/proth_number.py) * [Triangular Numbers](maths/special_numbers/triangular_numbers.py) * [Ugly Numbers](maths/special_numbers/ugly_numbers.py) * [Weird Number](maths/special_numbers/weird_number.py) * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py) * [Sum Of Digits](maths/sum_of_digits.py) * [Sum Of Geometric Progression](maths/sum_of_geometric_progression.py) * [Sum Of Harmonic Series](maths/sum_of_harmonic_series.py) * [Sumset](maths/sumset.py) * [Sylvester Sequence](maths/sylvester_sequence.py) * [Tanh](maths/tanh.py) * [Test Prime Check](maths/test_prime_check.py) * [Three Sum](maths/three_sum.py) * [Trapezoidal Rule](maths/trapezoidal_rule.py) * [Triplet Sum](maths/triplet_sum.py) * [Twin Prime](maths/twin_prime.py) * [Two Pointer](maths/two_pointer.py) * [Two Sum](maths/two_sum.py) * [Volume](maths/volume.py) * [Zellers Congruence](maths/zellers_congruence.py) ## Matrix * [Binary Search Matrix](matrix/binary_search_matrix.py) * [Count Islands In Matrix](matrix/count_islands_in_matrix.py) * [Count Negative Numbers In Sorted Matrix](matrix/count_negative_numbers_in_sorted_matrix.py) * [Count Paths](matrix/count_paths.py) * [Cramers Rule 2X2](matrix/cramers_rule_2x2.py) * [Inverse Of Matrix](matrix/inverse_of_matrix.py) * [Largest Square Area In Matrix](matrix/largest_square_area_in_matrix.py) * [Matrix Class](matrix/matrix_class.py) * [Matrix Multiplication Recursion](matrix/matrix_multiplication_recursion.py) * [Matrix Operation](matrix/matrix_operation.py) * [Max Area Of Island](matrix/max_area_of_island.py) * [Median Matrix](matrix/median_matrix.py) * [Nth Fibonacci Using Matrix Exponentiation](matrix/nth_fibonacci_using_matrix_exponentiation.py) * [Pascal Triangle](matrix/pascal_triangle.py) * [Rotate Matrix](matrix/rotate_matrix.py) * [Searching In Sorted Matrix](matrix/searching_in_sorted_matrix.py) * [Sherman Morrison](matrix/sherman_morrison.py) * [Spiral Print](matrix/spiral_print.py) * Tests * [Test Matrix Operation](matrix/tests/test_matrix_operation.py) * [Validate Sudoku Board](matrix/validate_sudoku_board.py) ## Networking Flow * [Ford Fulkerson](networking_flow/ford_fulkerson.py) * [Minimum Cut](networking_flow/minimum_cut.py) ## Neural Network * [2 Hidden Layers Neural Network](neural_network/2_hidden_layers_neural_network.py) * Activation Functions * [Binary Step](neural_network/activation_functions/binary_step.py) * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py) * [Leaky Rectified Linear Unit](neural_network/activation_functions/leaky_rectified_linear_unit.py) * [Mish](neural_network/activation_functions/mish.py) * [Rectified Linear Unit](neural_network/activation_functions/rectified_linear_unit.py) * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py) * [Soboleva Modified Hyperbolic Tangent](neural_network/activation_functions/soboleva_modified_hyperbolic_tangent.py) * [Softplus](neural_network/activation_functions/softplus.py) * [Squareplus](neural_network/activation_functions/squareplus.py) * [Swish](neural_network/activation_functions/swish.py) * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py) * [Convolution Neural Network](neural_network/convolution_neural_network.py) * [Simple Neural Network](neural_network/simple_neural_network.py) ## Other * [Activity Selection](other/activity_selection.py) * [Alternative List Arrange](other/alternative_list_arrange.py) * [Bankers Algorithm](other/bankers_algorithm.py) * [Davis Putnam Logemann Loveland](other/davis_putnam_logemann_loveland.py) * [Doomsday](other/doomsday.py) * [Fischer Yates Shuffle](other/fischer_yates_shuffle.py) * [Gauss Easter](other/gauss_easter.py) * [Graham Scan](other/graham_scan.py) * [Greedy](other/greedy.py) * [Guess The Number Search](other/guess_the_number_search.py) * [H Index](other/h_index.py) * [Least Recently Used](other/least_recently_used.py) * [Lfu Cache](other/lfu_cache.py) * [Linear Congruential Generator](other/linear_congruential_generator.py) * [Lru Cache](other/lru_cache.py) * [Magicdiamondpattern](other/magicdiamondpattern.py) * [Majority Vote Algorithm](other/majority_vote_algorithm.py) * [Maximum Subsequence](other/maximum_subsequence.py) * [Nested Brackets](other/nested_brackets.py) * [Number Container System](other/number_container_system.py) * [Password](other/password.py) * [Quine](other/quine.py) * [Scoring Algorithm](other/scoring_algorithm.py) * [Sdes](other/sdes.py) * [Tower Of Hanoi](other/tower_of_hanoi.py) * [Word Search](other/word_search.py) ## Physics * [Altitude Pressure](physics/altitude_pressure.py) * [Archimedes Principle Of Buoyant Force](physics/archimedes_principle_of_buoyant_force.py) * [Basic Orbital Capture](physics/basic_orbital_capture.py) * [Casimir Effect](physics/casimir_effect.py) * [Center Of Mass](physics/center_of_mass.py) * [Centripetal Force](physics/centripetal_force.py) * [Coulombs Law](physics/coulombs_law.py) * [Doppler Frequency](physics/doppler_frequency.py) * [Grahams Law](physics/grahams_law.py) * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py) * [Hubble Parameter](physics/hubble_parameter.py) * [Ideal Gas Law](physics/ideal_gas_law.py) * [In Static Equilibrium](physics/in_static_equilibrium.py) * [Kinetic Energy](physics/kinetic_energy.py) * [Lens Formulae](physics/lens_formulae.py) * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py) * [Malus Law](physics/malus_law.py) * [Mass Energy Equivalence](physics/mass_energy_equivalence.py) * [Mirror Formulae](physics/mirror_formulae.py) * [N Body Simulation](physics/n_body_simulation.py) * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py) * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py) * [Photoelectric Effect](physics/photoelectric_effect.py) * [Potential Energy](physics/potential_energy.py) * [Reynolds Number](physics/reynolds_number.py) * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py) * [Shear Stress](physics/shear_stress.py) * [Speed Of Sound](physics/speed_of_sound.py) * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py) * [Terminal Velocity](physics/terminal_velocity.py) ## Project Euler * Problem 001 * [Sol1](project_euler/problem_001/sol1.py) * [Sol2](project_euler/problem_001/sol2.py) * [Sol3](project_euler/problem_001/sol3.py) * [Sol4](project_euler/problem_001/sol4.py) * [Sol5](project_euler/problem_001/sol5.py) * [Sol6](project_euler/problem_001/sol6.py) * [Sol7](project_euler/problem_001/sol7.py) * Problem 002 * [Sol1](project_euler/problem_002/sol1.py) * [Sol2](project_euler/problem_002/sol2.py) * [Sol3](project_euler/problem_002/sol3.py) * [Sol4](project_euler/problem_002/sol4.py) * [Sol5](project_euler/problem_002/sol5.py) * Problem 003 * [Sol1](project_euler/problem_003/sol1.py) * [Sol2](project_euler/problem_003/sol2.py) * [Sol3](project_euler/problem_003/sol3.py) * Problem 004 * [Sol1](project_euler/problem_004/sol1.py) * [Sol2](project_euler/problem_004/sol2.py) * Problem 005 * [Sol1](project_euler/problem_005/sol1.py) * [Sol2](project_euler/problem_005/sol2.py) * Problem 006 * [Sol1](project_euler/problem_006/sol1.py) * [Sol2](project_euler/problem_006/sol2.py) * [Sol3](project_euler/problem_006/sol3.py) * [Sol4](project_euler/problem_006/sol4.py) * Problem 007 * [Sol1](project_euler/problem_007/sol1.py) * [Sol2](project_euler/problem_007/sol2.py) * [Sol3](project_euler/problem_007/sol3.py) * Problem 008 * [Sol1](project_euler/problem_008/sol1.py) * [Sol2](project_euler/problem_008/sol2.py) * [Sol3](project_euler/problem_008/sol3.py) * Problem 009 * [Sol1](project_euler/problem_009/sol1.py) * [Sol2](project_euler/problem_009/sol2.py) * [Sol3](project_euler/problem_009/sol3.py) * Problem 010 * [Sol1](project_euler/problem_010/sol1.py) * [Sol2](project_euler/problem_010/sol2.py) * [Sol3](project_euler/problem_010/sol3.py) * Problem 011 * [Sol1](project_euler/problem_011/sol1.py) * [Sol2](project_euler/problem_011/sol2.py) * Problem 012 * [Sol1](project_euler/problem_012/sol1.py) * [Sol2](project_euler/problem_012/sol2.py) * Problem 013 * [Sol1](project_euler/problem_013/sol1.py) * Problem 014 * [Sol1](project_euler/problem_014/sol1.py) * [Sol2](project_euler/problem_014/sol2.py) * Problem 015 * [Sol1](project_euler/problem_015/sol1.py) * Problem 016 * [Sol1](project_euler/problem_016/sol1.py) * [Sol2](project_euler/problem_016/sol2.py) * Problem 017 * [Sol1](project_euler/problem_017/sol1.py) * Problem 018 * [Solution](project_euler/problem_018/solution.py) * Problem 019 * [Sol1](project_euler/problem_019/sol1.py) * Problem 020 * [Sol1](project_euler/problem_020/sol1.py) * [Sol2](project_euler/problem_020/sol2.py) * [Sol3](project_euler/problem_020/sol3.py) * [Sol4](project_euler/problem_020/sol4.py) * Problem 021 * [Sol1](project_euler/problem_021/sol1.py) * Problem 022 * [Sol1](project_euler/problem_022/sol1.py) * [Sol2](project_euler/problem_022/sol2.py) * Problem 023 * [Sol1](project_euler/problem_023/sol1.py) * Problem 024 * [Sol1](project_euler/problem_024/sol1.py) * Problem 025 * [Sol1](project_euler/problem_025/sol1.py) * [Sol2](project_euler/problem_025/sol2.py) * [Sol3](project_euler/problem_025/sol3.py) * Problem 026 * [Sol1](project_euler/problem_026/sol1.py) * Problem 027 * [Sol1](project_euler/problem_027/sol1.py) * Problem 028 * [Sol1](project_euler/problem_028/sol1.py) * Problem 029 * [Sol1](project_euler/problem_029/sol1.py) * Problem 030 * [Sol1](project_euler/problem_030/sol1.py) * Problem 031 * [Sol1](project_euler/problem_031/sol1.py) * [Sol2](project_euler/problem_031/sol2.py) * Problem 032 * [Sol32](project_euler/problem_032/sol32.py) * Problem 033 * [Sol1](project_euler/problem_033/sol1.py) * Problem 034 * [Sol1](project_euler/problem_034/sol1.py) * Problem 035 * [Sol1](project_euler/problem_035/sol1.py) * Problem 036 * [Sol1](project_euler/problem_036/sol1.py) * Problem 037 * [Sol1](project_euler/problem_037/sol1.py) * Problem 038 * [Sol1](project_euler/problem_038/sol1.py) * Problem 039 * [Sol1](project_euler/problem_039/sol1.py) * Problem 040 * [Sol1](project_euler/problem_040/sol1.py) * Problem 041 * [Sol1](project_euler/problem_041/sol1.py) * Problem 042 * [Solution42](project_euler/problem_042/solution42.py) * Problem 043 * [Sol1](project_euler/problem_043/sol1.py) * Problem 044 * [Sol1](project_euler/problem_044/sol1.py) * Problem 045 * [Sol1](project_euler/problem_045/sol1.py) * Problem 046 * [Sol1](project_euler/problem_046/sol1.py) * Problem 047 * [Sol1](project_euler/problem_047/sol1.py) * Problem 048 * [Sol1](project_euler/problem_048/sol1.py) * Problem 049 * [Sol1](project_euler/problem_049/sol1.py) * Problem 050 * [Sol1](project_euler/problem_050/sol1.py) * Problem 051 * [Sol1](project_euler/problem_051/sol1.py) * Problem 052 * [Sol1](project_euler/problem_052/sol1.py) * Problem 053 * [Sol1](project_euler/problem_053/sol1.py) * Problem 054 * [Sol1](project_euler/problem_054/sol1.py) * [Test Poker Hand](project_euler/problem_054/test_poker_hand.py) * Problem 055 * [Sol1](project_euler/problem_055/sol1.py) * Problem 056 * [Sol1](project_euler/problem_056/sol1.py) * Problem 057 * [Sol1](project_euler/problem_057/sol1.py) * Problem 058 * [Sol1](project_euler/problem_058/sol1.py) * Problem 059 * [Sol1](project_euler/problem_059/sol1.py) * Problem 062 * [Sol1](project_euler/problem_062/sol1.py) * Problem 063 * [Sol1](project_euler/problem_063/sol1.py) * Problem 064 * [Sol1](project_euler/problem_064/sol1.py) * Problem 065 * [Sol1](project_euler/problem_065/sol1.py) * Problem 067 * [Sol1](project_euler/problem_067/sol1.py) * [Sol2](project_euler/problem_067/sol2.py) * Problem 068 * [Sol1](project_euler/problem_068/sol1.py) * Problem 069 * [Sol1](project_euler/problem_069/sol1.py) * Problem 070 * [Sol1](project_euler/problem_070/sol1.py) * Problem 071 * [Sol1](project_euler/problem_071/sol1.py) * Problem 072 * [Sol1](project_euler/problem_072/sol1.py) * [Sol2](project_euler/problem_072/sol2.py) * Problem 073 * [Sol1](project_euler/problem_073/sol1.py) * Problem 074 * [Sol1](project_euler/problem_074/sol1.py) * [Sol2](project_euler/problem_074/sol2.py) * Problem 075 * [Sol1](project_euler/problem_075/sol1.py) * Problem 076 * [Sol1](project_euler/problem_076/sol1.py) * Problem 077 * [Sol1](project_euler/problem_077/sol1.py) * Problem 078 * [Sol1](project_euler/problem_078/sol1.py) * Problem 079 * [Sol1](project_euler/problem_079/sol1.py) * Problem 080 * [Sol1](project_euler/problem_080/sol1.py) * Problem 081 * [Sol1](project_euler/problem_081/sol1.py) * Problem 082 * [Sol1](project_euler/problem_082/sol1.py) * Problem 085 * [Sol1](project_euler/problem_085/sol1.py) * Problem 086 * [Sol1](project_euler/problem_086/sol1.py) * Problem 087 * [Sol1](project_euler/problem_087/sol1.py) * Problem 089 * [Sol1](project_euler/problem_089/sol1.py) * Problem 091 * [Sol1](project_euler/problem_091/sol1.py) * Problem 092 * [Sol1](project_euler/problem_092/sol1.py) * Problem 094 * [Sol1](project_euler/problem_094/sol1.py) * Problem 097 * [Sol1](project_euler/problem_097/sol1.py) * Problem 099 * [Sol1](project_euler/problem_099/sol1.py) * Problem 100 * [Sol1](project_euler/problem_100/sol1.py) * Problem 101 * [Sol1](project_euler/problem_101/sol1.py) * Problem 102 * [Sol1](project_euler/problem_102/sol1.py) * Problem 104 * [Sol1](project_euler/problem_104/sol1.py) * Problem 107 * [Sol1](project_euler/problem_107/sol1.py) * Problem 109 * [Sol1](project_euler/problem_109/sol1.py) * Problem 112 * [Sol1](project_euler/problem_112/sol1.py) * Problem 113 * [Sol1](project_euler/problem_113/sol1.py) * Problem 114 * [Sol1](project_euler/problem_114/sol1.py) * Problem 115 * [Sol1](project_euler/problem_115/sol1.py) * Problem 116 * [Sol1](project_euler/problem_116/sol1.py) * Problem 117 * [Sol1](project_euler/problem_117/sol1.py) * Problem 119 * [Sol1](project_euler/problem_119/sol1.py) * Problem 120 * [Sol1](project_euler/problem_120/sol1.py) * Problem 121 * [Sol1](project_euler/problem_121/sol1.py) * Problem 123 * [Sol1](project_euler/problem_123/sol1.py) * Problem 125 * [Sol1](project_euler/problem_125/sol1.py) * Problem 129 * [Sol1](project_euler/problem_129/sol1.py) * Problem 131 * [Sol1](project_euler/problem_131/sol1.py) * Problem 135 * [Sol1](project_euler/problem_135/sol1.py) * Problem 144 * [Sol1](project_euler/problem_144/sol1.py) * Problem 145 * [Sol1](project_euler/problem_145/sol1.py) * Problem 173 * [Sol1](project_euler/problem_173/sol1.py) * Problem 174 * [Sol1](project_euler/problem_174/sol1.py) * Problem 180 * [Sol1](project_euler/problem_180/sol1.py) * Problem 187 * [Sol1](project_euler/problem_187/sol1.py) * Problem 188 * [Sol1](project_euler/problem_188/sol1.py) * Problem 191 * [Sol1](project_euler/problem_191/sol1.py) * Problem 203 * [Sol1](project_euler/problem_203/sol1.py) * Problem 205 * [Sol1](project_euler/problem_205/sol1.py) * Problem 206 * [Sol1](project_euler/problem_206/sol1.py) * Problem 207 * [Sol1](project_euler/problem_207/sol1.py) * Problem 234 * [Sol1](project_euler/problem_234/sol1.py) * Problem 301 * [Sol1](project_euler/problem_301/sol1.py) * Problem 493 * [Sol1](project_euler/problem_493/sol1.py) * Problem 551 * [Sol1](project_euler/problem_551/sol1.py) * Problem 587 * [Sol1](project_euler/problem_587/sol1.py) * Problem 686 * [Sol1](project_euler/problem_686/sol1.py) * Problem 800 * [Sol1](project_euler/problem_800/sol1.py) ## Quantum * [Q Fourier Transform](quantum/q_fourier_transform.py) ## Scheduling * [First Come First Served](scheduling/first_come_first_served.py) * [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py) * [Job Sequence With Deadline](scheduling/job_sequence_with_deadline.py) * [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py) * [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py) * [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py) * [Round Robin](scheduling/round_robin.py) * [Shortest Job First](scheduling/shortest_job_first.py) ## Searches * [Binary Search](searches/binary_search.py) * [Binary Tree Traversal](searches/binary_tree_traversal.py) * [Double Linear Search](searches/double_linear_search.py) * [Double Linear Search Recursion](searches/double_linear_search_recursion.py) * [Fibonacci Search](searches/fibonacci_search.py) * [Hill Climbing](searches/hill_climbing.py) * [Interpolation Search](searches/interpolation_search.py) * [Jump Search](searches/jump_search.py) * [Linear Search](searches/linear_search.py) * [Median Of Medians](searches/median_of_medians.py) * [Quick Select](searches/quick_select.py) * [Sentinel Linear Search](searches/sentinel_linear_search.py) * [Simple Binary Search](searches/simple_binary_search.py) * [Simulated Annealing](searches/simulated_annealing.py) * [Tabu Search](searches/tabu_search.py) * [Ternary Search](searches/ternary_search.py) ## Sorts * [Bead Sort](sorts/bead_sort.py) * [Binary Insertion Sort](sorts/binary_insertion_sort.py) * [Bitonic Sort](sorts/bitonic_sort.py) * [Bogo Sort](sorts/bogo_sort.py) * [Bubble Sort](sorts/bubble_sort.py) * [Bucket Sort](sorts/bucket_sort.py) * [Circle Sort](sorts/circle_sort.py) * [Cocktail Shaker Sort](sorts/cocktail_shaker_sort.py) * [Comb Sort](sorts/comb_sort.py) * [Counting Sort](sorts/counting_sort.py) * [Cycle Sort](sorts/cycle_sort.py) * [Double Sort](sorts/double_sort.py) * [Dutch National Flag Sort](sorts/dutch_national_flag_sort.py) * [Exchange Sort](sorts/exchange_sort.py) * [External Sort](sorts/external_sort.py) * [Gnome Sort](sorts/gnome_sort.py) * [Heap Sort](sorts/heap_sort.py) * [Insertion Sort](sorts/insertion_sort.py) * [Intro Sort](sorts/intro_sort.py) * [Iterative Merge Sort](sorts/iterative_merge_sort.py) * [Merge Insertion Sort](sorts/merge_insertion_sort.py) * [Merge Sort](sorts/merge_sort.py) * [Msd Radix Sort](sorts/msd_radix_sort.py) * [Natural Sort](sorts/natural_sort.py) * [Odd Even Sort](sorts/odd_even_sort.py) * [Odd Even Transposition Parallel](sorts/odd_even_transposition_parallel.py) * [Odd Even Transposition Single Threaded](sorts/odd_even_transposition_single_threaded.py) * [Pancake Sort](sorts/pancake_sort.py) * [Patience Sort](sorts/patience_sort.py) * [Pigeon Sort](sorts/pigeon_sort.py) * [Pigeonhole Sort](sorts/pigeonhole_sort.py) * [Quick Sort](sorts/quick_sort.py) * [Quick Sort 3 Partition](sorts/quick_sort_3_partition.py) * [Radix Sort](sorts/radix_sort.py) * [Recursive Insertion Sort](sorts/recursive_insertion_sort.py) * [Recursive Mergesort Array](sorts/recursive_mergesort_array.py) * [Recursive Quick Sort](sorts/recursive_quick_sort.py) * [Selection Sort](sorts/selection_sort.py) * [Shell Sort](sorts/shell_sort.py) * [Shrink Shell Sort](sorts/shrink_shell_sort.py) * [Slowsort](sorts/slowsort.py) * [Stooge Sort](sorts/stooge_sort.py) * [Strand Sort](sorts/strand_sort.py) * [Tim Sort](sorts/tim_sort.py) * [Topological Sort](sorts/topological_sort.py) * [Tree Sort](sorts/tree_sort.py) * [Unknown Sort](sorts/unknown_sort.py) * [Wiggle Sort](sorts/wiggle_sort.py) ## Strings * [Aho Corasick](strings/aho_corasick.py) * [Alternative String Arrange](strings/alternative_string_arrange.py) * [Anagrams](strings/anagrams.py) * [Autocomplete Using Trie](strings/autocomplete_using_trie.py) * [Barcode Validator](strings/barcode_validator.py) * [Bitap String Match](strings/bitap_string_match.py) * [Boyer Moore Search](strings/boyer_moore_search.py) * [Camel Case To Snake Case](strings/camel_case_to_snake_case.py) * [Can String Be Rearranged As Palindrome](strings/can_string_be_rearranged_as_palindrome.py) * [Capitalize](strings/capitalize.py) * [Check Anagrams](strings/check_anagrams.py) * [Credit Card Validator](strings/credit_card_validator.py) * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py) * [Detecting English Programmatically](strings/detecting_english_programmatically.py) * [Dna](strings/dna.py) * [Edit Distance](strings/edit_distance.py) * [Frequency Finder](strings/frequency_finder.py) * [Hamming Distance](strings/hamming_distance.py) * [Indian Phone Validator](strings/indian_phone_validator.py) * [Is Contains Unique Chars](strings/is_contains_unique_chars.py) * [Is Isogram](strings/is_isogram.py) * [Is Pangram](strings/is_pangram.py) * [Is Polish National Id](strings/is_polish_national_id.py) * [Is Spain National Id](strings/is_spain_national_id.py) * [Is Srilankan Phone Number](strings/is_srilankan_phone_number.py) * [Is Valid Email Address](strings/is_valid_email_address.py) * [Jaro Winkler](strings/jaro_winkler.py) * [Join](strings/join.py) * [Knuth Morris Pratt](strings/knuth_morris_pratt.py) * [Levenshtein Distance](strings/levenshtein_distance.py) * [Lower](strings/lower.py) * [Manacher](strings/manacher.py) * [Min Cost String Conversion](strings/min_cost_string_conversion.py) * [Naive String Search](strings/naive_string_search.py) * [Ngram](strings/ngram.py) * [Palindrome](strings/palindrome.py) * [Pig Latin](strings/pig_latin.py) * [Prefix Function](strings/prefix_function.py) * [Rabin Karp](strings/rabin_karp.py) * [Remove Duplicate](strings/remove_duplicate.py) * [Reverse Letters](strings/reverse_letters.py) * [Reverse Words](strings/reverse_words.py) * [Snake Case To Camel Pascal Case](strings/snake_case_to_camel_pascal_case.py) * [Split](strings/split.py) * [String Switch Case](strings/string_switch_case.py) * [Strip](strings/strip.py) * [Text Justification](strings/text_justification.py) * [Title](strings/title.py) * [Top K Frequent Words](strings/top_k_frequent_words.py) * [Upper](strings/upper.py) * [Wave](strings/wave.py) * [Wildcard Pattern Matching](strings/wildcard_pattern_matching.py) * [Word Occurrence](strings/word_occurrence.py) * [Word Patterns](strings/word_patterns.py) * [Z Function](strings/z_function.py) ## Web Programming * [Co2 Emission](web_programming/co2_emission.py) * [Covid Stats Via Xpath](web_programming/covid_stats_via_xpath.py) * [Crawl Google Results](web_programming/crawl_google_results.py) * [Crawl Google Scholar Citation](web_programming/crawl_google_scholar_citation.py) * [Currency Converter](web_programming/currency_converter.py) * [Current Stock Price](web_programming/current_stock_price.py) * [Current Weather](web_programming/current_weather.py) * [Daily Horoscope](web_programming/daily_horoscope.py) * [Download Images From Google Query](web_programming/download_images_from_google_query.py) * [Emails From Url](web_programming/emails_from_url.py) * [Fetch Anime And Play](web_programming/fetch_anime_and_play.py) * [Fetch Bbc News](web_programming/fetch_bbc_news.py) * [Fetch Github Info](web_programming/fetch_github_info.py) * [Fetch Jobs](web_programming/fetch_jobs.py) * [Fetch Quotes](web_programming/fetch_quotes.py) * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py) * [Get Amazon Product Data](web_programming/get_amazon_product_data.py) * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py) * [Get Imdbtop](web_programming/get_imdbtop.py) * [Get Top Billionaires](web_programming/get_top_billionaires.py) * [Get Top Hn Posts](web_programming/get_top_hn_posts.py) * [Get User Tweets](web_programming/get_user_tweets.py) * [Giphy](web_programming/giphy.py) * [Instagram Crawler](web_programming/instagram_crawler.py) * [Instagram Pic](web_programming/instagram_pic.py) * [Instagram Video](web_programming/instagram_video.py) * [Nasa Data](web_programming/nasa_data.py) * [Open Google Results](web_programming/open_google_results.py) * [Random Anime Character](web_programming/random_anime_character.py) * [Recaptcha Verification](web_programming/recaptcha_verification.py) * [Reddit](web_programming/reddit.py) * [Search Books By Isbn](web_programming/search_books_by_isbn.py) * [Slack Message](web_programming/slack_message.py) * [Test Fetch Github Info](web_programming/test_fetch_github_info.py) * [World Covid19 Stats](web_programming/world_covid19_stats.py)

## Audio Filters * [Butterworth Filter](audio_filters/butterworth_filter.py) * [Iir Filter](audio_filters/iir_filter.py) * [Show Response](audio_filters/show_response.py) ## Backtracking * [All Combinations](backtracking/all_combinations.py) * [All Permutations](backtracking/all_permutations.py) * [All Subsequences](backtracking/all_subsequences.py) * [Coloring](backtracking/coloring.py) * [Combination Sum](backtracking/combination_sum.py) * [Crossword Puzzle Solver](backtracking/crossword_puzzle_solver.py) * [Generate Parentheses](backtracking/generate_parentheses.py) * [Hamiltonian Cycle](backtracking/hamiltonian_cycle.py) * [Knight Tour](backtracking/knight_tour.py) * [Match Word Pattern](backtracking/match_word_pattern.py) * [Minimax](backtracking/minimax.py) * [N Queens](backtracking/n_queens.py) * [N Queens Math](backtracking/n_queens_math.py) * [Power Sum](backtracking/power_sum.py) * [Rat In Maze](backtracking/rat_in_maze.py) * [Sudoku](backtracking/sudoku.py) * [Sum Of Subsets](backtracking/sum_of_subsets.py) * [Word Search](backtracking/word_search.py) ## Bit Manipulation * [Binary And Operator](bit_manipulation/binary_and_operator.py) * [Binary Coded Decimal](bit_manipulation/binary_coded_decimal.py) * [Binary Count Setbits](bit_manipulation/binary_count_setbits.py) * [Binary Count Trailing Zeros](bit_manipulation/binary_count_trailing_zeros.py) * [Binary Or Operator](bit_manipulation/binary_or_operator.py) * [Binary Shifts](bit_manipulation/binary_shifts.py) * [Binary Twos Complement](bit_manipulation/binary_twos_complement.py) * [Binary Xor Operator](bit_manipulation/binary_xor_operator.py) * [Bitwise Addition Recursive](bit_manipulation/bitwise_addition_recursive.py) * [Count 1S Brian Kernighan Method](bit_manipulation/count_1s_brian_kernighan_method.py) * [Count Number Of One Bits](bit_manipulation/count_number_of_one_bits.py) * [Excess 3 Code](bit_manipulation/excess_3_code.py) * [Find Previous Power Of Two](bit_manipulation/find_previous_power_of_two.py) * [Gray Code Sequence](bit_manipulation/gray_code_sequence.py) * [Highest Set Bit](bit_manipulation/highest_set_bit.py) * [Index Of Rightmost Set Bit](bit_manipulation/index_of_rightmost_set_bit.py) * [Is Even](bit_manipulation/is_even.py) * [Is Power Of Two](bit_manipulation/is_power_of_two.py) * [Largest Pow Of Two Le Num](bit_manipulation/largest_pow_of_two_le_num.py) * [Missing Number](bit_manipulation/missing_number.py) * [Numbers Different Signs](bit_manipulation/numbers_different_signs.py) * [Power Of 4](bit_manipulation/power_of_4.py) * [Reverse Bits](bit_manipulation/reverse_bits.py) * [Single Bit Manipulation Operations](bit_manipulation/single_bit_manipulation_operations.py) * [Swap All Odd And Even Bits](bit_manipulation/swap_all_odd_and_even_bits.py) ## Blockchain * [Diophantine Equation](blockchain/diophantine_equation.py) ## Boolean Algebra * [And Gate](boolean_algebra/and_gate.py) * [Imply Gate](boolean_algebra/imply_gate.py) * [Karnaugh Map Simplification](boolean_algebra/karnaugh_map_simplification.py) * [Multiplexer](boolean_algebra/multiplexer.py) * [Nand Gate](boolean_algebra/nand_gate.py) * [Nimply Gate](boolean_algebra/nimply_gate.py) * [Nor Gate](boolean_algebra/nor_gate.py) * [Not Gate](boolean_algebra/not_gate.py) * [Or Gate](boolean_algebra/or_gate.py) * [Quine Mc Cluskey](boolean_algebra/quine_mc_cluskey.py) * [Xnor Gate](boolean_algebra/xnor_gate.py) * [Xor Gate](boolean_algebra/xor_gate.py) ## Cellular Automata * [Conways Game Of Life](cellular_automata/conways_game_of_life.py) * [Game Of Life](cellular_automata/game_of_life.py) * [Langtons Ant](cellular_automata/langtons_ant.py) * [Nagel Schrekenberg](cellular_automata/nagel_schrekenberg.py) * [One Dimensional](cellular_automata/one_dimensional.py) * [Wa Tor](cellular_automata/wa_tor.py) ## Ciphers * [A1Z26](ciphers/a1z26.py) * [Affine Cipher](ciphers/affine_cipher.py) * [Atbash](ciphers/atbash.py) * [Autokey](ciphers/autokey.py) * [Baconian Cipher](ciphers/baconian_cipher.py) * [Base16](ciphers/base16.py) * [Base32](ciphers/base32.py) * [Base64](ciphers/base64.py) * [Base85](ciphers/base85.py) * [Beaufort Cipher](ciphers/beaufort_cipher.py) * [Bifid](ciphers/bifid.py) * [Brute Force Caesar Cipher](ciphers/brute_force_caesar_cipher.py) * [Caesar Cipher](ciphers/caesar_cipher.py) * [Cryptomath Module](ciphers/cryptomath_module.py) * [Decrypt Caesar With Chi Squared](ciphers/decrypt_caesar_with_chi_squared.py) * [Deterministic Miller Rabin](ciphers/deterministic_miller_rabin.py) * [Diffie](ciphers/diffie.py) * [Diffie Hellman](ciphers/diffie_hellman.py) * [Elgamal Key Generator](ciphers/elgamal_key_generator.py) * [Enigma Machine2](ciphers/enigma_machine2.py) * [Fractionated Morse Cipher](ciphers/fractionated_morse_cipher.py) * [Hill Cipher](ciphers/hill_cipher.py) * [Mixed Keyword Cypher](ciphers/mixed_keyword_cypher.py) * [Mono Alphabetic Ciphers](ciphers/mono_alphabetic_ciphers.py) * [Morse Code](ciphers/morse_code.py) * [Onepad Cipher](ciphers/onepad_cipher.py) * [Permutation Cipher](ciphers/permutation_cipher.py) * [Playfair Cipher](ciphers/playfair_cipher.py) * [Polybius](ciphers/polybius.py) * [Porta Cipher](ciphers/porta_cipher.py) * [Rabin Miller](ciphers/rabin_miller.py) * [Rail Fence Cipher](ciphers/rail_fence_cipher.py) * [Rot13](ciphers/rot13.py) * [Rsa Cipher](ciphers/rsa_cipher.py) * [Rsa Factorization](ciphers/rsa_factorization.py) * [Rsa Key Generator](ciphers/rsa_key_generator.py) * [Running Key Cipher](ciphers/running_key_cipher.py) * [Shuffled Shift Cipher](ciphers/shuffled_shift_cipher.py) * [Simple Keyword Cypher](ciphers/simple_keyword_cypher.py) * [Simple Substitution Cipher](ciphers/simple_substitution_cipher.py) * [Transposition Cipher](ciphers/transposition_cipher.py) * [Transposition Cipher Encrypt Decrypt File](ciphers/transposition_cipher_encrypt_decrypt_file.py) * [Trifid Cipher](ciphers/trifid_cipher.py) * [Vernam Cipher](ciphers/vernam_cipher.py) * [Vigenere Cipher](ciphers/vigenere_cipher.py) * [Xor Cipher](ciphers/xor_cipher.py) ## Compression * [Burrows Wheeler](compression/burrows_wheeler.py) * [Huffman](compression/huffman.py) * [Lempel Ziv](compression/lempel_ziv.py) * [Lempel Ziv Decompress](compression/lempel_ziv_decompress.py) * [Lz77](compression/lz77.py) * [Peak Signal To Noise Ratio](compression/peak_signal_to_noise_ratio.py) * [Run Length Encoding](compression/run_length_encoding.py) ## Computer Vision * [Flip Augmentation](computer_vision/flip_augmentation.py) * [Haralick Descriptors](computer_vision/haralick_descriptors.py) * [Harris Corner](computer_vision/harris_corner.py) * [Horn Schunck](computer_vision/horn_schunck.py) * [Mean Threshold](computer_vision/mean_threshold.py) * [Mosaic Augmentation](computer_vision/mosaic_augmentation.py) * [Pooling Functions](computer_vision/pooling_functions.py) ## Conversions * [Astronomical Length Scale Conversion](conversions/astronomical_length_scale_conversion.py) * [Binary To Decimal](conversions/binary_to_decimal.py) * [Binary To Hexadecimal](conversions/binary_to_hexadecimal.py) * [Binary To Octal](conversions/binary_to_octal.py) * [Convert Number To Words](conversions/convert_number_to_words.py) * [Decimal To Any](conversions/decimal_to_any.py) * [Decimal To Binary](conversions/decimal_to_binary.py) * [Decimal To Hexadecimal](conversions/decimal_to_hexadecimal.py) * [Decimal To Octal](conversions/decimal_to_octal.py) * [Energy Conversions](conversions/energy_conversions.py) * [Excel Title To Column](conversions/excel_title_to_column.py) * [Hex To Bin](conversions/hex_to_bin.py) * [Hexadecimal To Decimal](conversions/hexadecimal_to_decimal.py) * [Ipv4 Conversion](conversions/ipv4_conversion.py) * [Length Conversion](conversions/length_conversion.py) * [Molecular Chemistry](conversions/molecular_chemistry.py) * [Octal To Binary](conversions/octal_to_binary.py) * [Octal To Decimal](conversions/octal_to_decimal.py) * [Octal To Hexadecimal](conversions/octal_to_hexadecimal.py) * [Prefix Conversions](conversions/prefix_conversions.py) * [Prefix Conversions String](conversions/prefix_conversions_string.py) * [Pressure Conversions](conversions/pressure_conversions.py) * [Rgb Cmyk Conversion](conversions/rgb_cmyk_conversion.py) * [Rgb Hsv Conversion](conversions/rgb_hsv_conversion.py) * [Roman Numerals](conversions/roman_numerals.py) * [Speed Conversions](conversions/speed_conversions.py) * [Temperature Conversions](conversions/temperature_conversions.py) * [Time Conversions](conversions/time_conversions.py) * [Volume Conversions](conversions/volume_conversions.py) * [Weight Conversion](conversions/weight_conversion.py) ## Data Structures * Arrays * [Equilibrium Index In Array](data_structures/arrays/equilibrium_index_in_array.py) * [Find Triplets With 0 Sum](data_structures/arrays/find_triplets_with_0_sum.py) * [Index 2D Array In 1D](data_structures/arrays/index_2d_array_in_1d.py) * [Kth Largest Element](data_structures/arrays/kth_largest_element.py) * [Median Two Array](data_structures/arrays/median_two_array.py) * [Monotonic Array](data_structures/arrays/monotonic_array.py) * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py) * [Permutations](data_structures/arrays/permutations.py) * [Prefix Sum](data_structures/arrays/prefix_sum.py) * [Product Sum](data_structures/arrays/product_sum.py) * [Sparse Table](data_structures/arrays/sparse_table.py) * [Sudoku Solver](data_structures/arrays/sudoku_solver.py) * Binary Tree * [Avl Tree](data_structures/binary_tree/avl_tree.py) * [Basic Binary Tree](data_structures/binary_tree/basic_binary_tree.py) * [Binary Search Tree](data_structures/binary_tree/binary_search_tree.py) * [Binary Search Tree Recursive](data_structures/binary_tree/binary_search_tree_recursive.py) * [Binary Tree Mirror](data_structures/binary_tree/binary_tree_mirror.py) * [Binary Tree Node Sum](data_structures/binary_tree/binary_tree_node_sum.py) * [Binary Tree Path Sum](data_structures/binary_tree/binary_tree_path_sum.py) * [Binary Tree Traversals](data_structures/binary_tree/binary_tree_traversals.py) * [Diameter Of Binary Tree](data_structures/binary_tree/diameter_of_binary_tree.py) * [Diff Views Of Binary Tree](data_structures/binary_tree/diff_views_of_binary_tree.py) * [Distribute Coins](data_structures/binary_tree/distribute_coins.py) * [Fenwick Tree](data_structures/binary_tree/fenwick_tree.py) * [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py) * [Floor And Ceiling](data_structures/binary_tree/floor_and_ceiling.py) * [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py) * [Is Sorted](data_structures/binary_tree/is_sorted.py) * [Is Sum Tree](data_structures/binary_tree/is_sum_tree.py) * [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py) * [Lowest Common Ancestor](data_structures/binary_tree/lowest_common_ancestor.py) * [Maximum Fenwick Tree](data_structures/binary_tree/maximum_fenwick_tree.py) * [Merge Two Binary Trees](data_structures/binary_tree/merge_two_binary_trees.py) * [Mirror Binary Tree](data_structures/binary_tree/mirror_binary_tree.py) * [Non Recursive Segment Tree](data_structures/binary_tree/non_recursive_segment_tree.py) * [Number Of Possible Binary Trees](data_structures/binary_tree/number_of_possible_binary_trees.py) * [Red Black Tree](data_structures/binary_tree/red_black_tree.py) * [Segment Tree](data_structures/binary_tree/segment_tree.py) * [Segment Tree Other](data_structures/binary_tree/segment_tree_other.py) * [Serialize Deserialize Binary Tree](data_structures/binary_tree/serialize_deserialize_binary_tree.py) * [Symmetric Tree](data_structures/binary_tree/symmetric_tree.py) * [Treap](data_structures/binary_tree/treap.py) * [Wavelet Tree](data_structures/binary_tree/wavelet_tree.py) * Disjoint Set * [Alternate Disjoint Set](data_structures/disjoint_set/alternate_disjoint_set.py) * [Disjoint Set](data_structures/disjoint_set/disjoint_set.py) * Hashing * [Bloom Filter](data_structures/hashing/bloom_filter.py) * [Double Hash](data_structures/hashing/double_hash.py) * [Hash Map](data_structures/hashing/hash_map.py) * [Hash Table](data_structures/hashing/hash_table.py) * [Hash Table With Linked List](data_structures/hashing/hash_table_with_linked_list.py) * Number Theory * [Prime Numbers](data_structures/hashing/number_theory/prime_numbers.py) * [Quadratic Probing](data_structures/hashing/quadratic_probing.py) * Tests * [Test Hash Map](data_structures/hashing/tests/test_hash_map.py) * Heap * [Binomial Heap](data_structures/heap/binomial_heap.py) * [Heap](data_structures/heap/heap.py) * [Heap Generic](data_structures/heap/heap_generic.py) * [Max Heap](data_structures/heap/max_heap.py) * [Min Heap](data_structures/heap/min_heap.py) * [Randomized Heap](data_structures/heap/randomized_heap.py) * [Skew Heap](data_structures/heap/skew_heap.py) * Linked List * [Circular Linked List](data_structures/linked_list/circular_linked_list.py) * [Deque Doubly](data_structures/linked_list/deque_doubly.py) * [Doubly Linked List](data_structures/linked_list/doubly_linked_list.py) * [Doubly Linked List Two](data_structures/linked_list/doubly_linked_list_two.py) * [Floyds Cycle Detection](data_structures/linked_list/floyds_cycle_detection.py) * [From Sequence](data_structures/linked_list/from_sequence.py) * [Has Loop](data_structures/linked_list/has_loop.py) * [Is Palindrome](data_structures/linked_list/is_palindrome.py) * [Merge Two Lists](data_structures/linked_list/merge_two_lists.py) * [Middle Element Of Linked List](data_structures/linked_list/middle_element_of_linked_list.py) * [Print Reverse](data_structures/linked_list/print_reverse.py) * [Reverse K Group](data_structures/linked_list/reverse_k_group.py) * [Rotate To The Right](data_structures/linked_list/rotate_to_the_right.py) * [Singly Linked List](data_structures/linked_list/singly_linked_list.py) * [Skip List](data_structures/linked_list/skip_list.py) * [Swap Nodes](data_structures/linked_list/swap_nodes.py) * Queue * [Circular Queue](data_structures/queue/circular_queue.py) * [Circular Queue Linked List](data_structures/queue/circular_queue_linked_list.py) * [Double Ended Queue](data_structures/queue/double_ended_queue.py) * [Linked Queue](data_structures/queue/linked_queue.py) * [Priority Queue Using List](data_structures/queue/priority_queue_using_list.py) * [Queue By List](data_structures/queue/queue_by_list.py) * [Queue By Two Stacks](data_structures/queue/queue_by_two_stacks.py) * [Queue On Pseudo Stack](data_structures/queue/queue_on_pseudo_stack.py) * Stacks * [Balanced Parentheses](data_structures/stacks/balanced_parentheses.py) * [Dijkstras Two Stack Algorithm](data_structures/stacks/dijkstras_two_stack_algorithm.py) * [Infix To Postfix Conversion](data_structures/stacks/infix_to_postfix_conversion.py) * [Infix To Prefix Conversion](data_structures/stacks/infix_to_prefix_conversion.py) * [Next Greater Element](data_structures/stacks/next_greater_element.py) * [Postfix Evaluation](data_structures/stacks/postfix_evaluation.py) * [Prefix Evaluation](data_structures/stacks/prefix_evaluation.py) * [Stack](data_structures/stacks/stack.py) * [Stack Using Two Queues](data_structures/stacks/stack_using_two_queues.py) * [Stack With Doubly Linked List](data_structures/stacks/stack_with_doubly_linked_list.py) * [Stack With Singly Linked List](data_structures/stacks/stack_with_singly_linked_list.py) * [Stock Span Problem](data_structures/stacks/stock_span_problem.py) * Trie * [Radix Tree](data_structures/trie/radix_tree.py) * [Trie](data_structures/trie/trie.py) ## Digital Image Processing * [Change Brightness](digital_image_processing/change_brightness.py) * [Change Contrast](digital_image_processing/change_contrast.py) * [Convert To Negative](digital_image_processing/convert_to_negative.py) * Dithering * [Burkes](digital_image_processing/dithering/burkes.py) * Edge Detection * [Canny](digital_image_processing/edge_detection/canny.py) * Filters * [Bilateral Filter](digital_image_processing/filters/bilateral_filter.py) * [Convolve](digital_image_processing/filters/convolve.py) * [Gabor Filter](digital_image_processing/filters/gabor_filter.py) * [Gaussian Filter](digital_image_processing/filters/gaussian_filter.py) * [Laplacian Filter](digital_image_processing/filters/laplacian_filter.py) * [Local Binary Pattern](digital_image_processing/filters/local_binary_pattern.py) * [Median Filter](digital_image_processing/filters/median_filter.py) * [Sobel Filter](digital_image_processing/filters/sobel_filter.py) * Histogram Equalization * [Histogram Stretch](digital_image_processing/histogram_equalization/histogram_stretch.py) * [Index Calculation](digital_image_processing/index_calculation.py) * Morphological Operations * [Dilation Operation](digital_image_processing/morphological_operations/dilation_operation.py) * [Erosion Operation](digital_image_processing/morphological_operations/erosion_operation.py) * Resize * [Resize](digital_image_processing/resize/resize.py) * Rotation * [Rotation](digital_image_processing/rotation/rotation.py) * [Sepia](digital_image_processing/sepia.py) * [Test Digital Image Processing](digital_image_processing/test_digital_image_processing.py) ## Divide And Conquer * [Closest Pair Of Points](divide_and_conquer/closest_pair_of_points.py) * [Convex Hull](divide_and_conquer/convex_hull.py) * [Heaps Algorithm](divide_and_conquer/heaps_algorithm.py) * [Heaps Algorithm Iterative](divide_and_conquer/heaps_algorithm_iterative.py) * [Inversions](divide_and_conquer/inversions.py) * [Kth Order Statistic](divide_and_conquer/kth_order_statistic.py) * [Max Difference Pair](divide_and_conquer/max_difference_pair.py) * [Max Subarray](divide_and_conquer/max_subarray.py) * [Mergesort](divide_and_conquer/mergesort.py) * [Peak](divide_and_conquer/peak.py) * [Power](divide_and_conquer/power.py) * [Strassen Matrix Multiplication](divide_and_conquer/strassen_matrix_multiplication.py) ## Dynamic Programming * [Abbreviation](dynamic_programming/abbreviation.py) * [All Construct](dynamic_programming/all_construct.py) * [Bitmask](dynamic_programming/bitmask.py) * [Catalan Numbers](dynamic_programming/catalan_numbers.py) * [Climbing Stairs](dynamic_programming/climbing_stairs.py) * [Combination Sum Iv](dynamic_programming/combination_sum_iv.py) * [Edit Distance](dynamic_programming/edit_distance.py) * [Factorial](dynamic_programming/factorial.py) * [Fast Fibonacci](dynamic_programming/fast_fibonacci.py) * [Fibonacci](dynamic_programming/fibonacci.py) * [Fizz Buzz](dynamic_programming/fizz_buzz.py) * [Floyd Warshall](dynamic_programming/floyd_warshall.py) * [Integer Partition](dynamic_programming/integer_partition.py) * [Iterating Through Submasks](dynamic_programming/iterating_through_submasks.py) * [Knapsack](dynamic_programming/knapsack.py) * [Largest Divisible Subset](dynamic_programming/largest_divisible_subset.py) * [Longest Common Subsequence](dynamic_programming/longest_common_subsequence.py) * [Longest Common Substring](dynamic_programming/longest_common_substring.py) * [Longest Increasing Subsequence](dynamic_programming/longest_increasing_subsequence.py) * [Longest Increasing Subsequence O(Nlogn)](dynamic_programming/longest_increasing_subsequence_o(nlogn).py) * [Longest Palindromic Subsequence](dynamic_programming/longest_palindromic_subsequence.py) * [Matrix Chain Multiplication](dynamic_programming/matrix_chain_multiplication.py) * [Matrix Chain Order](dynamic_programming/matrix_chain_order.py) * [Max Non Adjacent Sum](dynamic_programming/max_non_adjacent_sum.py) * [Max Product Subarray](dynamic_programming/max_product_subarray.py) * [Max Subarray Sum](dynamic_programming/max_subarray_sum.py) * [Min Distance Up Bottom](dynamic_programming/min_distance_up_bottom.py) * [Minimum Coin Change](dynamic_programming/minimum_coin_change.py) * [Minimum Cost Path](dynamic_programming/minimum_cost_path.py) * [Minimum Partition](dynamic_programming/minimum_partition.py) * [Minimum Size Subarray Sum](dynamic_programming/minimum_size_subarray_sum.py) * [Minimum Squares To Represent A Number](dynamic_programming/minimum_squares_to_represent_a_number.py) * [Minimum Steps To One](dynamic_programming/minimum_steps_to_one.py) * [Minimum Tickets Cost](dynamic_programming/minimum_tickets_cost.py) * [Optimal Binary Search Tree](dynamic_programming/optimal_binary_search_tree.py) * [Palindrome Partitioning](dynamic_programming/palindrome_partitioning.py) * [Regex Match](dynamic_programming/regex_match.py) * [Rod Cutting](dynamic_programming/rod_cutting.py) * [Smith Waterman](dynamic_programming/smith_waterman.py) * [Subset Generation](dynamic_programming/subset_generation.py) * [Sum Of Subset](dynamic_programming/sum_of_subset.py) * [Trapped Water](dynamic_programming/trapped_water.py) * [Tribonacci](dynamic_programming/tribonacci.py) * [Viterbi](dynamic_programming/viterbi.py) * [Wildcard Matching](dynamic_programming/wildcard_matching.py) * [Word Break](dynamic_programming/word_break.py) ## Electronics * [Apparent Power](electronics/apparent_power.py) * [Builtin Voltage](electronics/builtin_voltage.py) * [Capacitor Equivalence](electronics/capacitor_equivalence.py) * [Carrier Concentration](electronics/carrier_concentration.py) * [Charging Capacitor](electronics/charging_capacitor.py) * [Charging Inductor](electronics/charging_inductor.py) * [Circular Convolution](electronics/circular_convolution.py) * [Coulombs Law](electronics/coulombs_law.py) * [Electric Conductivity](electronics/electric_conductivity.py) * [Electric Power](electronics/electric_power.py) * [Electrical Impedance](electronics/electrical_impedance.py) * [Ic 555 Timer](electronics/ic_555_timer.py) * [Ind Reactance](electronics/ind_reactance.py) * [Ohms Law](electronics/ohms_law.py) * [Real And Reactive Power](electronics/real_and_reactive_power.py) * [Resistor Color Code](electronics/resistor_color_code.py) * [Resistor Equivalence](electronics/resistor_equivalence.py) * [Resonant Frequency](electronics/resonant_frequency.py) * [Wheatstone Bridge](electronics/wheatstone_bridge.py) ## File Transfer * [Receive File](file_transfer/receive_file.py) * [Send File](file_transfer/send_file.py) * Tests * [Test Send File](file_transfer/tests/test_send_file.py) ## Financial * [Equated Monthly Installments](financial/equated_monthly_installments.py) * [Exponential Moving Average](financial/exponential_moving_average.py) * [Interest](financial/interest.py) * [Present Value](financial/present_value.py) * [Price Plus Tax](financial/price_plus_tax.py) * [Simple Moving Average](financial/simple_moving_average.py) ## Fractals * [Julia Sets](fractals/julia_sets.py) * [Koch Snowflake](fractals/koch_snowflake.py) * [Mandelbrot](fractals/mandelbrot.py) * [Sierpinski Triangle](fractals/sierpinski_triangle.py) ## Fuzzy Logic * [Fuzzy Operations](fuzzy_logic/fuzzy_operations.py) ## Genetic Algorithm * [Basic String](genetic_algorithm/basic_string.py) ## Geodesy * [Haversine Distance](geodesy/haversine_distance.py) * [Lamberts Ellipsoidal Distance](geodesy/lamberts_ellipsoidal_distance.py) ## Graphics * [Bezier Curve](graphics/bezier_curve.py) * [Vector3 For 2D Rendering](graphics/vector3_for_2d_rendering.py) ## Graphs * [A Star](graphs/a_star.py) * [Articulation Points](graphs/articulation_points.py) * [Basic Graphs](graphs/basic_graphs.py) * [Bellman Ford](graphs/bellman_ford.py) * [Bi Directional Dijkstra](graphs/bi_directional_dijkstra.py) * [Bidirectional A Star](graphs/bidirectional_a_star.py) * [Bidirectional Breadth First Search](graphs/bidirectional_breadth_first_search.py) * [Boruvka](graphs/boruvka.py) * [Breadth First Search](graphs/breadth_first_search.py) * [Breadth First Search 2](graphs/breadth_first_search_2.py) * [Breadth First Search Shortest Path](graphs/breadth_first_search_shortest_path.py) * [Breadth First Search Shortest Path 2](graphs/breadth_first_search_shortest_path_2.py) * [Breadth First Search Zero One Shortest Path](graphs/breadth_first_search_zero_one_shortest_path.py) * [Check Bipatrite](graphs/check_bipatrite.py) * [Check Cycle](graphs/check_cycle.py) * [Connected Components](graphs/connected_components.py) * [Deep Clone Graph](graphs/deep_clone_graph.py) * [Depth First Search](graphs/depth_first_search.py) * [Depth First Search 2](graphs/depth_first_search_2.py) * [Dijkstra](graphs/dijkstra.py) * [Dijkstra 2](graphs/dijkstra_2.py) * [Dijkstra Algorithm](graphs/dijkstra_algorithm.py) * [Dijkstra Alternate](graphs/dijkstra_alternate.py) * [Dijkstra Binary Grid](graphs/dijkstra_binary_grid.py) * [Dinic](graphs/dinic.py) * [Directed And Undirected (Weighted) Graph](graphs/directed_and_undirected_(weighted)_graph.py) * [Edmonds Karp Multiple Source And Sink](graphs/edmonds_karp_multiple_source_and_sink.py) * [Eulerian Path And Circuit For Undirected Graph](graphs/eulerian_path_and_circuit_for_undirected_graph.py) * [Even Tree](graphs/even_tree.py) * [Finding Bridges](graphs/finding_bridges.py) * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py) * [G Topological Sort](graphs/g_topological_sort.py) * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py) * [Graph Adjacency List](graphs/graph_adjacency_list.py) * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py) * [Graph List](graphs/graph_list.py) * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py) * [Greedy Best First](graphs/greedy_best_first.py) * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py) * [Kahns Algorithm Long](graphs/kahns_algorithm_long.py) * [Kahns Algorithm Topo](graphs/kahns_algorithm_topo.py) * [Karger](graphs/karger.py) * [Markov Chain](graphs/markov_chain.py) * [Matching Min Vertex Cover](graphs/matching_min_vertex_cover.py) * [Minimum Path Sum](graphs/minimum_path_sum.py) * [Minimum Spanning Tree Boruvka](graphs/minimum_spanning_tree_boruvka.py) * [Minimum Spanning Tree Kruskal](graphs/minimum_spanning_tree_kruskal.py) * [Minimum Spanning Tree Kruskal2](graphs/minimum_spanning_tree_kruskal2.py) * [Minimum Spanning Tree Prims](graphs/minimum_spanning_tree_prims.py) * [Minimum Spanning Tree Prims2](graphs/minimum_spanning_tree_prims2.py) * [Multi Heuristic Astar](graphs/multi_heuristic_astar.py) * [Page Rank](graphs/page_rank.py) * [Prim](graphs/prim.py) * [Random Graph Generator](graphs/random_graph_generator.py) * [Scc Kosaraju](graphs/scc_kosaraju.py) * [Strongly Connected Components](graphs/strongly_connected_components.py) * [Tarjans Scc](graphs/tarjans_scc.py) * Tests * [Test Min Spanning Tree Kruskal](graphs/tests/test_min_spanning_tree_kruskal.py) * [Test Min Spanning Tree Prim](graphs/tests/test_min_spanning_tree_prim.py) ## Greedy Methods * [Best Time To Buy And Sell Stock](greedy_methods/best_time_to_buy_and_sell_stock.py) * [Fractional Cover Problem](greedy_methods/fractional_cover_problem.py) * [Fractional Knapsack](greedy_methods/fractional_knapsack.py) * [Fractional Knapsack 2](greedy_methods/fractional_knapsack_2.py) * [Gas Station](greedy_methods/gas_station.py) * [Minimum Coin Change](greedy_methods/minimum_coin_change.py) * [Minimum Waiting Time](greedy_methods/minimum_waiting_time.py) * [Optimal Merge Pattern](greedy_methods/optimal_merge_pattern.py) ## Hashes * [Adler32](hashes/adler32.py) * [Chaos Machine](hashes/chaos_machine.py) * [Djb2](hashes/djb2.py) * [Elf](hashes/elf.py) * [Enigma Machine](hashes/enigma_machine.py) * [Fletcher16](hashes/fletcher16.py) * [Hamming Code](hashes/hamming_code.py) * [Luhn](hashes/luhn.py) * [Md5](hashes/md5.py) * [Sdbm](hashes/sdbm.py) * [Sha1](hashes/sha1.py) * [Sha256](hashes/sha256.py) ## Knapsack * [Greedy Knapsack](knapsack/greedy_knapsack.py) * [Knapsack](knapsack/knapsack.py) * [Recursive Approach Knapsack](knapsack/recursive_approach_knapsack.py) * Tests * [Test Greedy Knapsack](knapsack/tests/test_greedy_knapsack.py) * [Test Knapsack](knapsack/tests/test_knapsack.py) ## Linear Algebra * [Gaussian Elimination](linear_algebra/gaussian_elimination.py) * [Jacobi Iteration Method](linear_algebra/jacobi_iteration_method.py) * [Lu Decomposition](linear_algebra/lu_decomposition.py) * Src * [Conjugate Gradient](linear_algebra/src/conjugate_gradient.py) * Gaussian Elimination Pivoting * [Gaussian Elimination Pivoting](linear_algebra/src/gaussian_elimination_pivoting/gaussian_elimination_pivoting.py) * [Lib](linear_algebra/src/lib.py) * [Polynom For Points](linear_algebra/src/polynom_for_points.py) * [Power Iteration](linear_algebra/src/power_iteration.py) * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py) * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py) * [Schur Complement](linear_algebra/src/schur_complement.py) * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py) * [Transformations 2D](linear_algebra/src/transformations_2d.py) ## Linear Programming * [Simplex](linear_programming/simplex.py) ## Machine Learning * [Apriori Algorithm](machine_learning/apriori_algorithm.py) * [Astar](machine_learning/astar.py) * [Automatic Differentiation](machine_learning/automatic_differentiation.py) * [Data Transformations](machine_learning/data_transformations.py) * [Decision Tree](machine_learning/decision_tree.py) * [Dimensionality Reduction](machine_learning/dimensionality_reduction.py) * Forecasting * [Run](machine_learning/forecasting/run.py) * [Frequent Pattern Growth](machine_learning/frequent_pattern_growth.py) * [Gradient Boosting Classifier](machine_learning/gradient_boosting_classifier.py) * [Gradient Descent](machine_learning/gradient_descent.py) * [K Means Clust](machine_learning/k_means_clust.py) * [K Nearest Neighbours](machine_learning/k_nearest_neighbours.py) * [Linear Discriminant Analysis](machine_learning/linear_discriminant_analysis.py) * [Linear Regression](machine_learning/linear_regression.py) * Local Weighted Learning * [Local Weighted Learning](machine_learning/local_weighted_learning/local_weighted_learning.py) * [Logistic Regression](machine_learning/logistic_regression.py) * [Loss Functions](machine_learning/loss_functions.py) * [Mfcc](machine_learning/mfcc.py) * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py) * [Polynomial Regression](machine_learning/polynomial_regression.py) * [Scoring Functions](machine_learning/scoring_functions.py) * [Self Organizing Map](machine_learning/self_organizing_map.py) * [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py) * [Similarity Search](machine_learning/similarity_search.py) * [Support Vector Machines](machine_learning/support_vector_machines.py) * [Word Frequency Functions](machine_learning/word_frequency_functions.py) * [Xgboost Classifier](machine_learning/xgboost_classifier.py) * [Xgboost Regressor](machine_learning/xgboost_regressor.py) ## Maths * [Abs](maths/abs.py) * [Addition Without Arithmetic](maths/addition_without_arithmetic.py) * [Aliquot Sum](maths/aliquot_sum.py) * [Allocation Number](maths/allocation_number.py) * [Arc Length](maths/arc_length.py) * [Area](maths/area.py) * [Area Under Curve](maths/area_under_curve.py) * [Average Absolute Deviation](maths/average_absolute_deviation.py) * [Average Mean](maths/average_mean.py) * [Average Median](maths/average_median.py) * [Average Mode](maths/average_mode.py) * [Bailey Borwein Plouffe](maths/bailey_borwein_plouffe.py) * [Base Neg2 Conversion](maths/base_neg2_conversion.py) * [Basic Maths](maths/basic_maths.py) * [Binary Exponentiation](maths/binary_exponentiation.py) * [Binary Multiplication](maths/binary_multiplication.py) * [Binomial Coefficient](maths/binomial_coefficient.py) * [Binomial Distribution](maths/binomial_distribution.py) * [Ceil](maths/ceil.py) * [Chebyshev Distance](maths/chebyshev_distance.py) * [Check Polygon](maths/check_polygon.py) * [Chinese Remainder Theorem](maths/chinese_remainder_theorem.py) * [Chudnovsky Algorithm](maths/chudnovsky_algorithm.py) * [Collatz Sequence](maths/collatz_sequence.py) * [Combinations](maths/combinations.py) * [Continued Fraction](maths/continued_fraction.py) * [Decimal Isolate](maths/decimal_isolate.py) * [Decimal To Fraction](maths/decimal_to_fraction.py) * [Dodecahedron](maths/dodecahedron.py) * [Double Factorial](maths/double_factorial.py) * [Dual Number Automatic Differentiation](maths/dual_number_automatic_differentiation.py) * [Entropy](maths/entropy.py) * [Euclidean Distance](maths/euclidean_distance.py) * [Euler Method](maths/euler_method.py) * [Euler Modified](maths/euler_modified.py) * [Eulers Totient](maths/eulers_totient.py) * [Extended Euclidean Algorithm](maths/extended_euclidean_algorithm.py) * [Factorial](maths/factorial.py) * [Factors](maths/factors.py) * [Fast Inverse Sqrt](maths/fast_inverse_sqrt.py) * [Fermat Little Theorem](maths/fermat_little_theorem.py) * [Fibonacci](maths/fibonacci.py) * [Find Max](maths/find_max.py) * [Find Min](maths/find_min.py) * [Floor](maths/floor.py) * [Gamma](maths/gamma.py) * [Gaussian](maths/gaussian.py) * [Gaussian Error Linear Unit](maths/gaussian_error_linear_unit.py) * [Gcd Of N Numbers](maths/gcd_of_n_numbers.py) * [Germain Primes](maths/germain_primes.py) * [Greatest Common Divisor](maths/greatest_common_divisor.py) * [Hardy Ramanujanalgo](maths/hardy_ramanujanalgo.py) * [Integer Square Root](maths/integer_square_root.py) * [Interquartile Range](maths/interquartile_range.py) * [Is Int Palindrome](maths/is_int_palindrome.py) * [Is Ip V4 Address Valid](maths/is_ip_v4_address_valid.py) * [Is Square Free](maths/is_square_free.py) * [Jaccard Similarity](maths/jaccard_similarity.py) * [Joint Probability Distribution](maths/joint_probability_distribution.py) * [Josephus Problem](maths/josephus_problem.py) * [Juggler Sequence](maths/juggler_sequence.py) * [Karatsuba](maths/karatsuba.py) * [Kth Lexicographic Permutation](maths/kth_lexicographic_permutation.py) * [Largest Of Very Large Numbers](maths/largest_of_very_large_numbers.py) * [Least Common Multiple](maths/least_common_multiple.py) * [Line Length](maths/line_length.py) * [Liouville Lambda](maths/liouville_lambda.py) * [Lucas Lehmer Primality Test](maths/lucas_lehmer_primality_test.py) * [Lucas Series](maths/lucas_series.py) * [Maclaurin Series](maths/maclaurin_series.py) * [Manhattan Distance](maths/manhattan_distance.py) * [Matrix Exponentiation](maths/matrix_exponentiation.py) * [Max Sum Sliding Window](maths/max_sum_sliding_window.py) * [Median Of Two Arrays](maths/median_of_two_arrays.py) * [Minkowski Distance](maths/minkowski_distance.py) * [Mobius Function](maths/mobius_function.py) * [Modular Division](maths/modular_division.py) * [Modular Exponential](maths/modular_exponential.py) * [Monte Carlo](maths/monte_carlo.py) * [Monte Carlo Dice](maths/monte_carlo_dice.py) * [Number Of Digits](maths/number_of_digits.py) * Numerical Analysis * [Adams Bashforth](maths/numerical_analysis/adams_bashforth.py) * [Bisection](maths/numerical_analysis/bisection.py) * [Bisection 2](maths/numerical_analysis/bisection_2.py) * [Integration By Simpson Approx](maths/numerical_analysis/integration_by_simpson_approx.py) * [Intersection](maths/numerical_analysis/intersection.py) * [Nevilles Method](maths/numerical_analysis/nevilles_method.py) * [Newton Forward Interpolation](maths/numerical_analysis/newton_forward_interpolation.py) * [Newton Raphson](maths/numerical_analysis/newton_raphson.py) * [Numerical Integration](maths/numerical_analysis/numerical_integration.py) * [Runge Kutta](maths/numerical_analysis/runge_kutta.py) * [Runge Kutta Fehlberg 45](maths/numerical_analysis/runge_kutta_fehlberg_45.py) * [Runge Kutta Gills](maths/numerical_analysis/runge_kutta_gills.py) * [Secant Method](maths/numerical_analysis/secant_method.py) * [Simpson Rule](maths/numerical_analysis/simpson_rule.py) * [Square Root](maths/numerical_analysis/square_root.py) * [Odd Sieve](maths/odd_sieve.py) * [Perfect Cube](maths/perfect_cube.py) * [Perfect Number](maths/perfect_number.py) * [Perfect Square](maths/perfect_square.py) * [Persistence](maths/persistence.py) * [Pi Generator](maths/pi_generator.py) * [Pi Monte Carlo Estimation](maths/pi_monte_carlo_estimation.py) * [Points Are Collinear 3D](maths/points_are_collinear_3d.py) * [Pollard Rho](maths/pollard_rho.py) * [Polynomial Evaluation](maths/polynomial_evaluation.py) * Polynomials * [Single Indeterminate Operations](maths/polynomials/single_indeterminate_operations.py) * [Power Using Recursion](maths/power_using_recursion.py) * [Prime Check](maths/prime_check.py) * [Prime Factors](maths/prime_factors.py) * [Prime Numbers](maths/prime_numbers.py) * [Prime Sieve Eratosthenes](maths/prime_sieve_eratosthenes.py) * [Primelib](maths/primelib.py) * [Print Multiplication Table](maths/print_multiplication_table.py) * [Pythagoras](maths/pythagoras.py) * [Qr Decomposition](maths/qr_decomposition.py) * [Quadratic Equations Complex Numbers](maths/quadratic_equations_complex_numbers.py) * [Radians](maths/radians.py) * [Radix2 Fft](maths/radix2_fft.py) * [Remove Digit](maths/remove_digit.py) * [Segmented Sieve](maths/segmented_sieve.py) * Series * [Arithmetic](maths/series/arithmetic.py) * [Geometric](maths/series/geometric.py) * [Geometric Series](maths/series/geometric_series.py) * [Harmonic](maths/series/harmonic.py) * [Harmonic Series](maths/series/harmonic_series.py) * [Hexagonal Numbers](maths/series/hexagonal_numbers.py) * [P Series](maths/series/p_series.py) * [Sieve Of Eratosthenes](maths/sieve_of_eratosthenes.py) * [Sigmoid](maths/sigmoid.py) * [Signum](maths/signum.py) * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py) * [Sin](maths/sin.py) * [Sock Merchant](maths/sock_merchant.py) * [Softmax](maths/softmax.py) * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py) * Special Numbers * [Armstrong Numbers](maths/special_numbers/armstrong_numbers.py) * [Automorphic Number](maths/special_numbers/automorphic_number.py) * [Bell Numbers](maths/special_numbers/bell_numbers.py) * [Carmichael Number](maths/special_numbers/carmichael_number.py) * [Catalan Number](maths/special_numbers/catalan_number.py) * [Hamming Numbers](maths/special_numbers/hamming_numbers.py) * [Happy Number](maths/special_numbers/happy_number.py) * [Harshad Numbers](maths/special_numbers/harshad_numbers.py) * [Hexagonal Number](maths/special_numbers/hexagonal_number.py) * [Krishnamurthy Number](maths/special_numbers/krishnamurthy_number.py) * [Perfect Number](maths/special_numbers/perfect_number.py) * [Polygonal Numbers](maths/special_numbers/polygonal_numbers.py) * [Pronic Number](maths/special_numbers/pronic_number.py) * [Proth Number](maths/special_numbers/proth_number.py) * [Triangular Numbers](maths/special_numbers/triangular_numbers.py) * [Ugly Numbers](maths/special_numbers/ugly_numbers.py) * [Weird Number](maths/special_numbers/weird_number.py) * [Sum Of Arithmetic Series](maths/sum_of_arithmetic_series.py) * [Sum Of Digits](maths/sum_of_digits.py) * [Sum Of Geometric Progression](maths/sum_of_geometric_progression.py) * [Sum Of Harmonic Series](maths/sum_of_harmonic_series.py) * [Sumset](maths/sumset.py) * [Sylvester Sequence](maths/sylvester_sequence.py) * [Tanh](maths/tanh.py) * [Test Prime Check](maths/test_prime_check.py) * [Three Sum](maths/three_sum.py) * [Trapezoidal Rule](maths/trapezoidal_rule.py) * [Triplet Sum](maths/triplet_sum.py) * [Twin Prime](maths/twin_prime.py) * [Two Pointer](maths/two_pointer.py) * [Two Sum](maths/two_sum.py) * [Volume](maths/volume.py) * [Zellers Congruence](maths/zellers_congruence.py) ## Matrix * [Binary Search Matrix](matrix/binary_search_matrix.py) * [Count Islands In Matrix](matrix/count_islands_in_matrix.py) * [Count Negative Numbers In Sorted Matrix](matrix/count_negative_numbers_in_sorted_matrix.py) * [Count Paths](matrix/count_paths.py) * [Cramers Rule 2X2](matrix/cramers_rule_2x2.py) * [Inverse Of Matrix](matrix/inverse_of_matrix.py) * [Largest Square Area In Matrix](matrix/largest_square_area_in_matrix.py) * [Matrix Class](matrix/matrix_class.py) * [Matrix Multiplication Recursion](matrix/matrix_multiplication_recursion.py) * [Matrix Operation](matrix/matrix_operation.py) * [Max Area Of Island](matrix/max_area_of_island.py) * [Median Matrix](matrix/median_matrix.py) * [Nth Fibonacci Using Matrix Exponentiation](matrix/nth_fibonacci_using_matrix_exponentiation.py) * [Pascal Triangle](matrix/pascal_triangle.py) * [Rotate Matrix](matrix/rotate_matrix.py) * [Searching In Sorted Matrix](matrix/searching_in_sorted_matrix.py) * [Sherman Morrison](matrix/sherman_morrison.py) * [Spiral Print](matrix/spiral_print.py) * Tests * [Test Matrix Operation](matrix/tests/test_matrix_operation.py) * [Validate Sudoku Board](matrix/validate_sudoku_board.py) ## Networking Flow * [Ford Fulkerson](networking_flow/ford_fulkerson.py) * [Minimum Cut](networking_flow/minimum_cut.py) ## Neural Network * [2 Hidden Layers Neural Network](neural_network/2_hidden_layers_neural_network.py) * Activation Functions * [Binary Step](neural_network/activation_functions/binary_step.py) * [Exponential Linear Unit](neural_network/activation_functions/exponential_linear_unit.py) * [Leaky Rectified Linear Unit](neural_network/activation_functions/leaky_rectified_linear_unit.py) * [Mish](neural_network/activation_functions/mish.py) * [Rectified Linear Unit](neural_network/activation_functions/rectified_linear_unit.py) * [Scaled Exponential Linear Unit](neural_network/activation_functions/scaled_exponential_linear_unit.py) * [Soboleva Modified Hyperbolic Tangent](neural_network/activation_functions/soboleva_modified_hyperbolic_tangent.py) * [Softplus](neural_network/activation_functions/softplus.py) * [Squareplus](neural_network/activation_functions/squareplus.py) * [Swish](neural_network/activation_functions/swish.py) * [Back Propagation Neural Network](neural_network/back_propagation_neural_network.py) * [Convolution Neural Network](neural_network/convolution_neural_network.py) * [Simple Neural Network](neural_network/simple_neural_network.py) ## Other * [Activity Selection](other/activity_selection.py) * [Alternative List Arrange](other/alternative_list_arrange.py) * [Bankers Algorithm](other/bankers_algorithm.py) * [Davis Putnam Logemann Loveland](other/davis_putnam_logemann_loveland.py) * [Doomsday](other/doomsday.py) * [Fischer Yates Shuffle](other/fischer_yates_shuffle.py) * [Gauss Easter](other/gauss_easter.py) * [Graham Scan](other/graham_scan.py) * [Greedy](other/greedy.py) * [Guess The Number Search](other/guess_the_number_search.py) * [H Index](other/h_index.py) * [Least Recently Used](other/least_recently_used.py) * [Lfu Cache](other/lfu_cache.py) * [Linear Congruential Generator](other/linear_congruential_generator.py) * [Lru Cache](other/lru_cache.py) * [Magicdiamondpattern](other/magicdiamondpattern.py) * [Majority Vote Algorithm](other/majority_vote_algorithm.py) * [Maximum Subsequence](other/maximum_subsequence.py) * [Nested Brackets](other/nested_brackets.py) * [Number Container System](other/number_container_system.py) * [Password](other/password.py) * [Quine](other/quine.py) * [Scoring Algorithm](other/scoring_algorithm.py) * [Sdes](other/sdes.py) * [Tower Of Hanoi](other/tower_of_hanoi.py) * [Word Search](other/word_search.py) ## Physics * [Altitude Pressure](physics/altitude_pressure.py) * [Archimedes Principle Of Buoyant Force](physics/archimedes_principle_of_buoyant_force.py) * [Basic Orbital Capture](physics/basic_orbital_capture.py) * [Casimir Effect](physics/casimir_effect.py) * [Center Of Mass](physics/center_of_mass.py) * [Centripetal Force](physics/centripetal_force.py) * [Coulombs Law](physics/coulombs_law.py) * [Doppler Frequency](physics/doppler_frequency.py) * [Grahams Law](physics/grahams_law.py) * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py) * [Hubble Parameter](physics/hubble_parameter.py) * [Ideal Gas Law](physics/ideal_gas_law.py) * [In Static Equilibrium](physics/in_static_equilibrium.py) * [Kinetic Energy](physics/kinetic_energy.py) * [Lens Formulae](physics/lens_formulae.py) * [Lorentz Transformation Four Vector](physics/lorentz_transformation_four_vector.py) * [Malus Law](physics/malus_law.py) * [Mass Energy Equivalence](physics/mass_energy_equivalence.py) * [Mirror Formulae](physics/mirror_formulae.py) * [N Body Simulation](physics/n_body_simulation.py) * [Newtons Law Of Gravitation](physics/newtons_law_of_gravitation.py) * [Newtons Second Law Of Motion](physics/newtons_second_law_of_motion.py) * [Photoelectric Effect](physics/photoelectric_effect.py) * [Potential Energy](physics/potential_energy.py) * [Reynolds Number](physics/reynolds_number.py) * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py) * [Shear Stress](physics/shear_stress.py) * [Speed Of Sound](physics/speed_of_sound.py) * [Speeds Of Gas Molecules](physics/speeds_of_gas_molecules.py) * [Terminal Velocity](physics/terminal_velocity.py) ## Project Euler * Problem 001 * [Sol1](project_euler/problem_001/sol1.py) * [Sol2](project_euler/problem_001/sol2.py) * [Sol3](project_euler/problem_001/sol3.py) * [Sol4](project_euler/problem_001/sol4.py) * [Sol5](project_euler/problem_001/sol5.py) * [Sol6](project_euler/problem_001/sol6.py) * [Sol7](project_euler/problem_001/sol7.py) * Problem 002 * [Sol1](project_euler/problem_002/sol1.py) * [Sol2](project_euler/problem_002/sol2.py) * [Sol3](project_euler/problem_002/sol3.py) * [Sol4](project_euler/problem_002/sol4.py) * [Sol5](project_euler/problem_002/sol5.py) * Problem 003 * [Sol1](project_euler/problem_003/sol1.py) * [Sol2](project_euler/problem_003/sol2.py) * [Sol3](project_euler/problem_003/sol3.py) * Problem 004 * [Sol1](project_euler/problem_004/sol1.py) * [Sol2](project_euler/problem_004/sol2.py) * Problem 005 * [Sol1](project_euler/problem_005/sol1.py) * [Sol2](project_euler/problem_005/sol2.py) * Problem 006 * [Sol1](project_euler/problem_006/sol1.py) * [Sol2](project_euler/problem_006/sol2.py) * [Sol3](project_euler/problem_006/sol3.py) * [Sol4](project_euler/problem_006/sol4.py) * Problem 007 * [Sol1](project_euler/problem_007/sol1.py) * [Sol2](project_euler/problem_007/sol2.py) * [Sol3](project_euler/problem_007/sol3.py) * Problem 008 * [Sol1](project_euler/problem_008/sol1.py) * [Sol2](project_euler/problem_008/sol2.py) * [Sol3](project_euler/problem_008/sol3.py) * Problem 009 * [Sol1](project_euler/problem_009/sol1.py) * [Sol2](project_euler/problem_009/sol2.py) * [Sol3](project_euler/problem_009/sol3.py) * Problem 010 * [Sol1](project_euler/problem_010/sol1.py) * [Sol2](project_euler/problem_010/sol2.py) * [Sol3](project_euler/problem_010/sol3.py) * Problem 011 * [Sol1](project_euler/problem_011/sol1.py) * [Sol2](project_euler/problem_011/sol2.py) * Problem 012 * [Sol1](project_euler/problem_012/sol1.py) * [Sol2](project_euler/problem_012/sol2.py) * Problem 013 * [Sol1](project_euler/problem_013/sol1.py) * Problem 014 * [Sol1](project_euler/problem_014/sol1.py) * [Sol2](project_euler/problem_014/sol2.py) * Problem 015 * [Sol1](project_euler/problem_015/sol1.py) * Problem 016 * [Sol1](project_euler/problem_016/sol1.py) * [Sol2](project_euler/problem_016/sol2.py) * Problem 017 * [Sol1](project_euler/problem_017/sol1.py) * Problem 018 * [Solution](project_euler/problem_018/solution.py) * Problem 019 * [Sol1](project_euler/problem_019/sol1.py) * Problem 020 * [Sol1](project_euler/problem_020/sol1.py) * [Sol2](project_euler/problem_020/sol2.py) * [Sol3](project_euler/problem_020/sol3.py) * [Sol4](project_euler/problem_020/sol4.py) * Problem 021 * [Sol1](project_euler/problem_021/sol1.py) * Problem 022 * [Sol1](project_euler/problem_022/sol1.py) * [Sol2](project_euler/problem_022/sol2.py) * Problem 023 * [Sol1](project_euler/problem_023/sol1.py) * Problem 024 * [Sol1](project_euler/problem_024/sol1.py) * Problem 025 * [Sol1](project_euler/problem_025/sol1.py) * [Sol2](project_euler/problem_025/sol2.py) * [Sol3](project_euler/problem_025/sol3.py) * Problem 026 * [Sol1](project_euler/problem_026/sol1.py) * Problem 027 * [Sol1](project_euler/problem_027/sol1.py) * Problem 028 * [Sol1](project_euler/problem_028/sol1.py) * Problem 029 * [Sol1](project_euler/problem_029/sol1.py) * Problem 030 * [Sol1](project_euler/problem_030/sol1.py) * Problem 031 * [Sol1](project_euler/problem_031/sol1.py) * [Sol2](project_euler/problem_031/sol2.py) * Problem 032 * [Sol32](project_euler/problem_032/sol32.py) * Problem 033 * [Sol1](project_euler/problem_033/sol1.py) * Problem 034 * [Sol1](project_euler/problem_034/sol1.py) * Problem 035 * [Sol1](project_euler/problem_035/sol1.py) * Problem 036 * [Sol1](project_euler/problem_036/sol1.py) * Problem 037 * [Sol1](project_euler/problem_037/sol1.py) * Problem 038 * [Sol1](project_euler/problem_038/sol1.py) * Problem 039 * [Sol1](project_euler/problem_039/sol1.py) * Problem 040 * [Sol1](project_euler/problem_040/sol1.py) * Problem 041 * [Sol1](project_euler/problem_041/sol1.py) * Problem 042 * [Solution42](project_euler/problem_042/solution42.py) * Problem 043 * [Sol1](project_euler/problem_043/sol1.py) * Problem 044 * [Sol1](project_euler/problem_044/sol1.py) * Problem 045 * [Sol1](project_euler/problem_045/sol1.py) * Problem 046 * [Sol1](project_euler/problem_046/sol1.py) * Problem 047 * [Sol1](project_euler/problem_047/sol1.py) * Problem 048 * [Sol1](project_euler/problem_048/sol1.py) * Problem 049 * [Sol1](project_euler/problem_049/sol1.py) * Problem 050 * [Sol1](project_euler/problem_050/sol1.py) * Problem 051 * [Sol1](project_euler/problem_051/sol1.py) * Problem 052 * [Sol1](project_euler/problem_052/sol1.py) * Problem 053 * [Sol1](project_euler/problem_053/sol1.py) * Problem 054 * [Sol1](project_euler/problem_054/sol1.py) * [Test Poker Hand](project_euler/problem_054/test_poker_hand.py) * Problem 055 * [Sol1](project_euler/problem_055/sol1.py) * Problem 056 * [Sol1](project_euler/problem_056/sol1.py) * Problem 057 * [Sol1](project_euler/problem_057/sol1.py) * Problem 058 * [Sol1](project_euler/problem_058/sol1.py) * Problem 059 * [Sol1](project_euler/problem_059/sol1.py) * Problem 062 * [Sol1](project_euler/problem_062/sol1.py) * Problem 063 * [Sol1](project_euler/problem_063/sol1.py) * Problem 064 * [Sol1](project_euler/problem_064/sol1.py) * Problem 065 * [Sol1](project_euler/problem_065/sol1.py) * Problem 067 * [Sol1](project_euler/problem_067/sol1.py) * [Sol2](project_euler/problem_067/sol2.py) * Problem 068 * [Sol1](project_euler/problem_068/sol1.py) * Problem 069 * [Sol1](project_euler/problem_069/sol1.py) * Problem 070 * [Sol1](project_euler/problem_070/sol1.py) * Problem 071 * [Sol1](project_euler/problem_071/sol1.py) * Problem 072 * [Sol1](project_euler/problem_072/sol1.py) * [Sol2](project_euler/problem_072/sol2.py) * Problem 073 * [Sol1](project_euler/problem_073/sol1.py) * Problem 074 * [Sol1](project_euler/problem_074/sol1.py) * [Sol2](project_euler/problem_074/sol2.py) * Problem 075 * [Sol1](project_euler/problem_075/sol1.py) * Problem 076 * [Sol1](project_euler/problem_076/sol1.py) * Problem 077 * [Sol1](project_euler/problem_077/sol1.py) * Problem 078 * [Sol1](project_euler/problem_078/sol1.py) * Problem 079 * [Sol1](project_euler/problem_079/sol1.py) * Problem 080 * [Sol1](project_euler/problem_080/sol1.py) * Problem 081 * [Sol1](project_euler/problem_081/sol1.py) * Problem 082 * [Sol1](project_euler/problem_082/sol1.py) * Problem 085 * [Sol1](project_euler/problem_085/sol1.py) * Problem 086 * [Sol1](project_euler/problem_086/sol1.py) * Problem 087 * [Sol1](project_euler/problem_087/sol1.py) * Problem 089 * [Sol1](project_euler/problem_089/sol1.py) * Problem 091 * [Sol1](project_euler/problem_091/sol1.py) * Problem 092 * [Sol1](project_euler/problem_092/sol1.py) * Problem 094 * [Sol1](project_euler/problem_094/sol1.py) * Problem 097 * [Sol1](project_euler/problem_097/sol1.py) * Problem 099 * [Sol1](project_euler/problem_099/sol1.py) * Problem 100 * [Sol1](project_euler/problem_100/sol1.py) * Problem 101 * [Sol1](project_euler/problem_101/sol1.py) * Problem 102 * [Sol1](project_euler/problem_102/sol1.py) * Problem 104 * [Sol1](project_euler/problem_104/sol1.py) * Problem 107 * [Sol1](project_euler/problem_107/sol1.py) * Problem 109 * [Sol1](project_euler/problem_109/sol1.py) * Problem 112 * [Sol1](project_euler/problem_112/sol1.py) * Problem 113 * [Sol1](project_euler/problem_113/sol1.py) * Problem 114 * [Sol1](project_euler/problem_114/sol1.py) * Problem 115 * [Sol1](project_euler/problem_115/sol1.py) * Problem 116 * [Sol1](project_euler/problem_116/sol1.py) * Problem 117 * [Sol1](project_euler/problem_117/sol1.py) * Problem 119 * [Sol1](project_euler/problem_119/sol1.py) * Problem 120 * [Sol1](project_euler/problem_120/sol1.py) * Problem 121 * [Sol1](project_euler/problem_121/sol1.py) * Problem 123 * [Sol1](project_euler/problem_123/sol1.py) * Problem 125 * [Sol1](project_euler/problem_125/sol1.py) * Problem 129 * [Sol1](project_euler/problem_129/sol1.py) * Problem 131 * [Sol1](project_euler/problem_131/sol1.py) * Problem 135 * [Sol1](project_euler/problem_135/sol1.py) * Problem 144 * [Sol1](project_euler/problem_144/sol1.py) * Problem 145 * [Sol1](project_euler/problem_145/sol1.py) * Problem 173 * [Sol1](project_euler/problem_173/sol1.py) * Problem 174 * [Sol1](project_euler/problem_174/sol1.py) * Problem 180 * [Sol1](project_euler/problem_180/sol1.py) * Problem 187 * [Sol1](project_euler/problem_187/sol1.py) * Problem 188 * [Sol1](project_euler/problem_188/sol1.py) * Problem 191 * [Sol1](project_euler/problem_191/sol1.py) * Problem 203 * [Sol1](project_euler/problem_203/sol1.py) * Problem 205 * [Sol1](project_euler/problem_205/sol1.py) * Problem 206 * [Sol1](project_euler/problem_206/sol1.py) * Problem 207 * [Sol1](project_euler/problem_207/sol1.py) * Problem 234 * [Sol1](project_euler/problem_234/sol1.py) * Problem 301 * [Sol1](project_euler/problem_301/sol1.py) * Problem 493 * [Sol1](project_euler/problem_493/sol1.py) * Problem 551 * [Sol1](project_euler/problem_551/sol1.py) * Problem 587 * [Sol1](project_euler/problem_587/sol1.py) * Problem 686 * [Sol1](project_euler/problem_686/sol1.py) * Problem 800 * [Sol1](project_euler/problem_800/sol1.py) ## Quantum * [Q Fourier Transform](quantum/q_fourier_transform.py) ## Scheduling * [First Come First Served](scheduling/first_come_first_served.py) * [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py) * [Job Sequence With Deadline](scheduling/job_sequence_with_deadline.py) * [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py) * [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py) * [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py) * [Round Robin](scheduling/round_robin.py) * [Shortest Job First](scheduling/shortest_job_first.py) ## Searches * [Binary Search](searches/binary_search.py) * [Binary Tree Traversal](searches/binary_tree_traversal.py) * [Double Linear Search](searches/double_linear_search.py) * [Double Linear Search Recursion](searches/double_linear_search_recursion.py) * [Fibonacci Search](searches/fibonacci_search.py) * [Hill Climbing](searches/hill_climbing.py) * [Interpolation Search](searches/interpolation_search.py) * [Jump Search](searches/jump_search.py) * [Linear Search](searches/linear_search.py) * [Median Of Medians](searches/median_of_medians.py) * [Quick Select](searches/quick_select.py) * [Sentinel Linear Search](searches/sentinel_linear_search.py) * [Simple Binary Search](searches/simple_binary_search.py) * [Simulated Annealing](searches/simulated_annealing.py) * [Tabu Search](searches/tabu_search.py) * [Ternary Search](searches/ternary_search.py) ## Sorts * [Bead Sort](sorts/bead_sort.py) * [Binary Insertion Sort](sorts/binary_insertion_sort.py) * [Bitonic Sort](sorts/bitonic_sort.py) * [Bogo Sort](sorts/bogo_sort.py) * [Bubble Sort](sorts/bubble_sort.py) * [Bucket Sort](sorts/bucket_sort.py) * [Circle Sort](sorts/circle_sort.py) * [Cocktail Shaker Sort](sorts/cocktail_shaker_sort.py) * [Comb Sort](sorts/comb_sort.py) * [Counting Sort](sorts/counting_sort.py) * [Cycle Sort](sorts/cycle_sort.py) * [Double Sort](sorts/double_sort.py) * [Dutch National Flag Sort](sorts/dutch_national_flag_sort.py) * [Exchange Sort](sorts/exchange_sort.py) * [External Sort](sorts/external_sort.py) * [Gnome Sort](sorts/gnome_sort.py) * [Heap Sort](sorts/heap_sort.py) * [Insertion Sort](sorts/insertion_sort.py) * [Intro Sort](sorts/intro_sort.py) * [Iterative Merge Sort](sorts/iterative_merge_sort.py) * [Merge Insertion Sort](sorts/merge_insertion_sort.py) * [Merge Sort](sorts/merge_sort.py) * [Msd Radix Sort](sorts/msd_radix_sort.py) * [Natural Sort](sorts/natural_sort.py) * [Odd Even Sort](sorts/odd_even_sort.py) * [Odd Even Transposition Parallel](sorts/odd_even_transposition_parallel.py) * [Odd Even Transposition Single Threaded](sorts/odd_even_transposition_single_threaded.py) * [Pancake Sort](sorts/pancake_sort.py) * [Patience Sort](sorts/patience_sort.py) * [Pigeon Sort](sorts/pigeon_sort.py) * [Pigeonhole Sort](sorts/pigeonhole_sort.py) * [Quick Sort](sorts/quick_sort.py) * [Quick Sort 3 Partition](sorts/quick_sort_3_partition.py) * [Radix Sort](sorts/radix_sort.py) * [Recursive Insertion Sort](sorts/recursive_insertion_sort.py) * [Recursive Mergesort Array](sorts/recursive_mergesort_array.py) * [Recursive Quick Sort](sorts/recursive_quick_sort.py) * [Selection Sort](sorts/selection_sort.py) * [Shell Sort](sorts/shell_sort.py) * [Shrink Shell Sort](sorts/shrink_shell_sort.py) * [Slowsort](sorts/slowsort.py) * [Stooge Sort](sorts/stooge_sort.py) * [Strand Sort](sorts/strand_sort.py) * [Tim Sort](sorts/tim_sort.py) * [Topological Sort](sorts/topological_sort.py) * [Tree Sort](sorts/tree_sort.py) * [Unknown Sort](sorts/unknown_sort.py) * [Wiggle Sort](sorts/wiggle_sort.py) ## Strings * [Aho Corasick](strings/aho_corasick.py) * [Alternative String Arrange](strings/alternative_string_arrange.py) * [Anagrams](strings/anagrams.py) * [Autocomplete Using Trie](strings/autocomplete_using_trie.py) * [Barcode Validator](strings/barcode_validator.py) * [Bitap String Match](strings/bitap_string_match.py) * [Boyer Moore Search](strings/boyer_moore_search.py) * [Camel Case To Snake Case](strings/camel_case_to_snake_case.py) * [Can String Be Rearranged As Palindrome](strings/can_string_be_rearranged_as_palindrome.py) * [Capitalize](strings/capitalize.py) * [Check Anagrams](strings/check_anagrams.py) * [Credit Card Validator](strings/credit_card_validator.py) * [Damerau Levenshtein Distance](strings/damerau_levenshtein_distance.py) * [Detecting English Programmatically](strings/detecting_english_programmatically.py) * [Dna](strings/dna.py) * [Edit Distance](strings/edit_distance.py) * [Frequency Finder](strings/frequency_finder.py) * [Hamming Distance](strings/hamming_distance.py) * [Indian Phone Validator](strings/indian_phone_validator.py) * [Is Contains Unique Chars](strings/is_contains_unique_chars.py) * [Is Isogram](strings/is_isogram.py) * [Is Pangram](strings/is_pangram.py) * [Is Polish National Id](strings/is_polish_national_id.py) * [Is Spain National Id](strings/is_spain_national_id.py) * [Is Srilankan Phone Number](strings/is_srilankan_phone_number.py) * [Is Valid Email Address](strings/is_valid_email_address.py) * [Jaro Winkler](strings/jaro_winkler.py) * [Join](strings/join.py) * [Knuth Morris Pratt](strings/knuth_morris_pratt.py) * [Levenshtein Distance](strings/levenshtein_distance.py) * [Lower](strings/lower.py) * [Manacher](strings/manacher.py) * [Min Cost String Conversion](strings/min_cost_string_conversion.py) * [Naive String Search](strings/naive_string_search.py) * [Ngram](strings/ngram.py) * [Palindrome](strings/palindrome.py) * [Pig Latin](strings/pig_latin.py) * [Prefix Function](strings/prefix_function.py) * [Rabin Karp](strings/rabin_karp.py) * [Remove Duplicate](strings/remove_duplicate.py) * [Reverse Letters](strings/reverse_letters.py) * [Reverse Words](strings/reverse_words.py) * [Snake Case To Camel Pascal Case](strings/snake_case_to_camel_pascal_case.py) * [Split](strings/split.py) * [String Switch Case](strings/string_switch_case.py) * [Strip](strings/strip.py) * [Text Justification](strings/text_justification.py) * [Title](strings/title.py) * [Top K Frequent Words](strings/top_k_frequent_words.py) * [Upper](strings/upper.py) * [Wave](strings/wave.py) * [Wildcard Pattern Matching](strings/wildcard_pattern_matching.py) * [Word Occurrence](strings/word_occurrence.py) * [Word Patterns](strings/word_patterns.py) * [Z Function](strings/z_function.py) ## Web Programming * [Co2 Emission](web_programming/co2_emission.py) * [Covid Stats Via Xpath](web_programming/covid_stats_via_xpath.py) * [Crawl Google Results](web_programming/crawl_google_results.py) * [Crawl Google Scholar Citation](web_programming/crawl_google_scholar_citation.py) * [Currency Converter](web_programming/currency_converter.py) * [Current Stock Price](web_programming/current_stock_price.py) * [Current Weather](web_programming/current_weather.py) * [Daily Horoscope](web_programming/daily_horoscope.py) * [Download Images From Google Query](web_programming/download_images_from_google_query.py) * [Emails From Url](web_programming/emails_from_url.py) * [Fetch Anime And Play](web_programming/fetch_anime_and_play.py) * [Fetch Bbc News](web_programming/fetch_bbc_news.py) * [Fetch Github Info](web_programming/fetch_github_info.py) * [Fetch Jobs](web_programming/fetch_jobs.py) * [Fetch Quotes](web_programming/fetch_quotes.py) * [Fetch Well Rx Price](web_programming/fetch_well_rx_price.py) * [Get Amazon Product Data](web_programming/get_amazon_product_data.py) * [Get Imdb Top 250 Movies Csv](web_programming/get_imdb_top_250_movies_csv.py) * [Get Imdbtop](web_programming/get_imdbtop.py) * [Get Ip Geolocation](web_programming/get_ip_geolocation.py) * [Get Top Billionaires](web_programming/get_top_billionaires.py) * [Get Top Hn Posts](web_programming/get_top_hn_posts.py) * [Get User Tweets](web_programming/get_user_tweets.py) * [Giphy](web_programming/giphy.py) * [Instagram Crawler](web_programming/instagram_crawler.py) * [Instagram Pic](web_programming/instagram_pic.py) * [Instagram Video](web_programming/instagram_video.py) * [Nasa Data](web_programming/nasa_data.py) * [Open Google Results](web_programming/open_google_results.py) * [Random Anime Character](web_programming/random_anime_character.py) * [Recaptcha Verification](web_programming/recaptcha_verification.py) * [Reddit](web_programming/reddit.py) * [Search Books By Isbn](web_programming/search_books_by_isbn.py) * [Slack Message](web_programming/slack_message.py) * [Test Fetch Github Info](web_programming/test_fetch_github_info.py) * [World Covid19 Stats](web_programming/world_covid19_stats.py)

TheAlgorithms/Python

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[tool.ruff] ignore = [ # `ruff rule S101` for a description of that rule "ARG001", # Unused function argument `amount` -- FIX ME? "B904", # Within an `except` clause, raise exceptions with `raise ... from err` -- FIX ME "B905", # `zip()` without an explicit `strict=` parameter -- FIX ME "DTZ001", # The use of `datetime.datetime()` without `tzinfo` argument is not allowed -- FIX ME "DTZ005", # The use of `datetime.datetime.now()` without `tzinfo` argument is not allowed -- FIX ME "E741", # Ambiguous variable name 'l' -- FIX ME "EM101", # Exception must not use a string literal, assign to variable first "EXE001", # Shebang is present but file is not executable" -- FIX ME "G004", # Logging statement uses f-string "ICN001", # `matplotlib.pyplot` should be imported as `plt` -- FIX ME "INP001", # File `x/y/z.py` is part of an implicit namespace package. Add an `__init__.py`. -- FIX ME "N999", # Invalid module name -- FIX ME "NPY002", # Replace legacy `np.random.choice` call with `np.random.Generator` -- FIX ME "PGH003", # Use specific rule codes when ignoring type issues -- FIX ME "PLC1901", # `{}` can be simplified to `{}` as an empty string is falsey "PLR5501", # Consider using `elif` instead of `else` -- FIX ME "PLW0120", # `else` clause on loop without a `break` statement -- FIX ME "PLW060", # Using global for `{name}` but no assignment is done -- DO NOT FIX "PLW2901", # PLW2901: Redefined loop variable -- FIX ME "PT011", # `pytest.raises(Exception)` is too broad, set the `match` parameter or use a more specific exception "PT018", # Assertion should be broken down into multiple parts "RUF00", # Ambiguous unicode character and other rules "RUF100", # Unused `noqa` directive -- FIX ME "S101", # Use of `assert` detected -- DO NOT FIX "S105", # Possible hardcoded password: 'password' "S113", # Probable use of requests call without timeout -- FIX ME "S311", # Standard pseudo-random generators are not suitable for cryptographic purposes -- FIX ME "SIM102", # Use a single `if` statement instead of nested `if` statements -- FIX ME "SLF001", # Private member accessed: `_Iterator` -- FIX ME "UP038", # Use `X | Y` in `{}` call instead of `(X, Y)` -- DO NOT FIX ] select = [ # https://beta.ruff.rs/docs/rules "A", # flake8-builtins "ARG", # flake8-unused-arguments "ASYNC", # flake8-async "B", # flake8-bugbear "BLE", # flake8-blind-except "C4", # flake8-comprehensions "C90", # McCabe cyclomatic complexity "DJ", # flake8-django "DTZ", # flake8-datetimez "E", # pycodestyle "EM", # flake8-errmsg "EXE", # flake8-executable "F", # Pyflakes "FA", # flake8-future-annotations "FLY", # flynt "G", # flake8-logging-format "I", # isort "ICN", # flake8-import-conventions "INP", # flake8-no-pep420 "INT", # flake8-gettext "ISC", # flake8-implicit-str-concat "N", # pep8-naming "NPY", # NumPy-specific rules "PD", # pandas-vet "PGH", # pygrep-hooks "PIE", # flake8-pie "PL", # Pylint "PT", # flake8-pytest-style "PYI", # flake8-pyi "RSE", # flake8-raise "RUF", # Ruff-specific rules "S", # flake8-bandit "SIM", # flake8-simplify "SLF", # flake8-self "T10", # flake8-debugger "TD", # flake8-todos "TID", # flake8-tidy-imports "UP", # pyupgrade "W", # pycodestyle "YTT", # flake8-2020 # "ANN", # flake8-annotations # FIX ME? # "COM", # flake8-commas # "D", # pydocstyle -- FIX ME? # "ERA", # eradicate -- DO NOT FIX # "FBT", # flake8-boolean-trap # FIX ME # "PTH", # flake8-use-pathlib # FIX ME # "Q", # flake8-quotes # "RET", # flake8-return # FIX ME? # "T20", # flake8-print # "TCH", # flake8-type-checking # "TRY", # tryceratops ] show-source = true target-version = "py311" [tool.ruff.mccabe] # DO NOT INCREASE THIS VALUE max-complexity = 17 # default: 10 [tool.ruff.per-file-ignores] "arithmetic_analysis/newton_raphson.py" = ["PGH001"] "audio_filters/show_response.py" = ["ARG002"] "data_structures/binary_tree/binary_search_tree_recursive.py" = ["BLE001"] "data_structures/binary_tree/treap.py" = ["SIM114"] "data_structures/hashing/hash_table.py" = ["ARG002"] "data_structures/hashing/quadratic_probing.py" = ["ARG002"] "data_structures/hashing/tests/test_hash_map.py" = ["BLE001"] "data_structures/heap/max_heap.py" = ["SIM114"] "graphs/minimum_spanning_tree_prims.py" = ["SIM114"] "hashes/enigma_machine.py" = ["BLE001"] "machine_learning/decision_tree.py" = ["SIM114"] "machine_learning/linear_discriminant_analysis.py" = ["ARG005"] "machine_learning/sequential_minimum_optimization.py" = ["SIM115"] "matrix/sherman_morrison.py" = ["SIM103", "SIM114"] "other/l*u_cache.py" = ["RUF012"] "physics/newtons_second_law_of_motion.py" = ["BLE001"] "project_euler/problem_099/sol1.py" = ["SIM115"] "sorts/external_sort.py" = ["SIM115"] [tool.ruff.pylint] # DO NOT INCREASE THESE VALUES allow-magic-value-types = ["float", "int", "str"] max-args = 10 # default: 5 max-branches = 20 # default: 12 max-returns = 8 # default: 6 max-statements = 88 # default: 50 [tool.pytest.ini_options] markers = [ "mat_ops: mark a test as utilizing matrix operations.", ] addopts = [ "--durations=10", "--doctest-modules", "--showlocals", ] [tool.coverage.report] omit = [ ".env/*", "project_euler/*" ] sort = "Cover" [tool.codespell] ignore-words-list = "3rt,ans,bitap,crate,damon,fo,followings,hist,iff,kwanza,manuel,mater,secant,som,sur,tim,toi,zar" skip = "./.*,*.json,ciphers/prehistoric_men.txt,project_euler/problem_022/p022_names.txt,pyproject.toml,strings/dictionary.txt,strings/words.txt"

[tool.ruff] ignore = [ # `ruff rule S101` for a description of that rule "ARG001", # Unused function argument `amount` -- FIX ME? "B904", # Within an `except` clause, raise exceptions with `raise ... from err` -- FIX ME "B905", # `zip()` without an explicit `strict=` parameter -- FIX ME "DTZ001", # The use of `datetime.datetime()` without `tzinfo` argument is not allowed -- FIX ME "DTZ005", # The use of `datetime.datetime.now()` without `tzinfo` argument is not allowed -- FIX ME "E741", # Ambiguous variable name 'l' -- FIX ME "EM101", # Exception must not use a string literal, assign to variable first "EXE001", # Shebang is present but file is not executable" -- FIX ME "G004", # Logging statement uses f-string "ICN001", # `matplotlib.pyplot` should be imported as `plt` -- FIX ME "INP001", # File `x/y/z.py` is part of an implicit namespace package. Add an `__init__.py`. -- FIX ME "N999", # Invalid module name -- FIX ME "NPY002", # Replace legacy `np.random.choice` call with `np.random.Generator` -- FIX ME "PGH003", # Use specific rule codes when ignoring type issues -- FIX ME "PLC1901", # `{}` can be simplified to `{}` as an empty string is falsey "PLR5501", # Consider using `elif` instead of `else` -- FIX ME "PLW0120", # `else` clause on loop without a `break` statement -- FIX ME "PLW060", # Using global for `{name}` but no assignment is done -- DO NOT FIX "PLW2901", # PLW2901: Redefined loop variable -- FIX ME "PT011", # `pytest.raises(Exception)` is too broad, set the `match` parameter or use a more specific exception "PT018", # Assertion should be broken down into multiple parts "RUF00", # Ambiguous unicode character and other rules "RUF100", # Unused `noqa` directive -- FIX ME "S101", # Use of `assert` detected -- DO NOT FIX "S105", # Possible hardcoded password: 'password' "S113", # Probable use of requests call without timeout -- FIX ME "S311", # Standard pseudo-random generators are not suitable for cryptographic purposes -- FIX ME "SIM102", # Use a single `if` statement instead of nested `if` statements -- FIX ME "SLF001", # Private member accessed: `_Iterator` -- FIX ME "UP038", # Use `X | Y` in `{}` call instead of `(X, Y)` -- DO NOT FIX ] select = [ # https://beta.ruff.rs/docs/rules "A", # flake8-builtins "ARG", # flake8-unused-arguments "ASYNC", # flake8-async "B", # flake8-bugbear "BLE", # flake8-blind-except "C4", # flake8-comprehensions "C90", # McCabe cyclomatic complexity "DJ", # flake8-django "DTZ", # flake8-datetimez "E", # pycodestyle "EM", # flake8-errmsg "EXE", # flake8-executable "F", # Pyflakes "FA", # flake8-future-annotations "FLY", # flynt "G", # flake8-logging-format "I", # isort "ICN", # flake8-import-conventions "INP", # flake8-no-pep420 "INT", # flake8-gettext "ISC", # flake8-implicit-str-concat "N", # pep8-naming "NPY", # NumPy-specific rules "PD", # pandas-vet "PGH", # pygrep-hooks "PIE", # flake8-pie "PL", # Pylint "PT", # flake8-pytest-style "PYI", # flake8-pyi "RSE", # flake8-raise "RUF", # Ruff-specific rules "S", # flake8-bandit "SIM", # flake8-simplify "SLF", # flake8-self "T10", # flake8-debugger "TD", # flake8-todos "TID", # flake8-tidy-imports "UP", # pyupgrade "W", # pycodestyle "YTT", # flake8-2020 # "ANN", # flake8-annotations # FIX ME? # "COM", # flake8-commas # "D", # pydocstyle -- FIX ME? # "ERA", # eradicate -- DO NOT FIX # "FBT", # flake8-boolean-trap # FIX ME # "PTH", # flake8-use-pathlib # FIX ME # "Q", # flake8-quotes # "RET", # flake8-return # FIX ME? # "T20", # flake8-print # "TCH", # flake8-type-checking # "TRY", # tryceratops ] show-source = true target-version = "py311" [tool.ruff.mccabe] # DO NOT INCREASE THIS VALUE max-complexity = 17 # default: 10 [tool.ruff.per-file-ignores] "arithmetic_analysis/newton_raphson.py" = ["PGH001"] "audio_filters/show_response.py" = ["ARG002"] "data_structures/binary_tree/binary_search_tree_recursive.py" = ["BLE001"] "data_structures/binary_tree/treap.py" = ["SIM114"] "data_structures/hashing/hash_table.py" = ["ARG002"] "data_structures/hashing/quadratic_probing.py" = ["ARG002"] "data_structures/hashing/tests/test_hash_map.py" = ["BLE001"] "data_structures/heap/max_heap.py" = ["SIM114"] "graphs/minimum_spanning_tree_prims.py" = ["SIM114"] "hashes/enigma_machine.py" = ["BLE001"] "machine_learning/decision_tree.py" = ["SIM114"] "machine_learning/linear_discriminant_analysis.py" = ["ARG005"] "machine_learning/sequential_minimum_optimization.py" = ["SIM115"] "matrix/sherman_morrison.py" = ["SIM103", "SIM114"] "other/l*u_cache.py" = ["RUF012"] "physics/newtons_second_law_of_motion.py" = ["BLE001"] "project_euler/problem_099/sol1.py" = ["SIM115"] "sorts/external_sort.py" = ["SIM115"] [tool.ruff.pylint] # DO NOT INCREASE THESE VALUES allow-magic-value-types = ["float", "int", "str"] max-args = 10 # default: 5 max-branches = 20 # default: 12 max-returns = 8 # default: 6 max-statements = 88 # default: 50 [tool.codespell] ignore-words-list = "3rt,ans,bitap,crate,damon,fo,followings,hist,iff,kwanza,manuel,mater,secant,som,sur,tim,toi,zar" skip = "./.*,*.json,ciphers/prehistoric_men.txt,project_euler/problem_022/p022_names.txt,pyproject.toml,strings/dictionary.txt,strings/words.txt" [tool.pytest.ini_options] markers = [ "mat_ops: mark a test as utilizing matrix operations.", ] addopts = [ "--durations=10", "--doctest-modules", "--showlocals", ] [tool.coverage.report] omit = [ ".env/*", "project_euler/*" ] sort = "Cover"

TheAlgorithms/Python

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# Backtracking Backtracking is a way to speed up the search process by removing candidates when they can't be the solution of a problem. * <https://en.wikipedia.org/wiki/Backtracking> * <https://en.wikipedia.org/wiki/Decision_tree_pruning> * <https://medium.com/@priyankmistry1999/backtracking-sudoku-6e4439e4825c> * <https://www.geeksforgeeks.org/sudoku-backtracking-7/>

# Backtracking Backtracking is a way to speed up the search process by removing candidates when they can't be the solution of a problem. * <https://en.wikipedia.org/wiki/Backtracking> * <https://en.wikipedia.org/wiki/Decision_tree_pruning> * <https://medium.com/@priyankmistry1999/backtracking-sudoku-6e4439e4825c> * <https://www.geeksforgeeks.org/sudoku-backtracking-7/>

TheAlgorithms/Python

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# Compression Data compression is everywhere, you need it to store data without taking too much space. Either the compression loses some data (then we talk about lossy compression, such as .jpg) or it does not (and then it is lossless compression, such as .png) Lossless compression is mainly used for archive purpose as it allows storing data without losing information about the file archived. On the other hand, lossy compression is used for transfer of file where quality isn't necessarily what is required (i.e: images on Twitter). * <https://www.sciencedirect.com/topics/computer-science/compression-algorithm> * <https://en.wikipedia.org/wiki/Data_compression> * <https://en.wikipedia.org/wiki/Pigeonhole_principle>

# Compression Data compression is everywhere, you need it to store data without taking too much space. Either the compression loses some data (then we talk about lossy compression, such as .jpg) or it does not (and then it is lossless compression, such as .png) Lossless compression is mainly used for archive purpose as it allows storing data without losing information about the file archived. On the other hand, lossy compression is used for transfer of file where quality isn't necessarily what is required (i.e: images on Twitter). * <https://www.sciencedirect.com/topics/computer-science/compression-algorithm> * <https://en.wikipedia.org/wiki/Data_compression> * <https://en.wikipedia.org/wiki/Pigeonhole_principle>

TheAlgorithms/Python

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# Boolean Algebra Boolean algebra is used to do arithmetic with bits of values True (1) or False (0). There are three basic operations: 'and', 'or' and 'not'. * <https://en.wikipedia.org/wiki/Boolean_algebra> * <https://plato.stanford.edu/entries/boolalg-math/>

# Boolean Algebra Boolean algebra is used to do arithmetic with bits of values True (1) or False (0). There are three basic operations: 'and', 'or' and 'not'. * <https://en.wikipedia.org/wiki/Boolean_algebra> * <https://plato.stanford.edu/entries/boolalg-math/>

TheAlgorithms/Python

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# Conversion Conversion programs convert a type of data, a number from a numerical base or unit into one of another type, base or unit, e.g. binary to decimal, integer to string or foot to meters. * <https://en.wikipedia.org/wiki/Data_conversion> * <https://en.wikipedia.org/wiki/Transcoding>

# Conversion Conversion programs convert a type of data, a number from a numerical base or unit into one of another type, base or unit, e.g. binary to decimal, integer to string or foot to meters. * <https://en.wikipedia.org/wiki/Data_conversion> * <https://en.wikipedia.org/wiki/Transcoding>

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# Blockchain A Blockchain is a type of **distributed ledger** technology (DLT) that consists of growing list of records, called **blocks**, that are securely linked together using **cryptography**. Let's breakdown the terminologies in the above definition. We find below terminologies, - Digital Ledger Technology (DLT) - Blocks - Cryptography ## Digital Ledger Technology It is otherwise called as distributed ledger technology. It is simply the opposite of centralized database. Firstly, what is a **ledger**? A ledger is a book or collection of accounts that records account transactions. *Why is Blockchain addressed as digital ledger if it can record more than account transactions? What other transaction details and information can it hold?* Digital Ledger Technology is just a ledger which is shared among multiple nodes. This way there exist no need for central authority to hold the info. Okay, how is it differentiated from central database and what are their benefits? There is an organization which has 4 branches whose data are stored in a centralized database. So even if one branch needs any data from ledger they need an approval from database in charge. And if one hacks the central database he gets to tamper and control all the data. Now lets assume every branch has a copy of the ledger and then once anything is added to the ledger by anyone branch it is gonna automatically reflect in all other ledgers available in other branch. This is done using Peer-to-peer network. So this means even if information is tampered in one branch we can find out. If one branch is hacked we can be alerted ,so we can safeguard other branches. Now, assume these branches as computers or nodes and the ledger is a transaction record or digital receipt. If one ledger is hacked in a node we can detect since there will be a mismatch in comparison with other node information. So this is the concept of Digital Ledger Technology. *Is it required for all nodes to have access to all information in other nodes? Wouldn't this require enormous storage space in each node?* ## Blocks In short a block is nothing but collections of records with a labelled header. These are connected cryptographically. Once a new block is added to a chain, the previous block is connected, more precisely said as locked and hence, will remain unaltered. We can understand this concept once we get a clear understanding of working mechanism of blockchain. ## Cryptography It is the practice and study of secure communication techniques in the midst of adversarial behavior. More broadly, cryptography is the creation and analysis of protocols that prevent third parties or the general public from accessing private messages. *Which cryptography technology is most widely used in blockchain and why?* So, in general, blockchain technology is a distributed record holder which records the information about ownership of an asset. To define precisely, > Blockchain is a distributed, immutable ledger that makes it easier to record transactions and track assets in a corporate network. An asset could be tangible (such as a house, car, cash, or land) or intangible (such as a business) (intellectual property, patents, copyrights, branding). A blockchain network can track and sell almost anything of value, lowering risk and costs for everyone involved. So this is all about introduction to blockchain technology. To learn more about the topic refer below links.... * <https://en.wikipedia.org/wiki/Blockchain> * <https://en.wikipedia.org/wiki/Chinese_remainder_theorem> * <https://en.wikipedia.org/wiki/Diophantine_equation> * <https://www.geeksforgeeks.org/modular-division/>

# Blockchain A Blockchain is a type of **distributed ledger** technology (DLT) that consists of growing list of records, called **blocks**, that are securely linked together using **cryptography**. Let's breakdown the terminologies in the above definition. We find below terminologies, - Digital Ledger Technology (DLT) - Blocks - Cryptography ## Digital Ledger Technology It is otherwise called as distributed ledger technology. It is simply the opposite of centralized database. Firstly, what is a **ledger**? A ledger is a book or collection of accounts that records account transactions. *Why is Blockchain addressed as digital ledger if it can record more than account transactions? What other transaction details and information can it hold?* Digital Ledger Technology is just a ledger which is shared among multiple nodes. This way there exist no need for central authority to hold the info. Okay, how is it differentiated from central database and what are their benefits? There is an organization which has 4 branches whose data are stored in a centralized database. So even if one branch needs any data from ledger they need an approval from database in charge. And if one hacks the central database he gets to tamper and control all the data. Now lets assume every branch has a copy of the ledger and then once anything is added to the ledger by anyone branch it is gonna automatically reflect in all other ledgers available in other branch. This is done using Peer-to-peer network. So this means even if information is tampered in one branch we can find out. If one branch is hacked we can be alerted ,so we can safeguard other branches. Now, assume these branches as computers or nodes and the ledger is a transaction record or digital receipt. If one ledger is hacked in a node we can detect since there will be a mismatch in comparison with other node information. So this is the concept of Digital Ledger Technology. *Is it required for all nodes to have access to all information in other nodes? Wouldn't this require enormous storage space in each node?* ## Blocks In short a block is nothing but collections of records with a labelled header. These are connected cryptographically. Once a new block is added to a chain, the previous block is connected, more precisely said as locked and hence, will remain unaltered. We can understand this concept once we get a clear understanding of working mechanism of blockchain. ## Cryptography It is the practice and study of secure communication techniques in the midst of adversarial behavior. More broadly, cryptography is the creation and analysis of protocols that prevent third parties or the general public from accessing private messages. *Which cryptography technology is most widely used in blockchain and why?* So, in general, blockchain technology is a distributed record holder which records the information about ownership of an asset. To define precisely, > Blockchain is a distributed, immutable ledger that makes it easier to record transactions and track assets in a corporate network. An asset could be tangible (such as a house, car, cash, or land) or intangible (such as a business) (intellectual property, patents, copyrights, branding). A blockchain network can track and sell almost anything of value, lowering risk and costs for everyone involved. So this is all about introduction to blockchain technology. To learn more about the topic refer below links.... * <https://en.wikipedia.org/wiki/Blockchain> * <https://en.wikipedia.org/wiki/Chinese_remainder_theorem> * <https://en.wikipedia.org/wiki/Diophantine_equation> * <https://www.geeksforgeeks.org/modular-division/>

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# Welcome to Quantum Algorithms Started at https://github.com/TheAlgorithms/Python/issues/1831 * D-Wave: https://www.dwavesys.com and https://github.com/dwavesystems * Google: https://research.google/teams/applied-science/quantum * IBM: https://qiskit.org and https://github.com/Qiskit * Rigetti: https://rigetti.com and https://github.com/rigetti * Zapata: https://www.zapatacomputing.com and https://github.com/zapatacomputing ## IBM Qiskit - Start using by installing `pip install qiskit`, refer the [docs](https://qiskit.org/documentation/install.html) for more info. - Tutorials & References - https://github.com/Qiskit/qiskit-tutorials - https://quantum-computing.ibm.com/docs/iql/first-circuit - https://medium.com/qiskit/how-to-program-a-quantum-computer-982a9329ed02 ## Google Cirq - Start using by installing `python -m pip install cirq`, refer the [docs](https://quantumai.google/cirq/start/install) for more info. - Tutorials & references - https://github.com/quantumlib/cirq - https://quantumai.google/cirq/experiments - https://tanishabassan.medium.com/quantum-programming-with-google-cirq-3209805279bc

# Welcome to Quantum Algorithms Started at https://github.com/TheAlgorithms/Python/issues/1831 * D-Wave: https://www.dwavesys.com and https://github.com/dwavesystems * Google: https://research.google/teams/applied-science/quantum * IBM: https://qiskit.org and https://github.com/Qiskit * Rigetti: https://rigetti.com and https://github.com/rigetti * Zapata: https://www.zapatacomputing.com and https://github.com/zapatacomputing ## IBM Qiskit - Start using by installing `pip install qiskit`, refer the [docs](https://qiskit.org/documentation/install.html) for more info. - Tutorials & References - https://github.com/Qiskit/qiskit-tutorials - https://quantum-computing.ibm.com/docs/iql/first-circuit - https://medium.com/qiskit/how-to-program-a-quantum-computer-982a9329ed02 ## Google Cirq - Start using by installing `python -m pip install cirq`, refer the [docs](https://quantumai.google/cirq/start/install) for more info. - Tutorials & references - https://github.com/quantumlib/cirq - https://quantumai.google/cirq/experiments - https://tanishabassan.medium.com/quantum-programming-with-google-cirq-3209805279bc

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# A naive recursive implementation of 0-1 Knapsack Problem This overview is taken from: https://en.wikipedia.org/wiki/Knapsack_problem --- ## Overview The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897 The name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. --- ## Documentation This module uses docstrings to enable the use of Python's in-built `help(...)` function. For instance, try `help(Vector)`, `help(unit_basis_vector)`, and `help(CLASSNAME.METHODNAME)`. --- ## Usage Import the module `knapsack.py` from the **.** directory into your project. --- ## Tests `.` contains Python unit tests which can be run with `python3 -m unittest -v`.

# A naive recursive implementation of 0-1 Knapsack Problem This overview is taken from: https://en.wikipedia.org/wiki/Knapsack_problem --- ## Overview The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897 The name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. --- ## Documentation This module uses docstrings to enable the use of Python's in-built `help(...)` function. For instance, try `help(Vector)`, `help(unit_basis_vector)`, and `help(CLASSNAME.METHODNAME)`. --- ## Usage Import the module `knapsack.py` from the **.** directory into your project. --- ## Tests `.` contains Python unit tests which can be run with `python3 -m unittest -v`.

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### Interest * Compound Interest: "Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one." [Compound Interest](https://www.investopedia.com/) * Simple Interest: "Simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. " [Simple Interest](https://www.investopedia.com/)

### Interest * Compound Interest: "Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one." [Compound Interest](https://www.investopedia.com/) * Simple Interest: "Simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. " [Simple Interest](https://www.investopedia.com/)

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MIT License Copyright (c) 2016-2022 TheAlgorithms and contributors Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

MIT License Copyright (c) 2016-2022 TheAlgorithms and contributors Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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# Sorting Algorithms Sorting is the process of putting data in a specific order. The way to arrange data in a specific order is specified by the sorting algorithm. The most typical orders are lexical or numerical. The significance of sorting lies in the fact that, if data is stored in a sorted manner, data searching can be highly optimised. Another use for sorting is to represent data in a more readable manner. This section contains a lot of important algorithms that help us to use sorting algorithms in various scenarios. ## References * <https://www.tutorialspoint.com/python_data_structure/python_sorting_algorithms.htm> * <https://www.geeksforgeeks.org/sorting-algorithms-in-python> * <https://realpython.com/sorting-algorithms-python>

# Sorting Algorithms Sorting is the process of putting data in a specific order. The way to arrange data in a specific order is specified by the sorting algorithm. The most typical orders are lexical or numerical. The significance of sorting lies in the fact that, if data is stored in a sorted manner, data searching can be highly optimised. Another use for sorting is to represent data in a more readable manner. This section contains a lot of important algorithms that help us to use sorting algorithms in various scenarios. ## References * <https://www.tutorialspoint.com/python_data_structure/python_sorting_algorithms.htm> * <https://www.geeksforgeeks.org/sorting-algorithms-in-python> * <https://realpython.com/sorting-algorithms-python>

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# Hashes Hashing is the process of mapping any amount of data to a specified size using an algorithm. This is known as a hash value (or, if you're feeling fancy, a hash code, hash sums, or even a hash digest). Hashing is a one-way function, whereas encryption is a two-way function. While it is functionally conceivable to reverse-hash stuff, the required computing power makes it impractical. Hashing is a one-way street. Unlike encryption, which is intended to protect data in transit, hashing is intended to authenticate that a file or piece of data has not been altered—that it is authentic. In other words, it functions as a checksum. ## Common hashing algorithms ### MD5 This is one of the first algorithms that has gained widespread acceptance. MD5 is hashing algorithm made by Ray Rivest that is known to suffer vulnerabilities. It was created in 1992 as the successor to MD4. Currently MD6 is in the works, but as of 2009 Rivest had removed it from NIST consideration for SHA-3. ### SHA SHA stands for Security Hashing Algorithm and it’s probably best known as the hashing algorithm used in most SSL/TLS cipher suites. A cipher suite is a collection of ciphers and algorithms that are used for SSL/TLS connections. SHA handles the hashing aspects. SHA-1, as we mentioned earlier, is now deprecated. SHA-2 is now mandatory. SHA-2 is sometimes known as SHA-256, though variants with longer bit lengths are also available. ### SHA256 SHA 256 is a member of the SHA 2 algorithm family, under which SHA stands for Secure Hash Algorithm. It was a collaborative effort between both the NSA and NIST to implement a successor to the SHA 1 family, which was beginning to lose potency against brute force attacks. It was published in 2001. The importance of the 256 in the name refers to the final hash digest value, i.e. the hash value will remain 256 bits regardless of the size of the plaintext/cleartext. Other algorithms in the SHA family are similar to SHA 256 in some ways. ### Luhn The Luhn algorithm, also renowned as the modulus 10 or mod 10 algorithm, is a straightforward checksum formula used to validate a wide range of identification numbers, including credit card numbers, IMEI numbers, and Canadian Social Insurance Numbers. A community of mathematicians developed the LUHN formula in the late 1960s. Companies offering credit cards quickly followed suit. Since the algorithm is in the public interest, anyone can use it. The algorithm is used by most credit cards and many government identification numbers as a simple method of differentiating valid figures from mistyped or otherwise incorrect numbers. It was created to guard against unintentional errors, not malicious attacks.

# Hashes Hashing is the process of mapping any amount of data to a specified size using an algorithm. This is known as a hash value (or, if you're feeling fancy, a hash code, hash sums, or even a hash digest). Hashing is a one-way function, whereas encryption is a two-way function. While it is functionally conceivable to reverse-hash stuff, the required computing power makes it impractical. Hashing is a one-way street. Unlike encryption, which is intended to protect data in transit, hashing is intended to authenticate that a file or piece of data has not been altered—that it is authentic. In other words, it functions as a checksum. ## Common hashing algorithms ### MD5 This is one of the first algorithms that has gained widespread acceptance. MD5 is hashing algorithm made by Ray Rivest that is known to suffer vulnerabilities. It was created in 1992 as the successor to MD4. Currently MD6 is in the works, but as of 2009 Rivest had removed it from NIST consideration for SHA-3. ### SHA SHA stands for Security Hashing Algorithm and it’s probably best known as the hashing algorithm used in most SSL/TLS cipher suites. A cipher suite is a collection of ciphers and algorithms that are used for SSL/TLS connections. SHA handles the hashing aspects. SHA-1, as we mentioned earlier, is now deprecated. SHA-2 is now mandatory. SHA-2 is sometimes known as SHA-256, though variants with longer bit lengths are also available. ### SHA256 SHA 256 is a member of the SHA 2 algorithm family, under which SHA stands for Secure Hash Algorithm. It was a collaborative effort between both the NSA and NIST to implement a successor to the SHA 1 family, which was beginning to lose potency against brute force attacks. It was published in 2001. The importance of the 256 in the name refers to the final hash digest value, i.e. the hash value will remain 256 bits regardless of the size of the plaintext/cleartext. Other algorithms in the SHA family are similar to SHA 256 in some ways. ### Luhn The Luhn algorithm, also renowned as the modulus 10 or mod 10 algorithm, is a straightforward checksum formula used to validate a wide range of identification numbers, including credit card numbers, IMEI numbers, and Canadian Social Insurance Numbers. A community of mathematicians developed the LUHN formula in the late 1960s. Companies offering credit cards quickly followed suit. Since the algorithm is in the public interest, anyone can use it. The algorithm is used by most credit cards and many government identification numbers as a simple method of differentiating valid figures from mistyped or otherwise incorrect numbers. It was created to guard against unintentional errors, not malicious attacks.

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<div align="center"> <!-- Title: --> <a href="https://github.com/TheAlgorithms/"> <img src="https://raw.githubusercontent.com/TheAlgorithms/website/1cd824df116b27029f17c2d1b42d81731f28a920/public/logo.svg" height="100"> </a> <h1><a href="https://github.com/TheAlgorithms/">The Algorithms</a> - Python</h1> <!-- Labels: --> <!-- First row: --> <a href="https://gitpod.io/#https://github.com/TheAlgorithms/Python"> <img src="https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod&style=flat-square" height="20" alt="Gitpod Ready-to-Code"> </a> <a href="https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md"> <img src="https://img.shields.io/static/v1.svg?label=Contributions&message=Welcome&color=0059b3&style=flat-square" height="20" alt="Contributions Welcome"> </a> <img src="https://img.shields.io/github/repo-size/TheAlgorithms/Python.svg?label=Repo%20size&style=flat-square" height="20"> <a href="https://the-algorithms.com/discord"> <img src="https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square" height="20" alt="Discord chat"> </a> <a href="https://gitter.im/TheAlgorithms/community"> <img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&logo=gitter&style=flat-square" height="20" alt="Gitter chat"> </a> <!-- Second row: --> <br> <a href="https://github.com/TheAlgorithms/Python/actions"> <img src="https://img.shields.io/github/actions/workflow/status/TheAlgorithms/Python/build.yml?branch=master&label=CI&logo=github&style=flat-square" height="20" alt="GitHub Workflow Status"> </a> <a href="https://github.com/pre-commit/pre-commit"> <img src="https://img.shields.io/badge/pre--commit-enabled-brightgreen?logo=pre-commit&logoColor=white&style=flat-square" height="20" alt="pre-commit"> </a> <a href="https://github.com/psf/black"> <img src="https://img.shields.io/static/v1?label=code%20style&message=black&color=black&style=flat-square" height="20" alt="code style: black"> </a> <!-- Short description: --> <h3>All algorithms implemented in Python - for education</h3> </div> Implementations are for learning purposes only. They may be less efficient than the implementations in the Python standard library. Use them at your discretion. ## Getting Started Read through our [Contribution Guidelines](CONTRIBUTING.md) before you contribute. ## Community Channels We are on [Discord](https://the-algorithms.com/discord) and [Gitter](https://gitter.im/TheAlgorithms/community)! Community channels are a great way for you to ask questions and get help. Please join us! ## List of Algorithms See our [directory](DIRECTORY.md) for easier navigation and a better overview of the project.

<div align="center"> <!-- Title: --> <a href="https://github.com/TheAlgorithms/"> <img src="https://raw.githubusercontent.com/TheAlgorithms/website/1cd824df116b27029f17c2d1b42d81731f28a920/public/logo.svg" height="100"> </a> <h1><a href="https://github.com/TheAlgorithms/">The Algorithms</a> - Python</h1> <!-- Labels: --> <!-- First row: --> <a href="https://gitpod.io/#https://github.com/TheAlgorithms/Python"> <img src="https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod&style=flat-square" height="20" alt="Gitpod Ready-to-Code"> </a> <a href="https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md"> <img src="https://img.shields.io/static/v1.svg?label=Contributions&message=Welcome&color=0059b3&style=flat-square" height="20" alt="Contributions Welcome"> </a> <img src="https://img.shields.io/github/repo-size/TheAlgorithms/Python.svg?label=Repo%20size&style=flat-square" height="20"> <a href="https://the-algorithms.com/discord"> <img src="https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square" height="20" alt="Discord chat"> </a> <a href="https://gitter.im/TheAlgorithms/community"> <img src="https://img.shields.io/badge/Chat-Gitter-ff69b4.svg?label=Chat&logo=gitter&style=flat-square" height="20" alt="Gitter chat"> </a> <!-- Second row: --> <br> <a href="https://github.com/TheAlgorithms/Python/actions"> <img src="https://img.shields.io/github/actions/workflow/status/TheAlgorithms/Python/build.yml?branch=master&label=CI&logo=github&style=flat-square" height="20" alt="GitHub Workflow Status"> </a> <a href="https://github.com/pre-commit/pre-commit"> <img src="https://img.shields.io/badge/pre--commit-enabled-brightgreen?logo=pre-commit&logoColor=white&style=flat-square" height="20" alt="pre-commit"> </a> <a href="https://github.com/psf/black"> <img src="https://img.shields.io/static/v1?label=code%20style&message=black&color=black&style=flat-square" height="20" alt="code style: black"> </a> <!-- Short description: --> <h3>All algorithms implemented in Python - for education</h3> </div> Implementations are for learning purposes only. They may be less efficient than the implementations in the Python standard library. Use them at your discretion. ## Getting Started Read through our [Contribution Guidelines](CONTRIBUTING.md) before you contribute. ## Community Channels We are on [Discord](https://the-algorithms.com/discord) and [Gitter](https://gitter.im/TheAlgorithms/community)! Community channels are a great way for you to ask questions and get help. Please join us! ## List of Algorithms See our [directory](DIRECTORY.md) for easier navigation and a better overview of the project.

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# Audio Filter Audio filters work on the frequency of an audio signal to attenuate unwanted frequency and amplify wanted ones. They are used within anything related to sound, whether it is radio communication or a hi-fi system. * <https://www.masteringbox.com/filter-types/> * <http://ethanwiner.com/filters.html> * <https://en.wikipedia.org/wiki/Audio_filter> * <https://en.wikipedia.org/wiki/Electronic_filter>

# Audio Filter Audio filters work on the frequency of an audio signal to attenuate unwanted frequency and amplify wanted ones. They are used within anything related to sound, whether it is radio communication or a hi-fi system. * <https://www.masteringbox.com/filter-types/> * <http://ethanwiner.com/filters.html> * <https://en.wikipedia.org/wiki/Audio_filter> * <https://en.wikipedia.org/wiki/Electronic_filter>

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# Project Euler Problems are taken from https://projecteuler.net/, the Project Euler. [Problems are licensed under CC BY-NC-SA 4.0](https://projecteuler.net/copyright). Project Euler is a series of challenging mathematical/computer programming problems that require more than just mathematical insights to solve. Project Euler is ideal for mathematicians who are learning to code. The solutions will be checked by our [automated testing on GitHub Actions](https://github.com/TheAlgorithms/Python/actions) with the help of [this script](https://github.com/TheAlgorithms/Python/blob/master/scripts/validate_solutions.py). The efficiency of your code is also checked. You can view the top 10 slowest solutions on GitHub Actions logs (under `slowest 10 durations`) and open a pull request to improve those solutions. ## Solution Guidelines Welcome to [TheAlgorithms/Python](https://github.com/TheAlgorithms/Python)! Before reading the solution guidelines, make sure you read the whole [Contributing Guidelines](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md) as it won't be repeated in here. If you have any doubt on the guidelines, please feel free to [state it clearly in an issue](https://github.com/TheAlgorithms/Python/issues/new) or ask the community in [Gitter](https://gitter.im/TheAlgorithms/community). You can use the [template](https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md#solution-template) we have provided below as your starting point but be sure to read the [Coding Style](https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md#coding-style) part first. ### Coding Style * Please maintain consistency in project directory and solution file names. Keep the following points in mind: * Create a new directory only for the problems which do not exist yet. * If you create a new directory, please create an empty `__init__.py` file inside it as well. * Please name the project **directory** as `problem_<problem_number>` where `problem_number` should be filled with 0s so as to occupy 3 digits. Example: `problem_001`, `problem_002`, `problem_067`, `problem_145`, and so on. * Please provide a link to the problem and other references, if used, in the **module-level docstring**. * All imports should come ***after*** the module-level docstring. * You can have as many helper functions as you want but there should be one main function called `solution` which should satisfy the conditions as stated below: * It should contain positional argument(s) whose default value is the question input. Example: Please take a look at [Problem 1](https://projecteuler.net/problem=1) where the question is to *Find the sum of all the multiples of 3 or 5 below 1000.* In this case the main solution function will be `solution(limit: int = 1000)`. * When the `solution` function is called without any arguments like so: `solution()`, it should return the answer to the problem. * Every function, which includes all the helper functions, if any, and the main solution function, should have `doctest` in the function docstring along with a brief statement mentioning what the function is about. * There should not be a `doctest` for testing the answer as that is done by our GitHub Actions build using this [script](https://github.com/TheAlgorithms/Python/blob/master/scripts/validate_solutions.py). Keeping in mind the above example of [Problem 1](https://projecteuler.net/problem=1): ```python def solution(limit: int = 1000): """ A brief statement mentioning what the function is about. You can have a detailed explanation about the solution method in the module-level docstring. >>> solution(1) ... >>> solution(16) ... >>> solution(100) ... """ ``` ### Solution Template You can use the below template as your starting point but please read the [Coding Style](https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md#coding-style) first to understand how the template works. Please change the name of the helper functions accordingly, change the parameter names with a descriptive one, replace the content within `[square brackets]` (including the brackets) with the appropriate content. ```python """ Project Euler Problem [problem number]: [link to the original problem] ... [Entire problem statement] ... ... [Solution explanation - Optional] ... References [Optional]: - [Wikipedia link to the topic] - [Stackoverflow link] ... """ import module1 import module2 ... def helper1(arg1: [type hint], arg2: [type hint], ...) -> [Return type hint]: """ A brief statement explaining what the function is about. ... A more elaborate description ... [Optional] ... [Doctest] ... """ ... # calculations ... return # You can have multiple helper functions but the solution function should be # after all the helper functions ... def solution(arg1: [type hint], arg2: [type hint], ...) -> [Return type hint]: """ A brief statement mentioning what the function is about. You can have a detailed explanation about the solution in the module-level docstring. ... [Doctest as mentioned above] ... """ ... # calculations ... return answer if __name__ == "__main__": print(f"{solution() = }") ```

# Project Euler Problems are taken from https://projecteuler.net/, the Project Euler. [Problems are licensed under CC BY-NC-SA 4.0](https://projecteuler.net/copyright). Project Euler is a series of challenging mathematical/computer programming problems that require more than just mathematical insights to solve. Project Euler is ideal for mathematicians who are learning to code. The solutions will be checked by our [automated testing on GitHub Actions](https://github.com/TheAlgorithms/Python/actions) with the help of [this script](https://github.com/TheAlgorithms/Python/blob/master/scripts/validate_solutions.py). The efficiency of your code is also checked. You can view the top 10 slowest solutions on GitHub Actions logs (under `slowest 10 durations`) and open a pull request to improve those solutions. ## Solution Guidelines Welcome to [TheAlgorithms/Python](https://github.com/TheAlgorithms/Python)! Before reading the solution guidelines, make sure you read the whole [Contributing Guidelines](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md) as it won't be repeated in here. If you have any doubt on the guidelines, please feel free to [state it clearly in an issue](https://github.com/TheAlgorithms/Python/issues/new) or ask the community in [Gitter](https://gitter.im/TheAlgorithms/community). You can use the [template](https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md#solution-template) we have provided below as your starting point but be sure to read the [Coding Style](https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md#coding-style) part first. ### Coding Style * Please maintain consistency in project directory and solution file names. Keep the following points in mind: * Create a new directory only for the problems which do not exist yet. * If you create a new directory, please create an empty `__init__.py` file inside it as well. * Please name the project **directory** as `problem_<problem_number>` where `problem_number` should be filled with 0s so as to occupy 3 digits. Example: `problem_001`, `problem_002`, `problem_067`, `problem_145`, and so on. * Please provide a link to the problem and other references, if used, in the **module-level docstring**. * All imports should come ***after*** the module-level docstring. * You can have as many helper functions as you want but there should be one main function called `solution` which should satisfy the conditions as stated below: * It should contain positional argument(s) whose default value is the question input. Example: Please take a look at [Problem 1](https://projecteuler.net/problem=1) where the question is to *Find the sum of all the multiples of 3 or 5 below 1000.* In this case the main solution function will be `solution(limit: int = 1000)`. * When the `solution` function is called without any arguments like so: `solution()`, it should return the answer to the problem. * Every function, which includes all the helper functions, if any, and the main solution function, should have `doctest` in the function docstring along with a brief statement mentioning what the function is about. * There should not be a `doctest` for testing the answer as that is done by our GitHub Actions build using this [script](https://github.com/TheAlgorithms/Python/blob/master/scripts/validate_solutions.py). Keeping in mind the above example of [Problem 1](https://projecteuler.net/problem=1): ```python def solution(limit: int = 1000): """ A brief statement mentioning what the function is about. You can have a detailed explanation about the solution method in the module-level docstring. >>> solution(1) ... >>> solution(16) ... >>> solution(100) ... """ ``` ### Solution Template You can use the below template as your starting point but please read the [Coding Style](https://github.com/TheAlgorithms/Python/blob/master/project_euler/README.md#coding-style) first to understand how the template works. Please change the name of the helper functions accordingly, change the parameter names with a descriptive one, replace the content within `[square brackets]` (including the brackets) with the appropriate content. ```python """ Project Euler Problem [problem number]: [link to the original problem] ... [Entire problem statement] ... ... [Solution explanation - Optional] ... References [Optional]: - [Wikipedia link to the topic] - [Stackoverflow link] ... """ import module1 import module2 ... def helper1(arg1: [type hint], arg2: [type hint], ...) -> [Return type hint]: """ A brief statement explaining what the function is about. ... A more elaborate description ... [Optional] ... [Doctest] ... """ ... # calculations ... return # You can have multiple helper functions but the solution function should be # after all the helper functions ... def solution(arg1: [type hint], arg2: [type hint], ...) -> [Return type hint]: """ A brief statement mentioning what the function is about. You can have a detailed explanation about the solution in the module-level docstring. ... [Doctest as mentioned above] ... """ ... # calculations ... return answer if __name__ == "__main__": print(f"{solution() = }") ```

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# Bit manipulation Bit manipulation is the act of manipulating bits to detect errors (hamming code), encrypts and decrypts messages (more on that in the 'ciphers' folder) or just do anything at the lowest level of your computer. * <https://en.wikipedia.org/wiki/Bit_manipulation> * <https://docs.python.org/3/reference/expressions.html#binary-bitwise-operations> * <https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations> * <https://docs.python.org/3/library/stdtypes.html#bitwise-operations-on-integer-types> * <https://wiki.python.org/moin/BitManipulation> * <https://wiki.python.org/moin/BitwiseOperators> * <https://www.tutorialspoint.com/python3/bitwise_operators_example.htm>

# Bit manipulation Bit manipulation is the act of manipulating bits to detect errors (hamming code), encrypts and decrypts messages (more on that in the 'ciphers' folder) or just do anything at the lowest level of your computer. * <https://en.wikipedia.org/wiki/Bit_manipulation> * <https://docs.python.org/3/reference/expressions.html#binary-bitwise-operations> * <https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations> * <https://docs.python.org/3/library/stdtypes.html#bitwise-operations-on-integer-types> * <https://wiki.python.org/moin/BitManipulation> * <https://wiki.python.org/moin/BitwiseOperators> * <https://www.tutorialspoint.com/python3/bitwise_operators_example.htm>

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# Linear algebra library for Python This module contains classes and functions for doing linear algebra. --- ## Overview ### class Vector - - This class represents a vector of arbitrary size and related operations. **Overview of the methods:** - constructor(components) : init the vector - set(components) : changes the vector components. - \_\_str\_\_() : toString method - component(i): gets the i-th component (0-indexed) - \_\_len\_\_() : gets the size / length of the vector (number of components) - euclidean_length() : returns the eulidean length of the vector - operator + : vector addition - operator - : vector subtraction - operator * : scalar multiplication and dot product - copy() : copies this vector and returns it - change_component(pos,value) : changes the specified component - function zero_vector(dimension) - returns a zero vector of 'dimension' - function unit_basis_vector(dimension, pos) - returns a unit basis vector with a one at index 'pos' (0-indexed) - function axpy(scalar, vector1, vector2) - computes the axpy operation - function random_vector(N, a, b) - returns a random vector of size N, with random integer components between 'a' and 'b' inclusive ### class Matrix - - This class represents a matrix of arbitrary size and operations on it. **Overview of the methods:** - \_\_str\_\_() : returns a string representation - operator * : implements the matrix vector multiplication implements the matrix-scalar multiplication. - change_component(x, y, value) : changes the specified component. - component(x, y) : returns the specified component. - width() : returns the width of the matrix - height() : returns the height of the matrix - determinant() : returns the determinant of the matrix if it is square - operator + : implements the matrix-addition. - operator - : implements the matrix-subtraction - function square_zero_matrix(N) - returns a square zero-matrix of dimension NxN - function random_matrix(W, H, a, b) - returns a random matrix WxH with integer components between 'a' and 'b' inclusive --- ## Documentation This module uses docstrings to enable the use of Python's in-built `help(...)` function. For instance, try `help(Vector)`, `help(unit_basis_vector)`, and `help(CLASSNAME.METHODNAME)`. --- ## Usage Import the module `lib.py` from the **src** directory into your project. Alternatively, you can directly use the Python bytecode file `lib.pyc`. --- ## Tests `src/tests.py` contains Python unit tests which can be run with `python3 -m unittest -v`.

# Linear algebra library for Python This module contains classes and functions for doing linear algebra. --- ## Overview ### class Vector - - This class represents a vector of arbitrary size and related operations. **Overview of the methods:** - constructor(components) : init the vector - set(components) : changes the vector components. - \_\_str\_\_() : toString method - component(i): gets the i-th component (0-indexed) - \_\_len\_\_() : gets the size / length of the vector (number of components) - euclidean_length() : returns the eulidean length of the vector - operator + : vector addition - operator - : vector subtraction - operator * : scalar multiplication and dot product - copy() : copies this vector and returns it - change_component(pos,value) : changes the specified component - function zero_vector(dimension) - returns a zero vector of 'dimension' - function unit_basis_vector(dimension, pos) - returns a unit basis vector with a one at index 'pos' (0-indexed) - function axpy(scalar, vector1, vector2) - computes the axpy operation - function random_vector(N, a, b) - returns a random vector of size N, with random integer components between 'a' and 'b' inclusive ### class Matrix - - This class represents a matrix of arbitrary size and operations on it. **Overview of the methods:** - \_\_str\_\_() : returns a string representation - operator * : implements the matrix vector multiplication implements the matrix-scalar multiplication. - change_component(x, y, value) : changes the specified component. - component(x, y) : returns the specified component. - width() : returns the width of the matrix - height() : returns the height of the matrix - determinant() : returns the determinant of the matrix if it is square - operator + : implements the matrix-addition. - operator - : implements the matrix-subtraction - function square_zero_matrix(N) - returns a square zero-matrix of dimension NxN - function random_matrix(W, H, a, b) - returns a random matrix WxH with integer components between 'a' and 'b' inclusive --- ## Documentation This module uses docstrings to enable the use of Python's in-built `help(...)` function. For instance, try `help(Vector)`, `help(unit_basis_vector)`, and `help(CLASSNAME.METHODNAME)`. --- ## Usage Import the module `lib.py` from the **src** directory into your project. Alternatively, you can directly use the Python bytecode file `lib.pyc`. --- ## Tests `src/tests.py` contains Python unit tests which can be run with `python3 -m unittest -v`.

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# Locally Weighted Linear Regression It is a non-parametric ML algorithm that does not learn on a fixed set of parameters such as **linear regression**. \ So, here comes a question of what is *linear regression*? \ **Linear regression** is a supervised learning algorithm used for computing linear relationships between input (X) and output (Y). \ ### Terminology Involved number_of_features(i) = Number of features involved. \ number_of_training_examples(m) = Number of training examples. \ output_sequence(y) = Output Sequence. \ $\theta$ $^T$ x = predicted point. \ J($\theta$) = COst function of point. The steps involved in ordinary linear regression are: Training phase: Compute \theta to minimize the cost. \ J($\theta$) = $\sum_{i=1}^m$ (($\theta$)$^T$ $x^i$ - $y^i$)$^2$ Predict output: for given query point x, \ return: ($\theta$)$^T$ x <img src="https://miro.medium.com/max/700/1*FZsLp8yTULf77qrp0Qd91g.png" alt="Linear Regression"> This training phase is possible when data points are linear, but there again comes a question can we predict non-linear relationship between x and y ? as shown below <img src="https://miro.medium.com/max/700/1*DHYvJg55uN-Kj8jHaxDKvQ.png" alt="Non-linear Data"> <br /> <br /> So, here comes the role of non-parametric algorithm which doesn't compute predictions based on fixed set of params. Rather parameters $\theta$ are computed individually for each query point/data point x. <br /> <br /> While Computing $\theta$ , a higher preference is given to points in the vicinity of x than points farther from x. Cost Function J($\theta$) = $\sum_{i=1}^m$ $w^i$ (($\theta$)$^T$ $x^i$ - $y^i$)$^2$ $w^i$ is non-negative weight associated to training point $x^i$. \ $w^i$ is large fr $x^i$'s lying closer to query point $x_i$. \ $w^i$ is small for $x^i$'s lying farther to query point $x_i$. A Typical weight can be computed using \ $w^i$ = $\exp$(-$\frac{(x^i-x)(x^i-x)^T}{2\tau^2}$) Where $\tau$ is the bandwidth parameter that controls $w^i$ distance from x. Let's look at a example : Suppose, we had a query point x=5.0 and training points $x^1$=4.9 and $x^2$=5.0 than we can calculate weights as : $w^i$ = $\exp$(-$\frac{(x^i-x)(x^i-x)^T}{2\tau^2}$) with $\tau$=0.5 $w^1$ = $\exp$(-$\frac{(4.9-5)^2}{2(0.5)^2}$) = 0.9802 $w^2$ = $\exp$(-$\frac{(3-5)^2}{2(0.5)^2}$) = 0.000335 So, J($\theta$) = 0.9802*($\theta$ $^T$ $x^1$ - $y^1$) + 0.000335*($\theta$ $^T$ $x^2$ - $y^2$) So, here by we can conclude that the weight fall exponentially as the distance between x & $x^i$ increases and So, does the contribution of error in prediction for $x^i$ to the cost. Steps involved in LWL are : \ Compute \theta to minimize the cost. J($\theta$) = $\sum_{i=1}^m$ $w^i$ (($\theta$)$^T$ $x^i$ - $y^i$)$^2$ \ Predict Output: for given query point x, \ return : $\theta$ $^T$ x <img src="https://miro.medium.com/max/700/1*H3QS05Q1GJtY-tiBL00iug.png" alt="LWL">

# Locally Weighted Linear Regression It is a non-parametric ML algorithm that does not learn on a fixed set of parameters such as **linear regression**. \ So, here comes a question of what is *linear regression*? \ **Linear regression** is a supervised learning algorithm used for computing linear relationships between input (X) and output (Y). \ ### Terminology Involved number_of_features(i) = Number of features involved. \ number_of_training_examples(m) = Number of training examples. \ output_sequence(y) = Output Sequence. \ $\theta$ $^T$ x = predicted point. \ J($\theta$) = COst function of point. The steps involved in ordinary linear regression are: Training phase: Compute \theta to minimize the cost. \ J($\theta$) = $\sum_{i=1}^m$ (($\theta$)$^T$ $x^i$ - $y^i$)$^2$ Predict output: for given query point x, \ return: ($\theta$)$^T$ x <img src="https://miro.medium.com/max/700/1*FZsLp8yTULf77qrp0Qd91g.png" alt="Linear Regression"> This training phase is possible when data points are linear, but there again comes a question can we predict non-linear relationship between x and y ? as shown below <img src="https://miro.medium.com/max/700/1*DHYvJg55uN-Kj8jHaxDKvQ.png" alt="Non-linear Data"> <br /> <br /> So, here comes the role of non-parametric algorithm which doesn't compute predictions based on fixed set of params. Rather parameters $\theta$ are computed individually for each query point/data point x. <br /> <br /> While Computing $\theta$ , a higher preference is given to points in the vicinity of x than points farther from x. Cost Function J($\theta$) = $\sum_{i=1}^m$ $w^i$ (($\theta$)$^T$ $x^i$ - $y^i$)$^2$ $w^i$ is non-negative weight associated to training point $x^i$. \ $w^i$ is large fr $x^i$'s lying closer to query point $x_i$. \ $w^i$ is small for $x^i$'s lying farther to query point $x_i$. A Typical weight can be computed using \ $w^i$ = $\exp$(-$\frac{(x^i-x)(x^i-x)^T}{2\tau^2}$) Where $\tau$ is the bandwidth parameter that controls $w^i$ distance from x. Let's look at a example : Suppose, we had a query point x=5.0 and training points $x^1$=4.9 and $x^2$=5.0 than we can calculate weights as : $w^i$ = $\exp$(-$\frac{(x^i-x)(x^i-x)^T}{2\tau^2}$) with $\tau$=0.5 $w^1$ = $\exp$(-$\frac{(4.9-5)^2}{2(0.5)^2}$) = 0.9802 $w^2$ = $\exp$(-$\frac{(3-5)^2}{2(0.5)^2}$) = 0.000335 So, J($\theta$) = 0.9802*($\theta$ $^T$ $x^1$ - $y^1$) + 0.000335*($\theta$ $^T$ $x^2$ - $y^2$) So, here by we can conclude that the weight fall exponentially as the distance between x & $x^i$ increases and So, does the contribution of error in prediction for $x^i$ to the cost. Steps involved in LWL are : \ Compute \theta to minimize the cost. J($\theta$) = $\sum_{i=1}^m$ $w^i$ (($\theta$)$^T$ $x^i$ - $y^i$)$^2$ \ Predict Output: for given query point x, \ return : $\theta$ $^T$ x <img src="https://miro.medium.com/max/700/1*H3QS05Q1GJtY-tiBL00iug.png" alt="LWL">

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# Computer Vision Computer vision is a field of computer science that works on enabling computers to see, identify and process images in the same way that human does, and provide appropriate output. It is like imparting human intelligence and instincts to a computer. Image processing and computer vision are a little different from each other. Image processing means applying some algorithms for transforming image from one form to the other like smoothing, contrasting, stretching, etc. While computer vision comes from modelling image processing using the techniques of machine learning, computer vision applies machine learning to recognize patterns for interpretation of images (much like the process of visual reasoning of human vision). * <https://en.wikipedia.org/wiki/Computer_vision> * <https://www.algorithmia.com/blog/introduction-to-computer-vision>

# Computer Vision Computer vision is a field of computer science that works on enabling computers to see, identify and process images in the same way that human does, and provide appropriate output. It is like imparting human intelligence and instincts to a computer. Image processing and computer vision are a little different from each other. Image processing means applying some algorithms for transforming image from one form to the other like smoothing, contrasting, stretching, etc. While computer vision comes from modelling image processing using the techniques of machine learning, computer vision applies machine learning to recognize patterns for interpretation of images (much like the process of visual reasoning of human vision). * <https://en.wikipedia.org/wiki/Computer_vision> * <https://www.algorithmia.com/blog/introduction-to-computer-vision>

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""" Project Euler Problem 493: https://projecteuler.net/problem=493 70 coloured balls are placed in an urn, 10 for each of the seven rainbow colours. What is the expected number of distinct colours in 20 randomly picked balls? Give your answer with nine digits after the decimal point (a.bcdefghij). ----- This combinatorial problem can be solved by decomposing the problem into the following steps: 1. Calculate the total number of possible picking combinations [combinations := binom_coeff(70, 20)] 2. Calculate the number of combinations with one colour missing [missing := binom_coeff(60, 20)] 3. Calculate the probability of one colour missing [missing_prob := missing / combinations] 4. Calculate the probability of no colour missing [no_missing_prob := 1 - missing_prob] 5. Calculate the expected number of distinct colours [expected = 7 * no_missing_prob] References: - https://en.wikipedia.org/wiki/Binomial_coefficient """ import math BALLS_PER_COLOUR = 10 NUM_COLOURS = 7 NUM_BALLS = BALLS_PER_COLOUR * NUM_COLOURS def solution(num_picks: int = 20) -> str: """ Calculates the expected number of distinct colours >>> solution(10) '5.669644129' >>> solution(30) '6.985042712' """ total = math.comb(NUM_BALLS, num_picks) missing_colour = math.comb(NUM_BALLS - BALLS_PER_COLOUR, num_picks) result = NUM_COLOURS * (1 - missing_colour / total) return f"{result:.9f}" if __name__ == "__main__": print(solution(20))

""" Project Euler Problem 493: https://projecteuler.net/problem=493 70 coloured balls are placed in an urn, 10 for each of the seven rainbow colours. What is the expected number of distinct colours in 20 randomly picked balls? Give your answer with nine digits after the decimal point (a.bcdefghij). ----- This combinatorial problem can be solved by decomposing the problem into the following steps: 1. Calculate the total number of possible picking combinations [combinations := binom_coeff(70, 20)] 2. Calculate the number of combinations with one colour missing [missing := binom_coeff(60, 20)] 3. Calculate the probability of one colour missing [missing_prob := missing / combinations] 4. Calculate the probability of no colour missing [no_missing_prob := 1 - missing_prob] 5. Calculate the expected number of distinct colours [expected = 7 * no_missing_prob] References: - https://en.wikipedia.org/wiki/Binomial_coefficient """ import math BALLS_PER_COLOUR = 10 NUM_COLOURS = 7 NUM_BALLS = BALLS_PER_COLOUR * NUM_COLOURS def solution(num_picks: int = 20) -> str: """ Calculates the expected number of distinct colours >>> solution(10) '5.669644129' >>> solution(30) '6.985042712' """ total = math.comb(NUM_BALLS, num_picks) missing_colour = math.comb(NUM_BALLS - BALLS_PER_COLOUR, num_picks) result = NUM_COLOURS * (1 - missing_colour / total) return f"{result:.9f}" if __name__ == "__main__": print(solution(20))

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""" https://en.wikipedia.org/wiki/Floor_and_ceiling_functions """ def floor(x: float) -> int: """ Return the floor of x as an Integral. :param x: the number :return: the largest integer <= x. >>> import math >>> all(floor(n) == math.floor(n) for n ... in (1, -1, 0, -0, 1.1, -1.1, 1.0, -1.0, 1_000_000_000)) True """ return int(x) if x - int(x) >= 0 else int(x) - 1 if __name__ == "__main__": import doctest doctest.testmod()

""" https://en.wikipedia.org/wiki/Floor_and_ceiling_functions """ def floor(x: float) -> int: """ Return the floor of x as an Integral. :param x: the number :return: the largest integer <= x. >>> import math >>> all(floor(n) == math.floor(n) for n ... in (1, -1, 0, -0, 1.1, -1.1, 1.0, -1.0, 1_000_000_000)) True """ return int(x) if x - int(x) >= 0 else int(x) - 1 if __name__ == "__main__": import doctest doctest.testmod()

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def search(list_data: list, key: int, left: int = 0, right: int = 0) -> int: """ Iterate through the array to find the index of key using recursion. :param list_data: the list to be searched :param key: the key to be searched :param left: the index of first element :param right: the index of last element :return: the index of key value if found, -1 otherwise. >>> search(list(range(0, 11)), 5) 5 >>> search([1, 2, 4, 5, 3], 4) 2 >>> search([1, 2, 4, 5, 3], 6) -1 >>> search([5], 5) 0 >>> search([], 1) -1 """ right = right or len(list_data) - 1 if left > right: return -1 elif list_data[left] == key: return left elif list_data[right] == key: return right else: return search(list_data, key, left + 1, right - 1) if __name__ == "__main__": import doctest doctest.testmod()

def search(list_data: list, key: int, left: int = 0, right: int = 0) -> int: """ Iterate through the array to find the index of key using recursion. :param list_data: the list to be searched :param key: the key to be searched :param left: the index of first element :param right: the index of last element :return: the index of key value if found, -1 otherwise. >>> search(list(range(0, 11)), 5) 5 >>> search([1, 2, 4, 5, 3], 4) 2 >>> search([1, 2, 4, 5, 3], 6) -1 >>> search([5], 5) 0 >>> search([], 1) -1 """ right = right or len(list_data) - 1 if left > right: return -1 elif list_data[left] == key: return left elif list_data[right] == key: return right else: return search(list_data, key, left + 1, right - 1) if __name__ == "__main__": import doctest doctest.testmod()

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def decimal_to_fraction(decimal: float | str) -> tuple[int, int]: """ Return a decimal number in its simplest fraction form >>> decimal_to_fraction(2) (2, 1) >>> decimal_to_fraction(89.) (89, 1) >>> decimal_to_fraction("67") (67, 1) >>> decimal_to_fraction("45.0") (45, 1) >>> decimal_to_fraction(1.5) (3, 2) >>> decimal_to_fraction("6.25") (25, 4) >>> decimal_to_fraction("78td") Traceback (most recent call last): ValueError: Please enter a valid number """ try: decimal = float(decimal) except ValueError: raise ValueError("Please enter a valid number") fractional_part = decimal - int(decimal) if fractional_part == 0: return int(decimal), 1 else: number_of_frac_digits = len(str(decimal).split(".")[1]) numerator = int(decimal * (10**number_of_frac_digits)) denominator = 10**number_of_frac_digits divisor, dividend = denominator, numerator while True: remainder = dividend % divisor if remainder == 0: break dividend, divisor = divisor, remainder numerator, denominator = numerator / divisor, denominator / divisor return int(numerator), int(denominator) if __name__ == "__main__": print(f"{decimal_to_fraction(2) = }") print(f"{decimal_to_fraction(89.0) = }") print(f"{decimal_to_fraction('67') = }") print(f"{decimal_to_fraction('45.0') = }") print(f"{decimal_to_fraction(1.5) = }") print(f"{decimal_to_fraction('6.25') = }") print(f"{decimal_to_fraction('78td') = }")

def decimal_to_fraction(decimal: float | str) -> tuple[int, int]: """ Return a decimal number in its simplest fraction form >>> decimal_to_fraction(2) (2, 1) >>> decimal_to_fraction(89.) (89, 1) >>> decimal_to_fraction("67") (67, 1) >>> decimal_to_fraction("45.0") (45, 1) >>> decimal_to_fraction(1.5) (3, 2) >>> decimal_to_fraction("6.25") (25, 4) >>> decimal_to_fraction("78td") Traceback (most recent call last): ValueError: Please enter a valid number """ try: decimal = float(decimal) except ValueError: raise ValueError("Please enter a valid number") fractional_part = decimal - int(decimal) if fractional_part == 0: return int(decimal), 1 else: number_of_frac_digits = len(str(decimal).split(".")[1]) numerator = int(decimal * (10**number_of_frac_digits)) denominator = 10**number_of_frac_digits divisor, dividend = denominator, numerator while True: remainder = dividend % divisor if remainder == 0: break dividend, divisor = divisor, remainder numerator, denominator = numerator / divisor, denominator / divisor return int(numerator), int(denominator) if __name__ == "__main__": print(f"{decimal_to_fraction(2) = }") print(f"{decimal_to_fraction(89.0) = }") print(f"{decimal_to_fraction('67') = }") print(f"{decimal_to_fraction('45.0') = }") print(f"{decimal_to_fraction(1.5) = }") print(f"{decimal_to_fraction('6.25') = }") print(f"{decimal_to_fraction('78td') = }")

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""" This script demonstrates the implementation of the Softmax function. Its a function that takes as input a vector of K real numbers, and normalizes it into a probability distribution consisting of K probabilities proportional to the exponentials of the input numbers. After softmax, the elements of the vector always sum up to 1. Script inspired from its corresponding Wikipedia article https://en.wikipedia.org/wiki/Softmax_function """ import numpy as np def softmax(vector): """ Implements the softmax function Parameters: vector (np.array,list,tuple): A numpy array of shape (1,n) consisting of real values or a similar list,tuple Returns: softmax_vec (np.array): The input numpy array after applying softmax. The softmax vector adds up to one. We need to ceil to mitigate for precision >>> np.ceil(np.sum(softmax([1,2,3,4]))) 1.0 >>> vec = np.array([5,5]) >>> softmax(vec) array([0.5, 0.5]) >>> softmax([0]) array([1.]) """ # Calculate e^x for each x in your vector where e is Euler's # number (approximately 2.718) exponent_vector = np.exp(vector) # Add up the all the exponentials sum_of_exponents = np.sum(exponent_vector) # Divide every exponent by the sum of all exponents softmax_vector = exponent_vector / sum_of_exponents return softmax_vector if __name__ == "__main__": print(softmax((0,)))

""" This script demonstrates the implementation of the Softmax function. Its a function that takes as input a vector of K real numbers, and normalizes it into a probability distribution consisting of K probabilities proportional to the exponentials of the input numbers. After softmax, the elements of the vector always sum up to 1. Script inspired from its corresponding Wikipedia article https://en.wikipedia.org/wiki/Softmax_function """ import numpy as np def softmax(vector): """ Implements the softmax function Parameters: vector (np.array,list,tuple): A numpy array of shape (1,n) consisting of real values or a similar list,tuple Returns: softmax_vec (np.array): The input numpy array after applying softmax. The softmax vector adds up to one. We need to ceil to mitigate for precision >>> np.ceil(np.sum(softmax([1,2,3,4]))) 1.0 >>> vec = np.array([5,5]) >>> softmax(vec) array([0.5, 0.5]) >>> softmax([0]) array([1.]) """ # Calculate e^x for each x in your vector where e is Euler's # number (approximately 2.718) exponent_vector = np.exp(vector) # Add up the all the exponentials sum_of_exponents = np.sum(exponent_vector) # Divide every exponent by the sum of all exponents softmax_vector = exponent_vector / sum_of_exponents return softmax_vector if __name__ == "__main__": print(softmax((0,)))

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# Numbers of alphabet which we call base alphabet_size = 256 # Modulus to hash a string modulus = 1000003 def rabin_karp(pattern: str, text: str) -> bool: """ The Rabin-Karp Algorithm for finding a pattern within a piece of text with complexity O(nm), most efficient when it is used with multiple patterns as it is able to check if any of a set of patterns match a section of text in o(1) given the precomputed hashes. This will be the simple version which only assumes one pattern is being searched for but it's not hard to modify 1) Calculate pattern hash 2) Step through the text one character at a time passing a window with the same length as the pattern calculating the hash of the text within the window compare it with the hash of the pattern. Only testing equality if the hashes match """ p_len = len(pattern) t_len = len(text) if p_len > t_len: return False p_hash = 0 text_hash = 0 modulus_power = 1 # Calculating the hash of pattern and substring of text for i in range(p_len): p_hash = (ord(pattern[i]) + p_hash * alphabet_size) % modulus text_hash = (ord(text[i]) + text_hash * alphabet_size) % modulus if i == p_len - 1: continue modulus_power = (modulus_power * alphabet_size) % modulus for i in range(t_len - p_len + 1): if text_hash == p_hash and text[i : i + p_len] == pattern: return True if i == t_len - p_len: continue # Calculate the https://en.wikipedia.org/wiki/Rolling_hash text_hash = ( (text_hash - ord(text[i]) * modulus_power) * alphabet_size + ord(text[i + p_len]) ) % modulus return False def test_rabin_karp() -> None: """ >>> test_rabin_karp() Success. """ # Test 1) pattern = "abc1abc12" text1 = "alskfjaldsabc1abc1abc12k23adsfabcabc" text2 = "alskfjaldsk23adsfabcabc" assert rabin_karp(pattern, text1) assert not rabin_karp(pattern, text2) # Test 2) pattern = "ABABX" text = "ABABZABABYABABX" assert rabin_karp(pattern, text) # Test 3) pattern = "AAAB" text = "ABAAAAAB" assert rabin_karp(pattern, text) # Test 4) pattern = "abcdabcy" text = "abcxabcdabxabcdabcdabcy" assert rabin_karp(pattern, text) # Test 5) pattern = "Lü" text = "Lüsai" assert rabin_karp(pattern, text) pattern = "Lue" assert not rabin_karp(pattern, text) print("Success.") if __name__ == "__main__": test_rabin_karp()

# Numbers of alphabet which we call base alphabet_size = 256 # Modulus to hash a string modulus = 1000003 def rabin_karp(pattern: str, text: str) -> bool: """ The Rabin-Karp Algorithm for finding a pattern within a piece of text with complexity O(nm), most efficient when it is used with multiple patterns as it is able to check if any of a set of patterns match a section of text in o(1) given the precomputed hashes. This will be the simple version which only assumes one pattern is being searched for but it's not hard to modify 1) Calculate pattern hash 2) Step through the text one character at a time passing a window with the same length as the pattern calculating the hash of the text within the window compare it with the hash of the pattern. Only testing equality if the hashes match """ p_len = len(pattern) t_len = len(text) if p_len > t_len: return False p_hash = 0 text_hash = 0 modulus_power = 1 # Calculating the hash of pattern and substring of text for i in range(p_len): p_hash = (ord(pattern[i]) + p_hash * alphabet_size) % modulus text_hash = (ord(text[i]) + text_hash * alphabet_size) % modulus if i == p_len - 1: continue modulus_power = (modulus_power * alphabet_size) % modulus for i in range(t_len - p_len + 1): if text_hash == p_hash and text[i : i + p_len] == pattern: return True if i == t_len - p_len: continue # Calculate the https://en.wikipedia.org/wiki/Rolling_hash text_hash = ( (text_hash - ord(text[i]) * modulus_power) * alphabet_size + ord(text[i + p_len]) ) % modulus return False def test_rabin_karp() -> None: """ >>> test_rabin_karp() Success. """ # Test 1) pattern = "abc1abc12" text1 = "alskfjaldsabc1abc1abc12k23adsfabcabc" text2 = "alskfjaldsk23adsfabcabc" assert rabin_karp(pattern, text1) assert not rabin_karp(pattern, text2) # Test 2) pattern = "ABABX" text = "ABABZABABYABABX" assert rabin_karp(pattern, text) # Test 3) pattern = "AAAB" text = "ABAAAAAB" assert rabin_karp(pattern, text) # Test 4) pattern = "abcdabcy" text = "abcxabcdabxabcdabcdabcy" assert rabin_karp(pattern, text) # Test 5) pattern = "Lü" text = "Lüsai" assert rabin_karp(pattern, text) pattern = "Lue" assert not rabin_karp(pattern, text) print("Success.") if __name__ == "__main__": test_rabin_karp()

TheAlgorithms/Python

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""" The Fletcher checksum is an algorithm for computing a position-dependent checksum devised by John G. Fletcher (1934–2012) at Lawrence Livermore Labs in the late 1970s.[1] The objective of the Fletcher checksum was to provide error-detection properties approaching those of a cyclic redundancy check but with the lower computational effort associated with summation techniques. Source: https://en.wikipedia.org/wiki/Fletcher%27s_checksum """ def fletcher16(text: str) -> int: """ Loop through every character in the data and add to two sums. >>> fletcher16('hello world') 6752 >>> fletcher16('onethousandfourhundredthirtyfour') 28347 >>> fletcher16('The quick brown fox jumps over the lazy dog.') 5655 """ data = bytes(text, "ascii") sum1 = 0 sum2 = 0 for character in data: sum1 = (sum1 + character) % 255 sum2 = (sum1 + sum2) % 255 return (sum2 << 8) | sum1 if __name__ == "__main__": import doctest doctest.testmod()

""" The Fletcher checksum is an algorithm for computing a position-dependent checksum devised by John G. Fletcher (1934–2012) at Lawrence Livermore Labs in the late 1970s.[1] The objective of the Fletcher checksum was to provide error-detection properties approaching those of a cyclic redundancy check but with the lower computational effort associated with summation techniques. Source: https://en.wikipedia.org/wiki/Fletcher%27s_checksum """ def fletcher16(text: str) -> int: """ Loop through every character in the data and add to two sums. >>> fletcher16('hello world') 6752 >>> fletcher16('onethousandfourhundredthirtyfour') 28347 >>> fletcher16('The quick brown fox jumps over the lazy dog.') 5655 """ data = bytes(text, "ascii") sum1 = 0 sum2 = 0 for character in data: sum1 = (sum1 + character) % 255 sum2 = (sum1 + sum2) % 255 return (sum2 << 8) | sum1 if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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# https://en.wikipedia.org/wiki/Continuous_knapsack_problem # https://www.guru99.com/fractional-knapsack-problem-greedy.html # https://medium.com/walkinthecode/greedy-algorithm-fractional-knapsack-problem-9aba1daecc93 from __future__ import annotations def fractional_knapsack( value: list[int], weight: list[int], capacity: int ) -> tuple[float, list[float]]: """ >>> value = [1, 3, 5, 7, 9] >>> weight = [0.9, 0.7, 0.5, 0.3, 0.1] >>> fractional_knapsack(value, weight, 5) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, 15) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, 25) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, 26) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, -1) (-90.0, [0, 0, 0, 0, -10.0]) >>> fractional_knapsack([1, 3, 5, 7], weight, 30) (16, [1, 1, 1, 1]) >>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack([], [], 30) (0, []) """ index = list(range(len(value))) ratio = [v / w for v, w in zip(value, weight)] index.sort(key=lambda i: ratio[i], reverse=True) max_value: float = 0 fractions: list[float] = [0] * len(value) for i in index: if weight[i] <= capacity: fractions[i] = 1 max_value += value[i] capacity -= weight[i] else: fractions[i] = capacity / weight[i] max_value += value[i] * capacity / weight[i] break return max_value, fractions if __name__ == "__main__": import doctest doctest.testmod()

# https://en.wikipedia.org/wiki/Continuous_knapsack_problem # https://www.guru99.com/fractional-knapsack-problem-greedy.html # https://medium.com/walkinthecode/greedy-algorithm-fractional-knapsack-problem-9aba1daecc93 from __future__ import annotations def fractional_knapsack( value: list[int], weight: list[int], capacity: int ) -> tuple[float, list[float]]: """ >>> value = [1, 3, 5, 7, 9] >>> weight = [0.9, 0.7, 0.5, 0.3, 0.1] >>> fractional_knapsack(value, weight, 5) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, 15) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, 25) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, 26) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack(value, weight, -1) (-90.0, [0, 0, 0, 0, -10.0]) >>> fractional_knapsack([1, 3, 5, 7], weight, 30) (16, [1, 1, 1, 1]) >>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30) (25, [1, 1, 1, 1, 1]) >>> fractional_knapsack([], [], 30) (0, []) """ index = list(range(len(value))) ratio = [v / w for v, w in zip(value, weight)] index.sort(key=lambda i: ratio[i], reverse=True) max_value: float = 0 fractions: list[float] = [0] * len(value) for i in index: if weight[i] <= capacity: fractions[i] = 1 max_value += value[i] capacity -= weight[i] else: fractions[i] = capacity / weight[i] max_value += value[i] * capacity / weight[i] break return max_value, fractions if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

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""" Ford-Fulkerson Algorithm for Maximum Flow Problem * https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm Description: (1) Start with initial flow as 0 (2) Choose the augmenting path from source to sink and add the path to flow """ graph = [ [0, 16, 13, 0, 0, 0], [0, 0, 10, 12, 0, 0], [0, 4, 0, 0, 14, 0], [0, 0, 9, 0, 0, 20], [0, 0, 0, 7, 0, 4], [0, 0, 0, 0, 0, 0], ] def breadth_first_search(graph: list, source: int, sink: int, parents: list) -> bool: """ This function returns True if there is a node that has not iterated. Args: graph: Adjacency matrix of graph source: Source sink: Sink parents: Parent list Returns: True if there is a node that has not iterated. >>> breadth_first_search(graph, 0, 5, [-1, -1, -1, -1, -1, -1]) True >>> breadth_first_search(graph, 0, 6, [-1, -1, -1, -1, -1, -1]) Traceback (most recent call last): ... IndexError: list index out of range """ visited = [False] * len(graph) # Mark all nodes as not visited queue = [] # breadth-first search queue # Source node queue.append(source) visited[source] = True while queue: u = queue.pop(0) # Pop the front node # Traverse all adjacent nodes of u for ind, node in enumerate(graph[u]): if visited[ind] is False and node > 0: queue.append(ind) visited[ind] = True parents[ind] = u return visited[sink] def ford_fulkerson(graph: list, source: int, sink: int) -> int: """ This function returns the maximum flow from source to sink in the given graph. CAUTION: This function changes the given graph. Args: graph: Adjacency matrix of graph source: Source sink: Sink Returns: Maximum flow >>> test_graph = [ ... [0, 16, 13, 0, 0, 0], ... [0, 0, 10, 12, 0, 0], ... [0, 4, 0, 0, 14, 0], ... [0, 0, 9, 0, 0, 20], ... [0, 0, 0, 7, 0, 4], ... [0, 0, 0, 0, 0, 0], ... ] >>> ford_fulkerson(test_graph, 0, 5) 23 """ # This array is filled by breadth-first search and to store path parent = [-1] * (len(graph)) max_flow = 0 # While there is a path from source to sink while breadth_first_search(graph, source, sink, parent): path_flow = int(1e9) # Infinite value s = sink while s != source: # Find the minimum value in the selected path path_flow = min(path_flow, graph[parent[s]][s]) s = parent[s] max_flow += path_flow v = sink while v != source: u = parent[v] graph[u][v] -= path_flow graph[v][u] += path_flow v = parent[v] return max_flow if __name__ == "__main__": from doctest import testmod testmod() print(f"{ford_fulkerson(graph, source=0, sink=5) = }")

""" Ford-Fulkerson Algorithm for Maximum Flow Problem * https://en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm Description: (1) Start with initial flow as 0 (2) Choose the augmenting path from source to sink and add the path to flow """ graph = [ [0, 16, 13, 0, 0, 0], [0, 0, 10, 12, 0, 0], [0, 4, 0, 0, 14, 0], [0, 0, 9, 0, 0, 20], [0, 0, 0, 7, 0, 4], [0, 0, 0, 0, 0, 0], ] def breadth_first_search(graph: list, source: int, sink: int, parents: list) -> bool: """ This function returns True if there is a node that has not iterated. Args: graph: Adjacency matrix of graph source: Source sink: Sink parents: Parent list Returns: True if there is a node that has not iterated. >>> breadth_first_search(graph, 0, 5, [-1, -1, -1, -1, -1, -1]) True >>> breadth_first_search(graph, 0, 6, [-1, -1, -1, -1, -1, -1]) Traceback (most recent call last): ... IndexError: list index out of range """ visited = [False] * len(graph) # Mark all nodes as not visited queue = [] # breadth-first search queue # Source node queue.append(source) visited[source] = True while queue: u = queue.pop(0) # Pop the front node # Traverse all adjacent nodes of u for ind, node in enumerate(graph[u]): if visited[ind] is False and node > 0: queue.append(ind) visited[ind] = True parents[ind] = u return visited[sink] def ford_fulkerson(graph: list, source: int, sink: int) -> int: """ This function returns the maximum flow from source to sink in the given graph. CAUTION: This function changes the given graph. Args: graph: Adjacency matrix of graph source: Source sink: Sink Returns: Maximum flow >>> test_graph = [ ... [0, 16, 13, 0, 0, 0], ... [0, 0, 10, 12, 0, 0], ... [0, 4, 0, 0, 14, 0], ... [0, 0, 9, 0, 0, 20], ... [0, 0, 0, 7, 0, 4], ... [0, 0, 0, 0, 0, 0], ... ] >>> ford_fulkerson(test_graph, 0, 5) 23 """ # This array is filled by breadth-first search and to store path parent = [-1] * (len(graph)) max_flow = 0 # While there is a path from source to sink while breadth_first_search(graph, source, sink, parent): path_flow = int(1e9) # Infinite value s = sink while s != source: # Find the minimum value in the selected path path_flow = min(path_flow, graph[parent[s]][s]) s = parent[s] max_flow += path_flow v = sink while v != source: u = parent[v] graph[u][v] -= path_flow graph[v][u] += path_flow v = parent[v] return max_flow if __name__ == "__main__": from doctest import testmod testmod() print(f"{ford_fulkerson(graph, source=0, sink=5) = }")

TheAlgorithms/Python

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""" Ordered fractions Problem 71 https://projecteuler.net/problem=71 Consider the fraction n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8 It can be seen that 2/5 is the fraction immediately to the left of 3/7. By listing the set of reduced proper fractions for d ≤ 1,000,000 in ascending order of size, find the numerator of the fraction immediately to the left of 3/7. """ def solution(numerator: int = 3, denominator: int = 7, limit: int = 1000000) -> int: """ Returns the closest numerator of the fraction immediately to the left of given fraction (numerator/denominator) from a list of reduced proper fractions. >>> solution() 428570 >>> solution(3, 7, 8) 2 >>> solution(6, 7, 60) 47 """ max_numerator = 0 max_denominator = 1 for current_denominator in range(1, limit + 1): current_numerator = current_denominator * numerator // denominator if current_denominator % denominator == 0: current_numerator -= 1 if current_numerator * max_denominator > current_denominator * max_numerator: max_numerator = current_numerator max_denominator = current_denominator return max_numerator if __name__ == "__main__": print(solution(numerator=3, denominator=7, limit=1000000))

""" Ordered fractions Problem 71 https://projecteuler.net/problem=71 Consider the fraction n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction. If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get: 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8 It can be seen that 2/5 is the fraction immediately to the left of 3/7. By listing the set of reduced proper fractions for d ≤ 1,000,000 in ascending order of size, find the numerator of the fraction immediately to the left of 3/7. """ def solution(numerator: int = 3, denominator: int = 7, limit: int = 1000000) -> int: """ Returns the closest numerator of the fraction immediately to the left of given fraction (numerator/denominator) from a list of reduced proper fractions. >>> solution() 428570 >>> solution(3, 7, 8) 2 >>> solution(6, 7, 60) 47 """ max_numerator = 0 max_denominator = 1 for current_denominator in range(1, limit + 1): current_numerator = current_denominator * numerator // denominator if current_denominator % denominator == 0: current_numerator -= 1 if current_numerator * max_denominator > current_denominator * max_numerator: max_numerator = current_numerator max_denominator = current_denominator return max_numerator if __name__ == "__main__": print(solution(numerator=3, denominator=7, limit=1000000))

TheAlgorithms/Python

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""" Project Euler Problem 206: https://projecteuler.net/problem=206 Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0, where each “_” is a single digit. ----- Instead of computing every single permutation of that number and going through a 10^9 search space, we can narrow it down considerably. If the square ends in a 0, then the square root must also end in a 0. Thus, the last missing digit must be 0 and the square root is a multiple of 10. We can narrow the search space down to the first 8 digits and multiply the result of that by 10 at the end. Now the last digit is a 9, which can only happen if the square root ends in a 3 or 7. From this point, we can try one of two different methods to find the answer: 1. Start at the lowest possible base number whose square would be in the format, and count up. The base we would start at is 101010103, whose square is the closest number to 10203040506070809. Alternate counting up by 4 and 6 so the last digit of the base is always a 3 or 7. 2. Start at the highest possible base number whose square would be in the format, and count down. That base would be 138902663, whose square is the closest number to 1929394959697989. Alternate counting down by 6 and 4 so the last digit of the base is always a 3 or 7. The solution does option 2 because the answer happens to be much closer to the starting point. """ def is_square_form(num: int) -> bool: """ Determines if num is in the form 1_2_3_4_5_6_7_8_9 >>> is_square_form(1) False >>> is_square_form(112233445566778899) True >>> is_square_form(123456789012345678) False """ digit = 9 while num > 0: if num % 10 != digit: return False num //= 100 digit -= 1 return True def solution() -> int: """ Returns the first integer whose square is of the form 1_2_3_4_5_6_7_8_9_0 """ num = 138902663 while not is_square_form(num * num): if num % 10 == 3: num -= 6 # (3 - 6) % 10 = 7 else: num -= 4 # (7 - 4) % 10 = 3 return num * 10 if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 206: https://projecteuler.net/problem=206 Find the unique positive integer whose square has the form 1_2_3_4_5_6_7_8_9_0, where each “_” is a single digit. ----- Instead of computing every single permutation of that number and going through a 10^9 search space, we can narrow it down considerably. If the square ends in a 0, then the square root must also end in a 0. Thus, the last missing digit must be 0 and the square root is a multiple of 10. We can narrow the search space down to the first 8 digits and multiply the result of that by 10 at the end. Now the last digit is a 9, which can only happen if the square root ends in a 3 or 7. From this point, we can try one of two different methods to find the answer: 1. Start at the lowest possible base number whose square would be in the format, and count up. The base we would start at is 101010103, whose square is the closest number to 10203040506070809. Alternate counting up by 4 and 6 so the last digit of the base is always a 3 or 7. 2. Start at the highest possible base number whose square would be in the format, and count down. That base would be 138902663, whose square is the closest number to 1929394959697989. Alternate counting down by 6 and 4 so the last digit of the base is always a 3 or 7. The solution does option 2 because the answer happens to be much closer to the starting point. """ def is_square_form(num: int) -> bool: """ Determines if num is in the form 1_2_3_4_5_6_7_8_9 >>> is_square_form(1) False >>> is_square_form(112233445566778899) True >>> is_square_form(123456789012345678) False """ digit = 9 while num > 0: if num % 10 != digit: return False num //= 100 digit -= 1 return True def solution() -> int: """ Returns the first integer whose square is of the form 1_2_3_4_5_6_7_8_9_0 """ num = 138902663 while not is_square_form(num * num): if num % 10 == 3: num -= 6 # (3 - 6) % 10 = 7 else: num -= 4 # (7 - 4) % 10 = 3 return num * 10 if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

[pre-commit.ci] pre-commit autoupdate

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pre-commit-ci[bot]

12e401650c8afd4b6cf69ddab09a882d1eb6ff5c

a13e9c21374caf40652ee75cc3620f3ac0c72ff3

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""" Totient maximum Problem 69: https://projecteuler.net/problem=69 Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6. n Relatively Prime φ(n) n/φ(n) 2 1 1 2 3 1,2 2 1.5 4 1,3 2 2 5 1,2,3,4 4 1.25 6 1,5 2 3 7 1,2,3,4,5,6 6 1.1666... 8 1,3,5,7 4 2 9 1,2,4,5,7,8 6 1.5 10 1,3,7,9 4 2.5 It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10. Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum. """ def solution(n: int = 10**6) -> int: """ Returns solution to problem. Algorithm: 1. Precompute φ(k) for all natural k, k <= n using product formula (wikilink below) https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler's_product_formula 2. Find k/φ(k) for all k ≤ n and return the k that attains maximum >>> solution(10) 6 >>> solution(100) 30 >>> solution(9973) 2310 """ if n <= 0: raise ValueError("Please enter an integer greater than 0") phi = list(range(n + 1)) for number in range(2, n + 1): if phi[number] == number: phi[number] -= 1 for multiple in range(number * 2, n + 1, number): phi[multiple] = (phi[multiple] // number) * (number - 1) answer = 1 for number in range(1, n + 1): if (answer / phi[answer]) < (number / phi[number]): answer = number return answer if __name__ == "__main__": print(solution())

""" Totient maximum Problem 69: https://projecteuler.net/problem=69 Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6. n Relatively Prime φ(n) n/φ(n) 2 1 1 2 3 1,2 2 1.5 4 1,3 2 2 5 1,2,3,4 4 1.25 6 1,5 2 3 7 1,2,3,4,5,6 6 1.1666... 8 1,3,5,7 4 2 9 1,2,4,5,7,8 6 1.5 10 1,3,7,9 4 2.5 It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10. Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum. """ def solution(n: int = 10**6) -> int: """ Returns solution to problem. Algorithm: 1. Precompute φ(k) for all natural k, k <= n using product formula (wikilink below) https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler's_product_formula 2. Find k/φ(k) for all k ≤ n and return the k that attains maximum >>> solution(10) 6 >>> solution(100) 30 >>> solution(9973) 2310 """ if n <= 0: raise ValueError("Please enter an integer greater than 0") phi = list(range(n + 1)) for number in range(2, n + 1): if phi[number] == number: phi[number] -= 1 for multiple in range(number * 2, n + 1, number): phi[multiple] = (phi[multiple] // number) * (number - 1) answer = 1 for number in range(1, n + 1): if (answer / phi[answer]) < (number / phi[number]): answer = number return answer if __name__ == "__main__": print(solution())

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

import random class Onepad: @staticmethod def encrypt(text: str) -> tuple[list[int], list[int]]: """Function to encrypt text using pseudo-random numbers""" plain = [ord(i) for i in text] key = [] cipher = [] for i in plain: k = random.randint(1, 300) c = (i + k) * k cipher.append(c) key.append(k) return cipher, key @staticmethod def decrypt(cipher: list[int], key: list[int]) -> str: """Function to decrypt text using pseudo-random numbers.""" plain = [] for i in range(len(key)): p = int((cipher[i] - (key[i]) ** 2) / key[i]) plain.append(chr(p)) return "".join(plain) if __name__ == "__main__": c, k = Onepad().encrypt("Hello") print(c, k) print(Onepad().decrypt(c, k))

import random class Onepad: @staticmethod def encrypt(text: str) -> tuple[list[int], list[int]]: """ Function to encrypt text using pseudo-random numbers >>> Onepad().encrypt("") ([], []) >>> Onepad().encrypt([]) ([], []) >>> random.seed(1) >>> Onepad().encrypt(" ") ([6969], [69]) >>> random.seed(1) >>> Onepad().encrypt("Hello") ([9729, 114756, 4653, 31309, 10492], [69, 292, 33, 131, 61]) >>> Onepad().encrypt(1) Traceback (most recent call last): ... TypeError: 'int' object is not iterable >>> Onepad().encrypt(1.1) Traceback (most recent call last): ... TypeError: 'float' object is not iterable """ plain = [ord(i) for i in text] key = [] cipher = [] for i in plain: k = random.randint(1, 300) c = (i + k) * k cipher.append(c) key.append(k) return cipher, key @staticmethod def decrypt(cipher: list[int], key: list[int]) -> str: """ Function to decrypt text using pseudo-random numbers. >>> Onepad().decrypt([], []) '' >>> Onepad().decrypt([35], []) '' >>> Onepad().decrypt([], [35]) Traceback (most recent call last): ... IndexError: list index out of range >>> random.seed(1) >>> Onepad().decrypt([9729, 114756, 4653, 31309, 10492], [69, 292, 33, 131, 61]) 'Hello' """ plain = [] for i in range(len(key)): p = int((cipher[i] - (key[i]) ** 2) / key[i]) plain.append(chr(p)) return "".join(plain) if __name__ == "__main__": c, k = Onepad().encrypt("Hello") print(c, k) print(Onepad().decrypt(c, k))

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

# Author: Abhijeeth S import math def res(x, y): if 0 not in (x, y): # We use the relation x^y = y*log10(x), where 10 is the base. return y * math.log10(x) else: if x == 0: # 0 raised to any number is 0 return 0 elif y == 0: return 1 # any number raised to 0 is 1 raise AssertionError("This should never happen") if __name__ == "__main__": # Main function # Read two numbers from input and typecast them to int using map function. # Here x is the base and y is the power. prompt = "Enter the base and the power separated by a comma: " x1, y1 = map(int, input(prompt).split(",")) x2, y2 = map(int, input(prompt).split(",")) # We find the log of each number, using the function res(), which takes two # arguments. res1 = res(x1, y1) res2 = res(x2, y2) # We check for the largest number if res1 > res2: print("Largest number is", x1, "^", y1) elif res2 > res1: print("Largest number is", x2, "^", y2) else: print("Both are equal")

# Author: Abhijeeth S import math def res(x, y): """ Reduces large number to a more manageable number >>> res(5, 7) 4.892790030352132 >>> res(0, 5) 0 >>> res(3, 0) 1 >>> res(-1, 5) Traceback (most recent call last): ... ValueError: math domain error """ if 0 not in (x, y): # We use the relation x^y = y*log10(x), where 10 is the base. return y * math.log10(x) else: if x == 0: # 0 raised to any number is 0 return 0 elif y == 0: return 1 # any number raised to 0 is 1 raise AssertionError("This should never happen") if __name__ == "__main__": # Main function # Read two numbers from input and typecast them to int using map function. # Here x is the base and y is the power. prompt = "Enter the base and the power separated by a comma: " x1, y1 = map(int, input(prompt).split(",")) x2, y2 = map(int, input(prompt).split(",")) # We find the log of each number, using the function res(), which takes two # arguments. res1 = res(x1, y1) res2 = res(x2, y2) # We check for the largest number if res1 > res2: print("Largest number is", x1, "^", y1) elif res2 > res1: print("Largest number is", x2, "^", y2) else: print("Both are equal")

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

def get_word_pattern(word: str) -> str: """ >>> get_word_pattern("pattern") '0.1.2.2.3.4.5' >>> get_word_pattern("word pattern") '0.1.2.3.4.5.6.7.7.8.2.9' >>> get_word_pattern("get word pattern") '0.1.2.3.4.5.6.7.3.8.9.2.2.1.6.10' """ word = word.upper() next_num = 0 letter_nums = {} word_pattern = [] for letter in word: if letter not in letter_nums: letter_nums[letter] = str(next_num) next_num += 1 word_pattern.append(letter_nums[letter]) return ".".join(word_pattern) if __name__ == "__main__": import pprint import time start_time = time.time() with open("dictionary.txt") as in_file: word_list = in_file.read().splitlines() all_patterns: dict = {} for word in word_list: pattern = get_word_pattern(word) if pattern in all_patterns: all_patterns[pattern].append(word) else: all_patterns[pattern] = [word] with open("word_patterns.txt", "w") as out_file: out_file.write(pprint.pformat(all_patterns)) total_time = round(time.time() - start_time, 2) print(f"Done! {len(all_patterns):,} word patterns found in {total_time} seconds.") # Done! 9,581 word patterns found in 0.58 seconds.

def get_word_pattern(word: str) -> str: """ Returns numerical pattern of character appearances in given word >>> get_word_pattern("") '' >>> get_word_pattern(" ") '0' >>> get_word_pattern("pattern") '0.1.2.2.3.4.5' >>> get_word_pattern("word pattern") '0.1.2.3.4.5.6.7.7.8.2.9' >>> get_word_pattern("get word pattern") '0.1.2.3.4.5.6.7.3.8.9.2.2.1.6.10' >>> get_word_pattern() Traceback (most recent call last): ... TypeError: get_word_pattern() missing 1 required positional argument: 'word' >>> get_word_pattern(1) Traceback (most recent call last): ... AttributeError: 'int' object has no attribute 'upper' >>> get_word_pattern(1.1) Traceback (most recent call last): ... AttributeError: 'float' object has no attribute 'upper' >>> get_word_pattern([]) Traceback (most recent call last): ... AttributeError: 'list' object has no attribute 'upper' """ word = word.upper() next_num = 0 letter_nums = {} word_pattern = [] for letter in word: if letter not in letter_nums: letter_nums[letter] = str(next_num) next_num += 1 word_pattern.append(letter_nums[letter]) return ".".join(word_pattern) if __name__ == "__main__": import pprint import time start_time = time.time() with open("dictionary.txt") as in_file: word_list = in_file.read().splitlines() all_patterns: dict = {} for word in word_list: pattern = get_word_pattern(word) if pattern in all_patterns: all_patterns[pattern].append(word) else: all_patterns[pattern] = [word] with open("word_patterns.txt", "w") as out_file: out_file.write(pprint.pformat(all_patterns)) total_time = round(time.time() - start_time, 2) print(f"Done! {len(all_patterns):,} word patterns found in {total_time} seconds.") # Done! 9,581 word patterns found in 0.58 seconds.

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Project Euler Problem 113: https://projecteuler.net/problem=113 Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349. As n increases, the proportion of bouncy numbers below n increases such that there are only 12951 numbers below one-million that are not bouncy and only 277032 non-bouncy numbers below 10^10. How many numbers below a googol (10^100) are not bouncy? """ def choose(n: int, r: int) -> int: """ Calculate the binomial coefficient c(n,r) using the multiplicative formula. >>> choose(4,2) 6 >>> choose(5,3) 10 >>> choose(20,6) 38760 """ ret = 1.0 for i in range(1, r + 1): ret *= (n + 1 - i) / i return round(ret) def non_bouncy_exact(n: int) -> int: """ Calculate the number of non-bouncy numbers with at most n digits. >>> non_bouncy_exact(1) 9 >>> non_bouncy_exact(6) 7998 >>> non_bouncy_exact(10) 136126 """ return choose(8 + n, n) + choose(9 + n, n) - 10 def non_bouncy_upto(n: int) -> int: """ Calculate the number of non-bouncy numbers with at most n digits. >>> non_bouncy_upto(1) 9 >>> non_bouncy_upto(6) 12951 >>> non_bouncy_upto(10) 277032 """ return sum(non_bouncy_exact(i) for i in range(1, n + 1)) def solution(num_digits: int = 100) -> int: """ Calculate the number of non-bouncy numbers less than a googol. >>> solution(6) 12951 >>> solution(10) 277032 """ return non_bouncy_upto(num_digits) if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 113: https://projecteuler.net/problem=113 Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468. Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420. We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349. As n increases, the proportion of bouncy numbers below n increases such that there are only 12951 numbers below one-million that are not bouncy and only 277032 non-bouncy numbers below 10^10. How many numbers below a googol (10^100) are not bouncy? """ def choose(n: int, r: int) -> int: """ Calculate the binomial coefficient c(n,r) using the multiplicative formula. >>> choose(4,2) 6 >>> choose(5,3) 10 >>> choose(20,6) 38760 """ ret = 1.0 for i in range(1, r + 1): ret *= (n + 1 - i) / i return round(ret) def non_bouncy_exact(n: int) -> int: """ Calculate the number of non-bouncy numbers with at most n digits. >>> non_bouncy_exact(1) 9 >>> non_bouncy_exact(6) 7998 >>> non_bouncy_exact(10) 136126 """ return choose(8 + n, n) + choose(9 + n, n) - 10 def non_bouncy_upto(n: int) -> int: """ Calculate the number of non-bouncy numbers with at most n digits. >>> non_bouncy_upto(1) 9 >>> non_bouncy_upto(6) 12951 >>> non_bouncy_upto(10) 277032 """ return sum(non_bouncy_exact(i) for i in range(1, n + 1)) def solution(num_digits: int = 100) -> int: """ Calculate the number of non-bouncy numbers less than a googol. >>> solution(6) 12951 >>> solution(10) 277032 """ return non_bouncy_upto(num_digits) if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Introspective Sort is hybrid sort (Quick Sort + Heap Sort + Insertion Sort) if the size of the list is under 16, use insertion sort https://en.wikipedia.org/wiki/Introsort """ import math def insertion_sort(array: list, start: int = 0, end: int = 0) -> list: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> insertion_sort(array, 0, len(array)) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] """ end = end or len(array) for i in range(start, end): temp_index = i temp_index_value = array[i] while temp_index != start and temp_index_value < array[temp_index - 1]: array[temp_index] = array[temp_index - 1] temp_index -= 1 array[temp_index] = temp_index_value return array def heapify(array: list, index: int, heap_size: int) -> None: # Max Heap """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> heapify(array, len(array) // 2 ,len(array)) """ largest = index left_index = 2 * index + 1 # Left Node right_index = 2 * index + 2 # Right Node if left_index < heap_size and array[largest] < array[left_index]: largest = left_index if right_index < heap_size and array[largest] < array[right_index]: largest = right_index if largest != index: array[index], array[largest] = array[largest], array[index] heapify(array, largest, heap_size) def heap_sort(array: list) -> list: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> heap_sort(array) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] """ n = len(array) for i in range(n // 2, -1, -1): heapify(array, i, n) for i in range(n - 1, 0, -1): array[i], array[0] = array[0], array[i] heapify(array, 0, i) return array def median_of_3( array: list, first_index: int, middle_index: int, last_index: int ) -> int: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> median_of_3(array, 0, 0 + ((len(array) - 0) // 2) + 1, len(array) - 1) 12 """ if (array[first_index] > array[middle_index]) != ( array[first_index] > array[last_index] ): return array[first_index] elif (array[middle_index] > array[first_index]) != ( array[middle_index] > array[last_index] ): return array[middle_index] else: return array[last_index] def partition(array: list, low: int, high: int, pivot: int) -> int: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> partition(array, 0, len(array), 12) 8 """ i = low j = high while True: while array[i] < pivot: i += 1 j -= 1 while pivot < array[j]: j -= 1 if i >= j: return i array[i], array[j] = array[j], array[i] i += 1 def sort(array: list) -> list: """ :param collection: some mutable ordered collection with heterogeneous comparable items inside :return: the same collection ordered by ascending Examples: >>> sort([4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] >>> sort([-1, -5, -3, -13, -44]) [-44, -13, -5, -3, -1] >>> sort([]) [] >>> sort([5]) [5] >>> sort([-3, 0, -7, 6, 23, -34]) [-34, -7, -3, 0, 6, 23] >>> sort([1.7, 1.0, 3.3, 2.1, 0.3 ]) [0.3, 1.0, 1.7, 2.1, 3.3] >>> sort(['d', 'a', 'b', 'e', 'c']) ['a', 'b', 'c', 'd', 'e'] """ if len(array) == 0: return array max_depth = 2 * math.ceil(math.log2(len(array))) size_threshold = 16 return intro_sort(array, 0, len(array), size_threshold, max_depth) def intro_sort( array: list, start: int, end: int, size_threshold: int, max_depth: int ) -> list: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> max_depth = 2 * math.ceil(math.log2(len(array))) >>> intro_sort(array, 0, len(array), 16, max_depth) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] """ while end - start > size_threshold: if max_depth == 0: return heap_sort(array) max_depth -= 1 pivot = median_of_3(array, start, start + ((end - start) // 2) + 1, end - 1) p = partition(array, start, end, pivot) intro_sort(array, p, end, size_threshold, max_depth) end = p return insertion_sort(array, start, end) if __name__ == "__main__": import doctest doctest.testmod() user_input = input("Enter numbers separated by a comma : ").strip() unsorted = [float(item) for item in user_input.split(",")] print(sort(unsorted))

""" Introspective Sort is hybrid sort (Quick Sort + Heap Sort + Insertion Sort) if the size of the list is under 16, use insertion sort https://en.wikipedia.org/wiki/Introsort """ import math def insertion_sort(array: list, start: int = 0, end: int = 0) -> list: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> insertion_sort(array, 0, len(array)) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] """ end = end or len(array) for i in range(start, end): temp_index = i temp_index_value = array[i] while temp_index != start and temp_index_value < array[temp_index - 1]: array[temp_index] = array[temp_index - 1] temp_index -= 1 array[temp_index] = temp_index_value return array def heapify(array: list, index: int, heap_size: int) -> None: # Max Heap """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> heapify(array, len(array) // 2 ,len(array)) """ largest = index left_index = 2 * index + 1 # Left Node right_index = 2 * index + 2 # Right Node if left_index < heap_size and array[largest] < array[left_index]: largest = left_index if right_index < heap_size and array[largest] < array[right_index]: largest = right_index if largest != index: array[index], array[largest] = array[largest], array[index] heapify(array, largest, heap_size) def heap_sort(array: list) -> list: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> heap_sort(array) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] """ n = len(array) for i in range(n // 2, -1, -1): heapify(array, i, n) for i in range(n - 1, 0, -1): array[i], array[0] = array[0], array[i] heapify(array, 0, i) return array def median_of_3( array: list, first_index: int, middle_index: int, last_index: int ) -> int: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> median_of_3(array, 0, 0 + ((len(array) - 0) // 2) + 1, len(array) - 1) 12 """ if (array[first_index] > array[middle_index]) != ( array[first_index] > array[last_index] ): return array[first_index] elif (array[middle_index] > array[first_index]) != ( array[middle_index] > array[last_index] ): return array[middle_index] else: return array[last_index] def partition(array: list, low: int, high: int, pivot: int) -> int: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> partition(array, 0, len(array), 12) 8 """ i = low j = high while True: while array[i] < pivot: i += 1 j -= 1 while pivot < array[j]: j -= 1 if i >= j: return i array[i], array[j] = array[j], array[i] i += 1 def sort(array: list) -> list: """ :param collection: some mutable ordered collection with heterogeneous comparable items inside :return: the same collection ordered by ascending Examples: >>> sort([4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] >>> sort([-1, -5, -3, -13, -44]) [-44, -13, -5, -3, -1] >>> sort([]) [] >>> sort([5]) [5] >>> sort([-3, 0, -7, 6, 23, -34]) [-34, -7, -3, 0, 6, 23] >>> sort([1.7, 1.0, 3.3, 2.1, 0.3 ]) [0.3, 1.0, 1.7, 2.1, 3.3] >>> sort(['d', 'a', 'b', 'e', 'c']) ['a', 'b', 'c', 'd', 'e'] """ if len(array) == 0: return array max_depth = 2 * math.ceil(math.log2(len(array))) size_threshold = 16 return intro_sort(array, 0, len(array), size_threshold, max_depth) def intro_sort( array: list, start: int, end: int, size_threshold: int, max_depth: int ) -> list: """ >>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12] >>> max_depth = 2 * math.ceil(math.log2(len(array))) >>> intro_sort(array, 0, len(array), 16, max_depth) [1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79] """ while end - start > size_threshold: if max_depth == 0: return heap_sort(array) max_depth -= 1 pivot = median_of_3(array, start, start + ((end - start) // 2) + 1, end - 1) p = partition(array, start, end, pivot) intro_sort(array, p, end, size_threshold, max_depth) end = p return insertion_sort(array, start, end) if __name__ == "__main__": import doctest doctest.testmod() user_input = input("Enter numbers separated by a comma : ").strip() unsorted = [float(item) for item in user_input.split(",")] print(sort(unsorted))

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" This program print the matrix in spiral form. This problem has been solved through recursive way. Matrix must satisfy below conditions i) matrix should be only one or two dimensional ii) number of column of all rows should be equal """ def check_matrix(matrix: list[list[int]]) -> bool: # must be matrix = [list(row) for row in matrix] if matrix and isinstance(matrix, list): if isinstance(matrix[0], list): prev_len = 0 for row in matrix: if prev_len == 0: prev_len = len(row) result = True else: result = prev_len == len(row) else: result = True else: result = False return result def spiral_print_clockwise(a: list[list[int]]) -> None: """ >>> spiral_print_clockwise([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) 1 2 3 4 8 12 11 10 9 5 6 7 """ if check_matrix(a) and len(a) > 0: a = [list(row) for row in a] mat_row = len(a) if isinstance(a[0], list): mat_col = len(a[0]) else: for dat in a: print(dat) return # horizotal printing increasing for i in range(mat_col): print(a[0][i]) # vertical printing down for i in range(1, mat_row): print(a[i][mat_col - 1]) # horizotal printing decreasing if mat_row > 1: for i in range(mat_col - 2, -1, -1): print(a[mat_row - 1][i]) # vertical printing up for i in range(mat_row - 2, 0, -1): print(a[i][0]) remain_mat = [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]] if len(remain_mat) > 0: spiral_print_clockwise(remain_mat) else: return else: print("Not a valid matrix") return # Other Easy to understand Approach def spiral_traversal(matrix: list[list]) -> list[int]: """ >>> spiral_traversal([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] Example: matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] Algorithm: Step 1. first pop the 0 index list. (which is [1,2,3,4] and concatenate the output of [step 2]) Step 2. Now perform matrix’s Transpose operation (Change rows to column and vice versa) and reverse the resultant matrix. Step 3. Pass the output of [2nd step], to same recursive function till base case hits. Dry Run: Stage 1. [1, 2, 3, 4] + spiral_traversal([ [8, 12], [7, 11], [6, 10], [5, 9]] ]) Stage 2. [1, 2, 3, 4, 8, 12] + spiral_traversal([ [11, 10, 9], [7, 6, 5] ]) Stage 3. [1, 2, 3, 4, 8, 12, 11, 10, 9] + spiral_traversal([ [5], [6], [7] ]) Stage 4. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([ [5], [6], [7] ]) Stage 5. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([[6, 7]]) Stage 6. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] + spiral_traversal([]) """ if matrix: return list(matrix.pop(0)) + spiral_traversal(list(zip(*matrix))[::-1]) else: return [] # driver code if __name__ == "__main__": import doctest doctest.testmod() a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] spiral_print_clockwise(a)

""" This program print the matrix in spiral form. This problem has been solved through recursive way. Matrix must satisfy below conditions i) matrix should be only one or two dimensional ii) number of column of all rows should be equal """ def check_matrix(matrix: list[list[int]]) -> bool: # must be matrix = [list(row) for row in matrix] if matrix and isinstance(matrix, list): if isinstance(matrix[0], list): prev_len = 0 for row in matrix: if prev_len == 0: prev_len = len(row) result = True else: result = prev_len == len(row) else: result = True else: result = False return result def spiral_print_clockwise(a: list[list[int]]) -> None: """ >>> spiral_print_clockwise([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) 1 2 3 4 8 12 11 10 9 5 6 7 """ if check_matrix(a) and len(a) > 0: a = [list(row) for row in a] mat_row = len(a) if isinstance(a[0], list): mat_col = len(a[0]) else: for dat in a: print(dat) return # horizotal printing increasing for i in range(mat_col): print(a[0][i]) # vertical printing down for i in range(1, mat_row): print(a[i][mat_col - 1]) # horizotal printing decreasing if mat_row > 1: for i in range(mat_col - 2, -1, -1): print(a[mat_row - 1][i]) # vertical printing up for i in range(mat_row - 2, 0, -1): print(a[i][0]) remain_mat = [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]] if len(remain_mat) > 0: spiral_print_clockwise(remain_mat) else: return else: print("Not a valid matrix") return # Other Easy to understand Approach def spiral_traversal(matrix: list[list]) -> list[int]: """ >>> spiral_traversal([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] Example: matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] Algorithm: Step 1. first pop the 0 index list. (which is [1,2,3,4] and concatenate the output of [step 2]) Step 2. Now perform matrix’s Transpose operation (Change rows to column and vice versa) and reverse the resultant matrix. Step 3. Pass the output of [2nd step], to same recursive function till base case hits. Dry Run: Stage 1. [1, 2, 3, 4] + spiral_traversal([ [8, 12], [7, 11], [6, 10], [5, 9]] ]) Stage 2. [1, 2, 3, 4, 8, 12] + spiral_traversal([ [11, 10, 9], [7, 6, 5] ]) Stage 3. [1, 2, 3, 4, 8, 12, 11, 10, 9] + spiral_traversal([ [5], [6], [7] ]) Stage 4. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([ [5], [6], [7] ]) Stage 5. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5] + spiral_traversal([[6, 7]]) Stage 6. [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7] + spiral_traversal([]) """ if matrix: return list(matrix.pop(0)) + spiral_traversal(list(zip(*matrix))[::-1]) else: return [] # driver code if __name__ == "__main__": import doctest doctest.testmod() a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] spiral_print_clockwise(a)

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" https://projecteuler.net/problem=234 For an integer n ≥ 4, we define the lower prime square root of n, denoted by lps(n), as the largest prime ≤ √n and the upper prime square root of n, ups(n), as the smallest prime ≥ √n. So, for example, lps(4) = 2 = ups(4), lps(1000) = 31, ups(1000) = 37. Let us call an integer n ≥ 4 semidivisible, if one of lps(n) and ups(n) divides n, but not both. The sum of the semidivisible numbers not exceeding 15 is 30, the numbers are 8, 10 and 12. 15 is not semidivisible because it is a multiple of both lps(15) = 3 and ups(15) = 5. As a further example, the sum of the 92 semidivisible numbers up to 1000 is 34825. What is the sum of all semidivisible numbers not exceeding 999966663333 ? """ import math def prime_sieve(n: int) -> list: """ Sieve of Erotosthenes Function to return all the prime numbers up to a certain number https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes >>> prime_sieve(3) [2] >>> prime_sieve(50) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] """ is_prime = [True] * n is_prime[0] = False is_prime[1] = False is_prime[2] = True for i in range(3, int(n**0.5 + 1), 2): index = i * 2 while index < n: is_prime[index] = False index = index + i primes = [2] for i in range(3, n, 2): if is_prime[i]: primes.append(i) return primes def solution(limit: int = 999_966_663_333) -> int: """ Computes the solution to the problem up to the specified limit >>> solution(1000) 34825 >>> solution(10_000) 1134942 >>> solution(100_000) 36393008 """ primes_upper_bound = math.floor(math.sqrt(limit)) + 100 primes = prime_sieve(primes_upper_bound) matches_sum = 0 prime_index = 0 last_prime = primes[prime_index] while (last_prime**2) <= limit: next_prime = primes[prime_index + 1] lower_bound = last_prime**2 upper_bound = next_prime**2 # Get numbers divisible by lps(current) current = lower_bound + last_prime while upper_bound > current <= limit: matches_sum += current current += last_prime # Reset the upper_bound while (upper_bound - next_prime) > limit: upper_bound -= next_prime # Add the numbers divisible by ups(current) current = upper_bound - next_prime while current > lower_bound: matches_sum += current current -= next_prime # Remove the numbers divisible by both ups and lps current = 0 while upper_bound > current <= limit: if current <= lower_bound: # Increment the current number current += last_prime * next_prime continue if current > limit: break # Remove twice since it was added by both ups and lps matches_sum -= current * 2 # Increment the current number current += last_prime * next_prime # Setup for next pair last_prime = next_prime prime_index += 1 return matches_sum if __name__ == "__main__": print(solution())

""" https://projecteuler.net/problem=234 For an integer n ≥ 4, we define the lower prime square root of n, denoted by lps(n), as the largest prime ≤ √n and the upper prime square root of n, ups(n), as the smallest prime ≥ √n. So, for example, lps(4) = 2 = ups(4), lps(1000) = 31, ups(1000) = 37. Let us call an integer n ≥ 4 semidivisible, if one of lps(n) and ups(n) divides n, but not both. The sum of the semidivisible numbers not exceeding 15 is 30, the numbers are 8, 10 and 12. 15 is not semidivisible because it is a multiple of both lps(15) = 3 and ups(15) = 5. As a further example, the sum of the 92 semidivisible numbers up to 1000 is 34825. What is the sum of all semidivisible numbers not exceeding 999966663333 ? """ import math def prime_sieve(n: int) -> list: """ Sieve of Erotosthenes Function to return all the prime numbers up to a certain number https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes >>> prime_sieve(3) [2] >>> prime_sieve(50) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] """ is_prime = [True] * n is_prime[0] = False is_prime[1] = False is_prime[2] = True for i in range(3, int(n**0.5 + 1), 2): index = i * 2 while index < n: is_prime[index] = False index = index + i primes = [2] for i in range(3, n, 2): if is_prime[i]: primes.append(i) return primes def solution(limit: int = 999_966_663_333) -> int: """ Computes the solution to the problem up to the specified limit >>> solution(1000) 34825 >>> solution(10_000) 1134942 >>> solution(100_000) 36393008 """ primes_upper_bound = math.floor(math.sqrt(limit)) + 100 primes = prime_sieve(primes_upper_bound) matches_sum = 0 prime_index = 0 last_prime = primes[prime_index] while (last_prime**2) <= limit: next_prime = primes[prime_index + 1] lower_bound = last_prime**2 upper_bound = next_prime**2 # Get numbers divisible by lps(current) current = lower_bound + last_prime while upper_bound > current <= limit: matches_sum += current current += last_prime # Reset the upper_bound while (upper_bound - next_prime) > limit: upper_bound -= next_prime # Add the numbers divisible by ups(current) current = upper_bound - next_prime while current > lower_bound: matches_sum += current current -= next_prime # Remove the numbers divisible by both ups and lps current = 0 while upper_bound > current <= limit: if current <= lower_bound: # Increment the current number current += last_prime * next_prime continue if current > limit: break # Remove twice since it was added by both ups and lps matches_sum -= current * 2 # Increment the current number current += last_prime * next_prime # Setup for next pair last_prime = next_prime prime_index += 1 return matches_sum if __name__ == "__main__": print(solution())

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

from bisect import bisect from itertools import accumulate def frac_knapsack(vl, wt, w, n): """ >>> frac_knapsack([60, 100, 120], [10, 20, 30], 50, 3) 240.0 """ r = sorted(zip(vl, wt), key=lambda x: x[0] / x[1], reverse=True) vl, wt = [i[0] for i in r], [i[1] for i in r] acc = list(accumulate(wt)) k = bisect(acc, w) return ( 0 if k == 0 else sum(vl[:k]) + (w - acc[k - 1]) * (vl[k]) / (wt[k]) if k != n else sum(vl[:k]) ) if __name__ == "__main__": import doctest doctest.testmod()

from bisect import bisect from itertools import accumulate def frac_knapsack(vl, wt, w, n): """ >>> frac_knapsack([60, 100, 120], [10, 20, 30], 50, 3) 240.0 """ r = sorted(zip(vl, wt), key=lambda x: x[0] / x[1], reverse=True) vl, wt = [i[0] for i in r], [i[1] for i in r] acc = list(accumulate(wt)) k = bisect(acc, w) return ( 0 if k == 0 else sum(vl[:k]) + (w - acc[k - 1]) * (vl[k]) / (wt[k]) if k != n else sum(vl[:k]) ) if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Polynomial regression is a type of regression analysis that models the relationship between a predictor x and the response y as an mth-degree polynomial: y = β₀ + β₁x + β₂x² + ... + βₘxᵐ + ε By treating x, x², ..., xᵐ as distinct variables, we see that polynomial regression is a special case of multiple linear regression. Therefore, we can use ordinary least squares (OLS) estimation to estimate the vector of model parameters β = (β₀, β₁, β₂, ..., βₘ) for polynomial regression: β = (XᵀX)⁻¹Xᵀy = X⁺y where X is the design matrix, y is the response vector, and X⁺ denotes the Moore–Penrose pseudoinverse of X. In the case of polynomial regression, the design matrix is |1 x₁ x₁² ⋯ x₁ᵐ| X = |1 x₂ x₂² ⋯ x₂ᵐ| |⋮ ⋮ ⋮ ⋱ ⋮ | |1 xₙ xₙ² ⋯ xₙᵐ| In OLS estimation, inverting XᵀX to compute X⁺ can be very numerically unstable. This implementation sidesteps this need to invert XᵀX by computing X⁺ using singular value decomposition (SVD): β = VΣ⁺Uᵀy where UΣVᵀ is an SVD of X. References: - https://en.wikipedia.org/wiki/Polynomial_regression - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse - https://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares - https://en.wikipedia.org/wiki/Singular_value_decomposition """ import matplotlib.pyplot as plt import numpy as np class PolynomialRegression: __slots__ = "degree", "params" def __init__(self, degree: int) -> None: """ @raises ValueError: if the polynomial degree is negative """ if degree < 0: raise ValueError("Polynomial degree must be non-negative") self.degree = degree self.params = None @staticmethod def _design_matrix(data: np.ndarray, degree: int) -> np.ndarray: """ Constructs a polynomial regression design matrix for the given input data. For input data x = (x₁, x₂, ..., xₙ) and polynomial degree m, the design matrix is the Vandermonde matrix |1 x₁ x₁² ⋯ x₁ᵐ| X = |1 x₂ x₂² ⋯ x₂ᵐ| |⋮ ⋮ ⋮ ⋱ ⋮ | |1 xₙ xₙ² ⋯ xₙᵐ| Reference: https://en.wikipedia.org/wiki/Vandermonde_matrix @param data: the input predictor values x, either for model fitting or for prediction @param degree: the polynomial degree m @returns: the Vandermonde matrix X (see above) @raises ValueError: if input data is not N x 1 >>> x = np.array([0, 1, 2]) >>> PolynomialRegression._design_matrix(x, degree=0) array([[1], [1], [1]]) >>> PolynomialRegression._design_matrix(x, degree=1) array([[1, 0], [1, 1], [1, 2]]) >>> PolynomialRegression._design_matrix(x, degree=2) array([[1, 0, 0], [1, 1, 1], [1, 2, 4]]) >>> PolynomialRegression._design_matrix(x, degree=3) array([[1, 0, 0, 0], [1, 1, 1, 1], [1, 2, 4, 8]]) >>> PolynomialRegression._design_matrix(np.array([[0, 0], [0 , 0]]), degree=3) Traceback (most recent call last): ... ValueError: Data must have dimensions N x 1 """ rows, *remaining = data.shape if remaining: raise ValueError("Data must have dimensions N x 1") return np.vander(data, N=degree + 1, increasing=True) def fit(self, x_train: np.ndarray, y_train: np.ndarray) -> None: """ Computes the polynomial regression model parameters using ordinary least squares (OLS) estimation: β = (XᵀX)⁻¹Xᵀy = X⁺y where X⁺ denotes the Moore–Penrose pseudoinverse of the design matrix X. This function computes X⁺ using singular value decomposition (SVD). References: - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse - https://en.wikipedia.org/wiki/Singular_value_decomposition - https://en.wikipedia.org/wiki/Multicollinearity @param x_train: the predictor values x for model fitting @param y_train: the response values y for model fitting @raises ArithmeticError: if X isn't full rank, then XᵀX is singular and β doesn't exist >>> x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) >>> y = x**3 - 2 * x**2 + 3 * x - 5 >>> poly_reg = PolynomialRegression(degree=3) >>> poly_reg.fit(x, y) >>> poly_reg.params array([-5., 3., -2., 1.]) >>> poly_reg = PolynomialRegression(degree=20) >>> poly_reg.fit(x, y) Traceback (most recent call last): ... ArithmeticError: Design matrix is not full rank, can't compute coefficients Make sure errors don't grow too large: >>> coefs = np.array([-250, 50, -2, 36, 20, -12, 10, 2, -1, -15, 1]) >>> y = PolynomialRegression._design_matrix(x, len(coefs) - 1) @ coefs >>> poly_reg = PolynomialRegression(degree=len(coefs) - 1) >>> poly_reg.fit(x, y) >>> np.allclose(poly_reg.params, coefs, atol=10e-3) True """ X = PolynomialRegression._design_matrix(x_train, self.degree) # noqa: N806 _, cols = X.shape if np.linalg.matrix_rank(X) < cols: raise ArithmeticError( "Design matrix is not full rank, can't compute coefficients" ) # np.linalg.pinv() computes the Moore–Penrose pseudoinverse using SVD self.params = np.linalg.pinv(X) @ y_train def predict(self, data: np.ndarray) -> np.ndarray: """ Computes the predicted response values y for the given input data by constructing the design matrix X and evaluating y = Xβ. @param data: the predictor values x for prediction @returns: the predicted response values y = Xβ @raises ArithmeticError: if this function is called before the model parameters are fit >>> x = np.array([0, 1, 2, 3, 4]) >>> y = x**3 - 2 * x**2 + 3 * x - 5 >>> poly_reg = PolynomialRegression(degree=3) >>> poly_reg.fit(x, y) >>> poly_reg.predict(np.array([-1])) array([-11.]) >>> poly_reg.predict(np.array([-2])) array([-27.]) >>> poly_reg.predict(np.array([6])) array([157.]) >>> PolynomialRegression(degree=3).predict(x) Traceback (most recent call last): ... ArithmeticError: Predictor hasn't been fit yet """ if self.params is None: raise ArithmeticError("Predictor hasn't been fit yet") return PolynomialRegression._design_matrix(data, self.degree) @ self.params def main() -> None: """ Fit a polynomial regression model to predict fuel efficiency using seaborn's mpg dataset >>> pass # Placeholder, function is only for demo purposes """ import seaborn as sns mpg_data = sns.load_dataset("mpg") poly_reg = PolynomialRegression(degree=2) poly_reg.fit(mpg_data.weight, mpg_data.mpg) weight_sorted = np.sort(mpg_data.weight) predictions = poly_reg.predict(weight_sorted) plt.scatter(mpg_data.weight, mpg_data.mpg, color="gray", alpha=0.5) plt.plot(weight_sorted, predictions, color="red", linewidth=3) plt.title("Predicting Fuel Efficiency Using Polynomial Regression") plt.xlabel("Weight (lbs)") plt.ylabel("Fuel Efficiency (mpg)") plt.show() if __name__ == "__main__": import doctest doctest.testmod() main()

""" Polynomial regression is a type of regression analysis that models the relationship between a predictor x and the response y as an mth-degree polynomial: y = β₀ + β₁x + β₂x² + ... + βₘxᵐ + ε By treating x, x², ..., xᵐ as distinct variables, we see that polynomial regression is a special case of multiple linear regression. Therefore, we can use ordinary least squares (OLS) estimation to estimate the vector of model parameters β = (β₀, β₁, β₂, ..., βₘ) for polynomial regression: β = (XᵀX)⁻¹Xᵀy = X⁺y where X is the design matrix, y is the response vector, and X⁺ denotes the Moore–Penrose pseudoinverse of X. In the case of polynomial regression, the design matrix is |1 x₁ x₁² ⋯ x₁ᵐ| X = |1 x₂ x₂² ⋯ x₂ᵐ| |⋮ ⋮ ⋮ ⋱ ⋮ | |1 xₙ xₙ² ⋯ xₙᵐ| In OLS estimation, inverting XᵀX to compute X⁺ can be very numerically unstable. This implementation sidesteps this need to invert XᵀX by computing X⁺ using singular value decomposition (SVD): β = VΣ⁺Uᵀy where UΣVᵀ is an SVD of X. References: - https://en.wikipedia.org/wiki/Polynomial_regression - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse - https://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares - https://en.wikipedia.org/wiki/Singular_value_decomposition """ import matplotlib.pyplot as plt import numpy as np class PolynomialRegression: __slots__ = "degree", "params" def __init__(self, degree: int) -> None: """ @raises ValueError: if the polynomial degree is negative """ if degree < 0: raise ValueError("Polynomial degree must be non-negative") self.degree = degree self.params = None @staticmethod def _design_matrix(data: np.ndarray, degree: int) -> np.ndarray: """ Constructs a polynomial regression design matrix for the given input data. For input data x = (x₁, x₂, ..., xₙ) and polynomial degree m, the design matrix is the Vandermonde matrix |1 x₁ x₁² ⋯ x₁ᵐ| X = |1 x₂ x₂² ⋯ x₂ᵐ| |⋮ ⋮ ⋮ ⋱ ⋮ | |1 xₙ xₙ² ⋯ xₙᵐ| Reference: https://en.wikipedia.org/wiki/Vandermonde_matrix @param data: the input predictor values x, either for model fitting or for prediction @param degree: the polynomial degree m @returns: the Vandermonde matrix X (see above) @raises ValueError: if input data is not N x 1 >>> x = np.array([0, 1, 2]) >>> PolynomialRegression._design_matrix(x, degree=0) array([[1], [1], [1]]) >>> PolynomialRegression._design_matrix(x, degree=1) array([[1, 0], [1, 1], [1, 2]]) >>> PolynomialRegression._design_matrix(x, degree=2) array([[1, 0, 0], [1, 1, 1], [1, 2, 4]]) >>> PolynomialRegression._design_matrix(x, degree=3) array([[1, 0, 0, 0], [1, 1, 1, 1], [1, 2, 4, 8]]) >>> PolynomialRegression._design_matrix(np.array([[0, 0], [0 , 0]]), degree=3) Traceback (most recent call last): ... ValueError: Data must have dimensions N x 1 """ rows, *remaining = data.shape if remaining: raise ValueError("Data must have dimensions N x 1") return np.vander(data, N=degree + 1, increasing=True) def fit(self, x_train: np.ndarray, y_train: np.ndarray) -> None: """ Computes the polynomial regression model parameters using ordinary least squares (OLS) estimation: β = (XᵀX)⁻¹Xᵀy = X⁺y where X⁺ denotes the Moore–Penrose pseudoinverse of the design matrix X. This function computes X⁺ using singular value decomposition (SVD). References: - https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse - https://en.wikipedia.org/wiki/Singular_value_decomposition - https://en.wikipedia.org/wiki/Multicollinearity @param x_train: the predictor values x for model fitting @param y_train: the response values y for model fitting @raises ArithmeticError: if X isn't full rank, then XᵀX is singular and β doesn't exist >>> x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) >>> y = x**3 - 2 * x**2 + 3 * x - 5 >>> poly_reg = PolynomialRegression(degree=3) >>> poly_reg.fit(x, y) >>> poly_reg.params array([-5., 3., -2., 1.]) >>> poly_reg = PolynomialRegression(degree=20) >>> poly_reg.fit(x, y) Traceback (most recent call last): ... ArithmeticError: Design matrix is not full rank, can't compute coefficients Make sure errors don't grow too large: >>> coefs = np.array([-250, 50, -2, 36, 20, -12, 10, 2, -1, -15, 1]) >>> y = PolynomialRegression._design_matrix(x, len(coefs) - 1) @ coefs >>> poly_reg = PolynomialRegression(degree=len(coefs) - 1) >>> poly_reg.fit(x, y) >>> np.allclose(poly_reg.params, coefs, atol=10e-3) True """ X = PolynomialRegression._design_matrix(x_train, self.degree) # noqa: N806 _, cols = X.shape if np.linalg.matrix_rank(X) < cols: raise ArithmeticError( "Design matrix is not full rank, can't compute coefficients" ) # np.linalg.pinv() computes the Moore–Penrose pseudoinverse using SVD self.params = np.linalg.pinv(X) @ y_train def predict(self, data: np.ndarray) -> np.ndarray: """ Computes the predicted response values y for the given input data by constructing the design matrix X and evaluating y = Xβ. @param data: the predictor values x for prediction @returns: the predicted response values y = Xβ @raises ArithmeticError: if this function is called before the model parameters are fit >>> x = np.array([0, 1, 2, 3, 4]) >>> y = x**3 - 2 * x**2 + 3 * x - 5 >>> poly_reg = PolynomialRegression(degree=3) >>> poly_reg.fit(x, y) >>> poly_reg.predict(np.array([-1])) array([-11.]) >>> poly_reg.predict(np.array([-2])) array([-27.]) >>> poly_reg.predict(np.array([6])) array([157.]) >>> PolynomialRegression(degree=3).predict(x) Traceback (most recent call last): ... ArithmeticError: Predictor hasn't been fit yet """ if self.params is None: raise ArithmeticError("Predictor hasn't been fit yet") return PolynomialRegression._design_matrix(data, self.degree) @ self.params def main() -> None: """ Fit a polynomial regression model to predict fuel efficiency using seaborn's mpg dataset >>> pass # Placeholder, function is only for demo purposes """ import seaborn as sns mpg_data = sns.load_dataset("mpg") poly_reg = PolynomialRegression(degree=2) poly_reg.fit(mpg_data.weight, mpg_data.mpg) weight_sorted = np.sort(mpg_data.weight) predictions = poly_reg.predict(weight_sorted) plt.scatter(mpg_data.weight, mpg_data.mpg, color="gray", alpha=0.5) plt.plot(weight_sorted, predictions, color="red", linewidth=3) plt.title("Predicting Fuel Efficiency Using Polynomial Regression") plt.xlabel("Weight (lbs)") plt.ylabel("Fuel Efficiency (mpg)") plt.show() if __name__ == "__main__": import doctest doctest.testmod() main()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

from collections.abc import Callable import numpy as np def euler_modified( ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float ) -> np.ndarray: """ Calculate solution at each step to an ODE using Euler's Modified Method The Euler Method is straightforward to implement, but can't give accurate solutions. So, some changes were proposed to improve accuracy. https://en.wikipedia.org/wiki/Euler_method Arguments: ode_func -- The ode as a function of x and y y0 -- the initial value for y x0 -- the initial value for x stepsize -- the increment value for x x_end -- the end value for x >>> # the exact solution is math.exp(x) >>> def f1(x, y): ... return -2*x*(y**2) >>> y = euler_modified(f1, 1.0, 0.0, 0.2, 1.0) >>> y[-1] 0.503338255442106 >>> import math >>> def f2(x, y): ... return -2*y + (x**3)*math.exp(-2*x) >>> y = euler_modified(f2, 1.0, 0.0, 0.1, 0.3) >>> y[-1] 0.5525976431951775 """ n = int(np.ceil((x_end - x0) / step_size)) y = np.zeros((n + 1,)) y[0] = y0 x = x0 for k in range(n): y_get = y[k] + step_size * ode_func(x, y[k]) y[k + 1] = y[k] + ( (step_size / 2) * (ode_func(x, y[k]) + ode_func(x + step_size, y_get)) ) x += step_size return y if __name__ == "__main__": import doctest doctest.testmod()

from collections.abc import Callable import numpy as np def euler_modified( ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float ) -> np.ndarray: """ Calculate solution at each step to an ODE using Euler's Modified Method The Euler Method is straightforward to implement, but can't give accurate solutions. So, some changes were proposed to improve accuracy. https://en.wikipedia.org/wiki/Euler_method Arguments: ode_func -- The ode as a function of x and y y0 -- the initial value for y x0 -- the initial value for x stepsize -- the increment value for x x_end -- the end value for x >>> # the exact solution is math.exp(x) >>> def f1(x, y): ... return -2*x*(y**2) >>> y = euler_modified(f1, 1.0, 0.0, 0.2, 1.0) >>> y[-1] 0.503338255442106 >>> import math >>> def f2(x, y): ... return -2*y + (x**3)*math.exp(-2*x) >>> y = euler_modified(f2, 1.0, 0.0, 0.1, 0.3) >>> y[-1] 0.5525976431951775 """ n = int(np.ceil((x_end - x0) / step_size)) y = np.zeros((n + 1,)) y[0] = y0 x = x0 for k in range(n): y_get = y[k] + step_size * ode_func(x, y[k]) y[k + 1] = y[k] + ( (step_size / 2) * (ode_func(x, y[k]) + ode_func(x + step_size, y_get)) ) x += step_size return y if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Implementation of gradient descent algorithm for minimizing cost of a linear hypothesis function. """ import numpy # List of input, output pairs train_data = ( ((5, 2, 3), 15), ((6, 5, 9), 25), ((11, 12, 13), 41), ((1, 1, 1), 8), ((11, 12, 13), 41), ) test_data = (((515, 22, 13), 555), ((61, 35, 49), 150)) parameter_vector = [2, 4, 1, 5] m = len(train_data) LEARNING_RATE = 0.009 def _error(example_no, data_set="train"): """ :param data_set: train data or test data :param example_no: example number whose error has to be checked :return: error in example pointed by example number. """ return calculate_hypothesis_value(example_no, data_set) - output( example_no, data_set ) def _hypothesis_value(data_input_tuple): """ Calculates hypothesis function value for a given input :param data_input_tuple: Input tuple of a particular example :return: Value of hypothesis function at that point. Note that there is an 'biased input' whose value is fixed as 1. It is not explicitly mentioned in input data.. But, ML hypothesis functions use it. So, we have to take care of it separately. Line 36 takes care of it. """ hyp_val = 0 for i in range(len(parameter_vector) - 1): hyp_val += data_input_tuple[i] * parameter_vector[i + 1] hyp_val += parameter_vector[0] return hyp_val def output(example_no, data_set): """ :param data_set: test data or train data :param example_no: example whose output is to be fetched :return: output for that example """ if data_set == "train": return train_data[example_no][1] elif data_set == "test": return test_data[example_no][1] return None def calculate_hypothesis_value(example_no, data_set): """ Calculates hypothesis value for a given example :param data_set: test data or train_data :param example_no: example whose hypothesis value is to be calculated :return: hypothesis value for that example """ if data_set == "train": return _hypothesis_value(train_data[example_no][0]) elif data_set == "test": return _hypothesis_value(test_data[example_no][0]) return None def summation_of_cost_derivative(index, end=m): """ Calculates the sum of cost function derivative :param index: index wrt derivative is being calculated :param end: value where summation ends, default is m, number of examples :return: Returns the summation of cost derivative Note: If index is -1, this means we are calculating summation wrt to biased parameter. """ summation_value = 0 for i in range(end): if index == -1: summation_value += _error(i) else: summation_value += _error(i) * train_data[i][0][index] return summation_value def get_cost_derivative(index): """ :param index: index of the parameter vector wrt to derivative is to be calculated :return: derivative wrt to that index Note: If index is -1, this means we are calculating summation wrt to biased parameter. """ cost_derivative_value = summation_of_cost_derivative(index, m) / m return cost_derivative_value def run_gradient_descent(): global parameter_vector # Tune these values to set a tolerance value for predicted output absolute_error_limit = 0.000002 relative_error_limit = 0 j = 0 while True: j += 1 temp_parameter_vector = [0, 0, 0, 0] for i in range(len(parameter_vector)): cost_derivative = get_cost_derivative(i - 1) temp_parameter_vector[i] = ( parameter_vector[i] - LEARNING_RATE * cost_derivative ) if numpy.allclose( parameter_vector, temp_parameter_vector, atol=absolute_error_limit, rtol=relative_error_limit, ): break parameter_vector = temp_parameter_vector print(("Number of iterations:", j)) def test_gradient_descent(): for i in range(len(test_data)): print(("Actual output value:", output(i, "test"))) print(("Hypothesis output:", calculate_hypothesis_value(i, "test"))) if __name__ == "__main__": run_gradient_descent() print("\nTesting gradient descent for a linear hypothesis function.\n") test_gradient_descent()

""" Implementation of gradient descent algorithm for minimizing cost of a linear hypothesis function. """ import numpy # List of input, output pairs train_data = ( ((5, 2, 3), 15), ((6, 5, 9), 25), ((11, 12, 13), 41), ((1, 1, 1), 8), ((11, 12, 13), 41), ) test_data = (((515, 22, 13), 555), ((61, 35, 49), 150)) parameter_vector = [2, 4, 1, 5] m = len(train_data) LEARNING_RATE = 0.009 def _error(example_no, data_set="train"): """ :param data_set: train data or test data :param example_no: example number whose error has to be checked :return: error in example pointed by example number. """ return calculate_hypothesis_value(example_no, data_set) - output( example_no, data_set ) def _hypothesis_value(data_input_tuple): """ Calculates hypothesis function value for a given input :param data_input_tuple: Input tuple of a particular example :return: Value of hypothesis function at that point. Note that there is an 'biased input' whose value is fixed as 1. It is not explicitly mentioned in input data.. But, ML hypothesis functions use it. So, we have to take care of it separately. Line 36 takes care of it. """ hyp_val = 0 for i in range(len(parameter_vector) - 1): hyp_val += data_input_tuple[i] * parameter_vector[i + 1] hyp_val += parameter_vector[0] return hyp_val def output(example_no, data_set): """ :param data_set: test data or train data :param example_no: example whose output is to be fetched :return: output for that example """ if data_set == "train": return train_data[example_no][1] elif data_set == "test": return test_data[example_no][1] return None def calculate_hypothesis_value(example_no, data_set): """ Calculates hypothesis value for a given example :param data_set: test data or train_data :param example_no: example whose hypothesis value is to be calculated :return: hypothesis value for that example """ if data_set == "train": return _hypothesis_value(train_data[example_no][0]) elif data_set == "test": return _hypothesis_value(test_data[example_no][0]) return None def summation_of_cost_derivative(index, end=m): """ Calculates the sum of cost function derivative :param index: index wrt derivative is being calculated :param end: value where summation ends, default is m, number of examples :return: Returns the summation of cost derivative Note: If index is -1, this means we are calculating summation wrt to biased parameter. """ summation_value = 0 for i in range(end): if index == -1: summation_value += _error(i) else: summation_value += _error(i) * train_data[i][0][index] return summation_value def get_cost_derivative(index): """ :param index: index of the parameter vector wrt to derivative is to be calculated :return: derivative wrt to that index Note: If index is -1, this means we are calculating summation wrt to biased parameter. """ cost_derivative_value = summation_of_cost_derivative(index, m) / m return cost_derivative_value def run_gradient_descent(): global parameter_vector # Tune these values to set a tolerance value for predicted output absolute_error_limit = 0.000002 relative_error_limit = 0 j = 0 while True: j += 1 temp_parameter_vector = [0, 0, 0, 0] for i in range(len(parameter_vector)): cost_derivative = get_cost_derivative(i - 1) temp_parameter_vector[i] = ( parameter_vector[i] - LEARNING_RATE * cost_derivative ) if numpy.allclose( parameter_vector, temp_parameter_vector, atol=absolute_error_limit, rtol=relative_error_limit, ): break parameter_vector = temp_parameter_vector print(("Number of iterations:", j)) def test_gradient_descent(): for i in range(len(test_data)): print(("Actual output value:", output(i, "test"))) print(("Hypothesis output:", calculate_hypothesis_value(i, "test"))) if __name__ == "__main__": run_gradient_descent() print("\nTesting gradient descent for a linear hypothesis function.\n") test_gradient_descent()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" LeetCode 36. Valid Sudoku https://leetcode.com/problems/valid-sudoku/ https://en.wikipedia.org/wiki/Sudoku Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules: - Each row must contain the digits 1-9 without repetition. - Each column must contain the digits 1-9 without repetition. - Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition. Note: A Sudoku board (partially filled) could be valid but is not necessarily solvable. Only the filled cells need to be validated according to the mentioned rules. """ from collections import defaultdict NUM_SQUARES = 9 EMPTY_CELL = "." def is_valid_sudoku_board(sudoku_board: list[list[str]]) -> bool: """ This function validates (but does not solve) a sudoku board. The board may be valid but unsolvable. >>> is_valid_sudoku_board([ ... ["5","3",".",".","7",".",".",".","."] ... ,["6",".",".","1","9","5",".",".","."] ... ,[".","9","8",".",".",".",".","6","."] ... ,["8",".",".",".","6",".",".",".","3"] ... ,["4",".",".","8",".","3",".",".","1"] ... ,["7",".",".",".","2",".",".",".","6"] ... ,[".","6",".",".",".",".","2","8","."] ... ,[".",".",".","4","1","9",".",".","5"] ... ,[".",".",".",".","8",".",".","7","9"] ... ]) True >>> is_valid_sudoku_board([ ... ["8","3",".",".","7",".",".",".","."] ... ,["6",".",".","1","9","5",".",".","."] ... ,[".","9","8",".",".",".",".","6","."] ... ,["8",".",".",".","6",".",".",".","3"] ... ,["4",".",".","8",".","3",".",".","1"] ... ,["7",".",".",".","2",".",".",".","6"] ... ,[".","6",".",".",".",".","2","8","."] ... ,[".",".",".","4","1","9",".",".","5"] ... ,[".",".",".",".","8",".",".","7","9"] ... ]) False >>> is_valid_sudoku_board([["1", "2", "3", "4", "5", "6", "7", "8", "9"]]) Traceback (most recent call last): ... ValueError: Sudoku boards must be 9x9 squares. >>> is_valid_sudoku_board( ... [["1"], ["2"], ["3"], ["4"], ["5"], ["6"], ["7"], ["8"], ["9"]] ... ) Traceback (most recent call last): ... ValueError: Sudoku boards must be 9x9 squares. """ if len(sudoku_board) != NUM_SQUARES or ( any(len(row) != NUM_SQUARES for row in sudoku_board) ): error_message = f"Sudoku boards must be {NUM_SQUARES}x{NUM_SQUARES} squares." raise ValueError(error_message) row_values: defaultdict[int, set[str]] = defaultdict(set) col_values: defaultdict[int, set[str]] = defaultdict(set) box_values: defaultdict[tuple[int, int], set[str]] = defaultdict(set) for row in range(NUM_SQUARES): for col in range(NUM_SQUARES): value = sudoku_board[row][col] if value == EMPTY_CELL: continue box = (row // 3, col // 3) if ( value in row_values[row] or value in col_values[col] or value in box_values[box] ): return False row_values[row].add(value) col_values[col].add(value) box_values[box].add(value) return True if __name__ == "__main__": from doctest import testmod from timeit import timeit testmod() print(timeit("is_valid_sudoku_board(valid_board)", globals=globals())) print(timeit("is_valid_sudoku_board(invalid_board)", globals=globals()))

""" LeetCode 36. Valid Sudoku https://leetcode.com/problems/valid-sudoku/ https://en.wikipedia.org/wiki/Sudoku Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules: - Each row must contain the digits 1-9 without repetition. - Each column must contain the digits 1-9 without repetition. - Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition. Note: A Sudoku board (partially filled) could be valid but is not necessarily solvable. Only the filled cells need to be validated according to the mentioned rules. """ from collections import defaultdict NUM_SQUARES = 9 EMPTY_CELL = "." def is_valid_sudoku_board(sudoku_board: list[list[str]]) -> bool: """ This function validates (but does not solve) a sudoku board. The board may be valid but unsolvable. >>> is_valid_sudoku_board([ ... ["5","3",".",".","7",".",".",".","."] ... ,["6",".",".","1","9","5",".",".","."] ... ,[".","9","8",".",".",".",".","6","."] ... ,["8",".",".",".","6",".",".",".","3"] ... ,["4",".",".","8",".","3",".",".","1"] ... ,["7",".",".",".","2",".",".",".","6"] ... ,[".","6",".",".",".",".","2","8","."] ... ,[".",".",".","4","1","9",".",".","5"] ... ,[".",".",".",".","8",".",".","7","9"] ... ]) True >>> is_valid_sudoku_board([ ... ["8","3",".",".","7",".",".",".","."] ... ,["6",".",".","1","9","5",".",".","."] ... ,[".","9","8",".",".",".",".","6","."] ... ,["8",".",".",".","6",".",".",".","3"] ... ,["4",".",".","8",".","3",".",".","1"] ... ,["7",".",".",".","2",".",".",".","6"] ... ,[".","6",".",".",".",".","2","8","."] ... ,[".",".",".","4","1","9",".",".","5"] ... ,[".",".",".",".","8",".",".","7","9"] ... ]) False >>> is_valid_sudoku_board([["1", "2", "3", "4", "5", "6", "7", "8", "9"]]) Traceback (most recent call last): ... ValueError: Sudoku boards must be 9x9 squares. >>> is_valid_sudoku_board( ... [["1"], ["2"], ["3"], ["4"], ["5"], ["6"], ["7"], ["8"], ["9"]] ... ) Traceback (most recent call last): ... ValueError: Sudoku boards must be 9x9 squares. """ if len(sudoku_board) != NUM_SQUARES or ( any(len(row) != NUM_SQUARES for row in sudoku_board) ): error_message = f"Sudoku boards must be {NUM_SQUARES}x{NUM_SQUARES} squares." raise ValueError(error_message) row_values: defaultdict[int, set[str]] = defaultdict(set) col_values: defaultdict[int, set[str]] = defaultdict(set) box_values: defaultdict[tuple[int, int], set[str]] = defaultdict(set) for row in range(NUM_SQUARES): for col in range(NUM_SQUARES): value = sudoku_board[row][col] if value == EMPTY_CELL: continue box = (row // 3, col // 3) if ( value in row_values[row] or value in col_values[col] or value in box_values[box] ): return False row_values[row].add(value) col_values[col].add(value) box_values[box].add(value) return True if __name__ == "__main__": from doctest import testmod from timeit import timeit testmod() print(timeit("is_valid_sudoku_board(valid_board)", globals=globals())) print(timeit("is_valid_sudoku_board(invalid_board)", globals=globals()))

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Scraping jobs given job title and location from indeed website """ from __future__ import annotations from collections.abc import Generator import requests from bs4 import BeautifulSoup url = "https://www.indeed.co.in/jobs?q=mobile+app+development&l=" def fetch_jobs(location: str = "mumbai") -> Generator[tuple[str, str], None, None]: soup = BeautifulSoup(requests.get(url + location).content, "html.parser") # This attribute finds out all the specifics listed in a job for job in soup.find_all("div", attrs={"data-tn-component": "organicJob"}): job_title = job.find("a", attrs={"data-tn-element": "jobTitle"}).text.strip() company_name = job.find("span", {"class": "company"}).text.strip() yield job_title, company_name if __name__ == "__main__": for i, job in enumerate(fetch_jobs("Bangalore"), 1): print(f"Job {i:>2} is {job[0]} at {job[1]}")

""" Scraping jobs given job title and location from indeed website """ from __future__ import annotations from collections.abc import Generator import requests from bs4 import BeautifulSoup url = "https://www.indeed.co.in/jobs?q=mobile+app+development&l=" def fetch_jobs(location: str = "mumbai") -> Generator[tuple[str, str], None, None]: soup = BeautifulSoup(requests.get(url + location).content, "html.parser") # This attribute finds out all the specifics listed in a job for job in soup.find_all("div", attrs={"data-tn-component": "organicJob"}): job_title = job.find("a", attrs={"data-tn-element": "jobTitle"}).text.strip() company_name = job.find("span", {"class": "company"}).text.strip() yield job_title, company_name if __name__ == "__main__": for i, job in enumerate(fetch_jobs("Bangalore"), 1): print(f"Job {i:>2} is {job[0]} at {job[1]}")

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" The RGB color model is an additive color model in which red, green, and blue light are added together in various ways to reproduce a broad array of colors. The name of the model comes from the initials of the three additive primary colors, red, green, and blue. Meanwhile, the HSV representation models how colors appear under light. In it, colors are represented using three components: hue, saturation and (brightness-)value. This file provides functions for converting colors from one representation to the other. (description adapted from https://en.wikipedia.org/wiki/RGB_color_model and https://en.wikipedia.org/wiki/HSL_and_HSV). """ def hsv_to_rgb(hue: float, saturation: float, value: float) -> list[int]: """ Conversion from the HSV-representation to the RGB-representation. Expected RGB-values taken from https://www.rapidtables.com/convert/color/hsv-to-rgb.html >>> hsv_to_rgb(0, 0, 0) [0, 0, 0] >>> hsv_to_rgb(0, 0, 1) [255, 255, 255] >>> hsv_to_rgb(0, 1, 1) [255, 0, 0] >>> hsv_to_rgb(60, 1, 1) [255, 255, 0] >>> hsv_to_rgb(120, 1, 1) [0, 255, 0] >>> hsv_to_rgb(240, 1, 1) [0, 0, 255] >>> hsv_to_rgb(300, 1, 1) [255, 0, 255] >>> hsv_to_rgb(180, 0.5, 0.5) [64, 128, 128] >>> hsv_to_rgb(234, 0.14, 0.88) [193, 196, 224] >>> hsv_to_rgb(330, 0.75, 0.5) [128, 32, 80] """ if hue < 0 or hue > 360: raise Exception("hue should be between 0 and 360") if saturation < 0 or saturation > 1: raise Exception("saturation should be between 0 and 1") if value < 0 or value > 1: raise Exception("value should be between 0 and 1") chroma = value * saturation hue_section = hue / 60 second_largest_component = chroma * (1 - abs(hue_section % 2 - 1)) match_value = value - chroma if hue_section >= 0 and hue_section <= 1: red = round(255 * (chroma + match_value)) green = round(255 * (second_largest_component + match_value)) blue = round(255 * (match_value)) elif hue_section > 1 and hue_section <= 2: red = round(255 * (second_largest_component + match_value)) green = round(255 * (chroma + match_value)) blue = round(255 * (match_value)) elif hue_section > 2 and hue_section <= 3: red = round(255 * (match_value)) green = round(255 * (chroma + match_value)) blue = round(255 * (second_largest_component + match_value)) elif hue_section > 3 and hue_section <= 4: red = round(255 * (match_value)) green = round(255 * (second_largest_component + match_value)) blue = round(255 * (chroma + match_value)) elif hue_section > 4 and hue_section <= 5: red = round(255 * (second_largest_component + match_value)) green = round(255 * (match_value)) blue = round(255 * (chroma + match_value)) else: red = round(255 * (chroma + match_value)) green = round(255 * (match_value)) blue = round(255 * (second_largest_component + match_value)) return [red, green, blue] def rgb_to_hsv(red: int, green: int, blue: int) -> list[float]: """ Conversion from the RGB-representation to the HSV-representation. The tested values are the reverse values from the hsv_to_rgb-doctests. Function "approximately_equal_hsv" is needed because of small deviations due to rounding for the RGB-values. >>> approximately_equal_hsv(rgb_to_hsv(0, 0, 0), [0, 0, 0]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 255, 255), [0, 0, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 0, 0), [0, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 255, 0), [60, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(0, 255, 0), [120, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(0, 0, 255), [240, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 0, 255), [300, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(64, 128, 128), [180, 0.5, 0.5]) True >>> approximately_equal_hsv(rgb_to_hsv(193, 196, 224), [234, 0.14, 0.88]) True >>> approximately_equal_hsv(rgb_to_hsv(128, 32, 80), [330, 0.75, 0.5]) True """ if red < 0 or red > 255: raise Exception("red should be between 0 and 255") if green < 0 or green > 255: raise Exception("green should be between 0 and 255") if blue < 0 or blue > 255: raise Exception("blue should be between 0 and 255") float_red = red / 255 float_green = green / 255 float_blue = blue / 255 value = max(float_red, float_green, float_blue) chroma = value - min(float_red, float_green, float_blue) saturation = 0 if value == 0 else chroma / value if chroma == 0: hue = 0.0 elif value == float_red: hue = 60 * (0 + (float_green - float_blue) / chroma) elif value == float_green: hue = 60 * (2 + (float_blue - float_red) / chroma) else: hue = 60 * (4 + (float_red - float_green) / chroma) hue = (hue + 360) % 360 return [hue, saturation, value] def approximately_equal_hsv(hsv_1: list[float], hsv_2: list[float]) -> bool: """ Utility-function to check that two hsv-colors are approximately equal >>> approximately_equal_hsv([0, 0, 0], [0, 0, 0]) True >>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.500001, 0.30001]) True >>> approximately_equal_hsv([0, 0, 0], [1, 0, 0]) False >>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.6, 0.30001]) False """ check_hue = abs(hsv_1[0] - hsv_2[0]) < 0.2 check_saturation = abs(hsv_1[1] - hsv_2[1]) < 0.002 check_value = abs(hsv_1[2] - hsv_2[2]) < 0.002 return check_hue and check_saturation and check_value

""" The RGB color model is an additive color model in which red, green, and blue light are added together in various ways to reproduce a broad array of colors. The name of the model comes from the initials of the three additive primary colors, red, green, and blue. Meanwhile, the HSV representation models how colors appear under light. In it, colors are represented using three components: hue, saturation and (brightness-)value. This file provides functions for converting colors from one representation to the other. (description adapted from https://en.wikipedia.org/wiki/RGB_color_model and https://en.wikipedia.org/wiki/HSL_and_HSV). """ def hsv_to_rgb(hue: float, saturation: float, value: float) -> list[int]: """ Conversion from the HSV-representation to the RGB-representation. Expected RGB-values taken from https://www.rapidtables.com/convert/color/hsv-to-rgb.html >>> hsv_to_rgb(0, 0, 0) [0, 0, 0] >>> hsv_to_rgb(0, 0, 1) [255, 255, 255] >>> hsv_to_rgb(0, 1, 1) [255, 0, 0] >>> hsv_to_rgb(60, 1, 1) [255, 255, 0] >>> hsv_to_rgb(120, 1, 1) [0, 255, 0] >>> hsv_to_rgb(240, 1, 1) [0, 0, 255] >>> hsv_to_rgb(300, 1, 1) [255, 0, 255] >>> hsv_to_rgb(180, 0.5, 0.5) [64, 128, 128] >>> hsv_to_rgb(234, 0.14, 0.88) [193, 196, 224] >>> hsv_to_rgb(330, 0.75, 0.5) [128, 32, 80] """ if hue < 0 or hue > 360: raise Exception("hue should be between 0 and 360") if saturation < 0 or saturation > 1: raise Exception("saturation should be between 0 and 1") if value < 0 or value > 1: raise Exception("value should be between 0 and 1") chroma = value * saturation hue_section = hue / 60 second_largest_component = chroma * (1 - abs(hue_section % 2 - 1)) match_value = value - chroma if hue_section >= 0 and hue_section <= 1: red = round(255 * (chroma + match_value)) green = round(255 * (second_largest_component + match_value)) blue = round(255 * (match_value)) elif hue_section > 1 and hue_section <= 2: red = round(255 * (second_largest_component + match_value)) green = round(255 * (chroma + match_value)) blue = round(255 * (match_value)) elif hue_section > 2 and hue_section <= 3: red = round(255 * (match_value)) green = round(255 * (chroma + match_value)) blue = round(255 * (second_largest_component + match_value)) elif hue_section > 3 and hue_section <= 4: red = round(255 * (match_value)) green = round(255 * (second_largest_component + match_value)) blue = round(255 * (chroma + match_value)) elif hue_section > 4 and hue_section <= 5: red = round(255 * (second_largest_component + match_value)) green = round(255 * (match_value)) blue = round(255 * (chroma + match_value)) else: red = round(255 * (chroma + match_value)) green = round(255 * (match_value)) blue = round(255 * (second_largest_component + match_value)) return [red, green, blue] def rgb_to_hsv(red: int, green: int, blue: int) -> list[float]: """ Conversion from the RGB-representation to the HSV-representation. The tested values are the reverse values from the hsv_to_rgb-doctests. Function "approximately_equal_hsv" is needed because of small deviations due to rounding for the RGB-values. >>> approximately_equal_hsv(rgb_to_hsv(0, 0, 0), [0, 0, 0]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 255, 255), [0, 0, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 0, 0), [0, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 255, 0), [60, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(0, 255, 0), [120, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(0, 0, 255), [240, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(255, 0, 255), [300, 1, 1]) True >>> approximately_equal_hsv(rgb_to_hsv(64, 128, 128), [180, 0.5, 0.5]) True >>> approximately_equal_hsv(rgb_to_hsv(193, 196, 224), [234, 0.14, 0.88]) True >>> approximately_equal_hsv(rgb_to_hsv(128, 32, 80), [330, 0.75, 0.5]) True """ if red < 0 or red > 255: raise Exception("red should be between 0 and 255") if green < 0 or green > 255: raise Exception("green should be between 0 and 255") if blue < 0 or blue > 255: raise Exception("blue should be between 0 and 255") float_red = red / 255 float_green = green / 255 float_blue = blue / 255 value = max(float_red, float_green, float_blue) chroma = value - min(float_red, float_green, float_blue) saturation = 0 if value == 0 else chroma / value if chroma == 0: hue = 0.0 elif value == float_red: hue = 60 * (0 + (float_green - float_blue) / chroma) elif value == float_green: hue = 60 * (2 + (float_blue - float_red) / chroma) else: hue = 60 * (4 + (float_red - float_green) / chroma) hue = (hue + 360) % 360 return [hue, saturation, value] def approximately_equal_hsv(hsv_1: list[float], hsv_2: list[float]) -> bool: """ Utility-function to check that two hsv-colors are approximately equal >>> approximately_equal_hsv([0, 0, 0], [0, 0, 0]) True >>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.500001, 0.30001]) True >>> approximately_equal_hsv([0, 0, 0], [1, 0, 0]) False >>> approximately_equal_hsv([180, 0.5, 0.3], [179.9999, 0.6, 0.30001]) False """ check_hue = abs(hsv_1[0] - hsv_2[0]) < 0.2 check_saturation = abs(hsv_1[1] - hsv_2[1]) < 0.002 check_value = abs(hsv_1[2] - hsv_2[2]) < 0.002 return check_hue and check_saturation and check_value

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Python program for the Fractionated Morse Cipher. The Fractionated Morse cipher first converts the plaintext to Morse code, then enciphers fixed-size blocks of Morse code back to letters. This procedure means plaintext letters are mixed into the ciphertext letters, making it more secure than substitution ciphers. http://practicalcryptography.com/ciphers/fractionated-morse-cipher/ """ import string MORSE_CODE_DICT = { "A": ".-", "B": "-...", "C": "-.-.", "D": "-..", "E": ".", "F": "..-.", "G": "--.", "H": "....", "I": "..", "J": ".---", "K": "-.-", "L": ".-..", "M": "--", "N": "-.", "O": "---", "P": ".--.", "Q": "--.-", "R": ".-.", "S": "...", "T": "-", "U": "..-", "V": "...-", "W": ".--", "X": "-..-", "Y": "-.--", "Z": "--..", " ": "", } # Define possible trigrams of Morse code MORSE_COMBINATIONS = [ "...", "..-", "..x", ".-.", ".--", ".-x", ".x.", ".x-", ".xx", "-..", "-.-", "-.x", "--.", "---", "--x", "-x.", "-x-", "-xx", "x..", "x.-", "x.x", "x-.", "x--", "x-x", "xx.", "xx-", "xxx", ] # Create a reverse dictionary for Morse code REVERSE_DICT = {value: key for key, value in MORSE_CODE_DICT.items()} def encode_to_morse(plaintext: str) -> str: """Encode a plaintext message into Morse code. Args: plaintext: The plaintext message to encode. Returns: The Morse code representation of the plaintext message. Example: >>> encode_to_morse("defend the east") '-..x.x..-.x.x-.x-..xx-x....x.xx.x.-x...x-' """ return "x".join([MORSE_CODE_DICT.get(letter.upper(), "") for letter in plaintext]) def encrypt_fractionated_morse(plaintext: str, key: str) -> str: """Encrypt a plaintext message using Fractionated Morse Cipher. Args: plaintext: The plaintext message to encrypt. key: The encryption key. Returns: The encrypted ciphertext. Example: >>> encrypt_fractionated_morse("defend the east","Roundtable") 'ESOAVVLJRSSTRX' """ morse_code = encode_to_morse(plaintext) key = key.upper() + string.ascii_uppercase key = "".join(sorted(set(key), key=key.find)) # Ensure morse_code length is a multiple of 3 padding_length = 3 - (len(morse_code) % 3) morse_code += "x" * padding_length fractionated_morse_dict = {v: k for k, v in zip(key, MORSE_COMBINATIONS)} fractionated_morse_dict["xxx"] = "" encrypted_text = "".join( [ fractionated_morse_dict[morse_code[i : i + 3]] for i in range(0, len(morse_code), 3) ] ) return encrypted_text def decrypt_fractionated_morse(ciphertext: str, key: str) -> str: """Decrypt a ciphertext message encrypted with Fractionated Morse Cipher. Args: ciphertext: The ciphertext message to decrypt. key: The decryption key. Returns: The decrypted plaintext message. Example: >>> decrypt_fractionated_morse("ESOAVVLJRSSTRX","Roundtable") 'DEFEND THE EAST' """ key = key.upper() + string.ascii_uppercase key = "".join(sorted(set(key), key=key.find)) inverse_fractionated_morse_dict = dict(zip(key, MORSE_COMBINATIONS)) morse_code = "".join( [inverse_fractionated_morse_dict.get(letter, "") for letter in ciphertext] ) decrypted_text = "".join( [REVERSE_DICT[code] for code in morse_code.split("x")] ).strip() return decrypted_text if __name__ == "__main__": """ Example usage of Fractionated Morse Cipher. """ plaintext = "defend the east" print("Plain Text:", plaintext) key = "ROUNDTABLE" ciphertext = encrypt_fractionated_morse(plaintext, key) print("Encrypted:", ciphertext) decrypted_text = decrypt_fractionated_morse(ciphertext, key) print("Decrypted:", decrypted_text)

""" Python program for the Fractionated Morse Cipher. The Fractionated Morse cipher first converts the plaintext to Morse code, then enciphers fixed-size blocks of Morse code back to letters. This procedure means plaintext letters are mixed into the ciphertext letters, making it more secure than substitution ciphers. http://practicalcryptography.com/ciphers/fractionated-morse-cipher/ """ import string MORSE_CODE_DICT = { "A": ".-", "B": "-...", "C": "-.-.", "D": "-..", "E": ".", "F": "..-.", "G": "--.", "H": "....", "I": "..", "J": ".---", "K": "-.-", "L": ".-..", "M": "--", "N": "-.", "O": "---", "P": ".--.", "Q": "--.-", "R": ".-.", "S": "...", "T": "-", "U": "..-", "V": "...-", "W": ".--", "X": "-..-", "Y": "-.--", "Z": "--..", " ": "", } # Define possible trigrams of Morse code MORSE_COMBINATIONS = [ "...", "..-", "..x", ".-.", ".--", ".-x", ".x.", ".x-", ".xx", "-..", "-.-", "-.x", "--.", "---", "--x", "-x.", "-x-", "-xx", "x..", "x.-", "x.x", "x-.", "x--", "x-x", "xx.", "xx-", "xxx", ] # Create a reverse dictionary for Morse code REVERSE_DICT = {value: key for key, value in MORSE_CODE_DICT.items()} def encode_to_morse(plaintext: str) -> str: """Encode a plaintext message into Morse code. Args: plaintext: The plaintext message to encode. Returns: The Morse code representation of the plaintext message. Example: >>> encode_to_morse("defend the east") '-..x.x..-.x.x-.x-..xx-x....x.xx.x.-x...x-' """ return "x".join([MORSE_CODE_DICT.get(letter.upper(), "") for letter in plaintext]) def encrypt_fractionated_morse(plaintext: str, key: str) -> str: """Encrypt a plaintext message using Fractionated Morse Cipher. Args: plaintext: The plaintext message to encrypt. key: The encryption key. Returns: The encrypted ciphertext. Example: >>> encrypt_fractionated_morse("defend the east","Roundtable") 'ESOAVVLJRSSTRX' """ morse_code = encode_to_morse(plaintext) key = key.upper() + string.ascii_uppercase key = "".join(sorted(set(key), key=key.find)) # Ensure morse_code length is a multiple of 3 padding_length = 3 - (len(morse_code) % 3) morse_code += "x" * padding_length fractionated_morse_dict = {v: k for k, v in zip(key, MORSE_COMBINATIONS)} fractionated_morse_dict["xxx"] = "" encrypted_text = "".join( [ fractionated_morse_dict[morse_code[i : i + 3]] for i in range(0, len(morse_code), 3) ] ) return encrypted_text def decrypt_fractionated_morse(ciphertext: str, key: str) -> str: """Decrypt a ciphertext message encrypted with Fractionated Morse Cipher. Args: ciphertext: The ciphertext message to decrypt. key: The decryption key. Returns: The decrypted plaintext message. Example: >>> decrypt_fractionated_morse("ESOAVVLJRSSTRX","Roundtable") 'DEFEND THE EAST' """ key = key.upper() + string.ascii_uppercase key = "".join(sorted(set(key), key=key.find)) inverse_fractionated_morse_dict = dict(zip(key, MORSE_COMBINATIONS)) morse_code = "".join( [inverse_fractionated_morse_dict.get(letter, "") for letter in ciphertext] ) decrypted_text = "".join( [REVERSE_DICT[code] for code in morse_code.split("x")] ).strip() return decrypted_text if __name__ == "__main__": """ Example usage of Fractionated Morse Cipher. """ plaintext = "defend the east" print("Plain Text:", plaintext) key = "ROUNDTABLE" ciphertext = encrypt_fractionated_morse(plaintext, key) print("Encrypted:", ciphertext) decrypted_text = decrypt_fractionated_morse(ciphertext, key) print("Decrypted:", decrypted_text)

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Project Euler Problem 79: https://projecteuler.net/problem=79 Passcode derivation A common security method used for online banking is to ask the user for three random characters from a passcode. For example, if the passcode was 531278, they may ask for the 2nd, 3rd, and 5th characters; the expected reply would be: 317. The text file, keylog.txt, contains fifty successful login attempts. Given that the three characters are always asked for in order, analyse the file so as to determine the shortest possible secret passcode of unknown length. """ import itertools from pathlib import Path def find_secret_passcode(logins: list[str]) -> int: """ Returns the shortest possible secret passcode of unknown length. >>> find_secret_passcode(["135", "259", "235", "189", "690", "168", "120", ... "136", "289", "589", "160", "165", "580", "369", "250", "280"]) 12365890 >>> find_secret_passcode(["426", "281", "061", "819" "268", "406", "420", ... "428", "209", "689", "019", "421", "469", "261", "681", "201"]) 4206819 """ # Split each login by character e.g. '319' -> ('3', '1', '9') split_logins = [tuple(login) for login in logins] unique_chars = {char for login in split_logins for char in login} for permutation in itertools.permutations(unique_chars): satisfied = True for login in logins: if not ( permutation.index(login[0]) < permutation.index(login[1]) < permutation.index(login[2]) ): satisfied = False break if satisfied: return int("".join(permutation)) raise Exception("Unable to find the secret passcode") def solution(input_file: str = "keylog.txt") -> int: """ Returns the shortest possible secret passcode of unknown length for successful login attempts given by `input_file` text file. >>> solution("keylog_test.txt") 6312980 """ logins = Path(__file__).parent.joinpath(input_file).read_text().splitlines() return find_secret_passcode(logins) if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 79: https://projecteuler.net/problem=79 Passcode derivation A common security method used for online banking is to ask the user for three random characters from a passcode. For example, if the passcode was 531278, they may ask for the 2nd, 3rd, and 5th characters; the expected reply would be: 317. The text file, keylog.txt, contains fifty successful login attempts. Given that the three characters are always asked for in order, analyse the file so as to determine the shortest possible secret passcode of unknown length. """ import itertools from pathlib import Path def find_secret_passcode(logins: list[str]) -> int: """ Returns the shortest possible secret passcode of unknown length. >>> find_secret_passcode(["135", "259", "235", "189", "690", "168", "120", ... "136", "289", "589", "160", "165", "580", "369", "250", "280"]) 12365890 >>> find_secret_passcode(["426", "281", "061", "819" "268", "406", "420", ... "428", "209", "689", "019", "421", "469", "261", "681", "201"]) 4206819 """ # Split each login by character e.g. '319' -> ('3', '1', '9') split_logins = [tuple(login) for login in logins] unique_chars = {char for login in split_logins for char in login} for permutation in itertools.permutations(unique_chars): satisfied = True for login in logins: if not ( permutation.index(login[0]) < permutation.index(login[1]) < permutation.index(login[2]) ): satisfied = False break if satisfied: return int("".join(permutation)) raise Exception("Unable to find the secret passcode") def solution(input_file: str = "keylog.txt") -> int: """ Returns the shortest possible secret passcode of unknown length for successful login attempts given by `input_file` text file. >>> solution("keylog_test.txt") 6312980 """ logins = Path(__file__).parent.joinpath(input_file).read_text().splitlines() return find_secret_passcode(logins) if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

from __future__ import annotations import sys from collections import deque from typing import Generic, TypeVar T = TypeVar("T") class LRUCache(Generic[T]): """ Page Replacement Algorithm, Least Recently Used (LRU) Caching. >>> lru_cache: LRUCache[str | int] = LRUCache(4) >>> lru_cache.refer("A") >>> lru_cache.refer(2) >>> lru_cache.refer(3) >>> lru_cache LRUCache(4) => [3, 2, 'A'] >>> lru_cache.refer("A") >>> lru_cache LRUCache(4) => ['A', 3, 2] >>> lru_cache.refer(4) >>> lru_cache.refer(5) >>> lru_cache LRUCache(4) => [5, 4, 'A', 3] """ dq_store: deque[T] # Cache store of keys key_reference: set[T] # References of the keys in cache _MAX_CAPACITY: int = 10 # Maximum capacity of cache def __init__(self, n: int) -> None: """Creates an empty store and map for the keys. The LRUCache is set the size n. """ self.dq_store = deque() self.key_reference = set() if not n: LRUCache._MAX_CAPACITY = sys.maxsize elif n < 0: raise ValueError("n should be an integer greater than 0.") else: LRUCache._MAX_CAPACITY = n def refer(self, x: T) -> None: """ Looks for a page in the cache store and adds reference to the set. Remove the least recently used key if the store is full. Update store to reflect recent access. """ if x not in self.key_reference: if len(self.dq_store) == LRUCache._MAX_CAPACITY: last_element = self.dq_store.pop() self.key_reference.remove(last_element) else: self.dq_store.remove(x) self.dq_store.appendleft(x) self.key_reference.add(x) def display(self) -> None: """ Prints all the elements in the store. """ for k in self.dq_store: print(k) def __repr__(self) -> str: return f"LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store)}" if __name__ == "__main__": import doctest doctest.testmod() lru_cache: LRUCache[str | int] = LRUCache(4) lru_cache.refer("A") lru_cache.refer(2) lru_cache.refer(3) lru_cache.refer("A") lru_cache.refer(4) lru_cache.refer(5) lru_cache.display() print(lru_cache) assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"

from __future__ import annotations import sys from collections import deque from typing import Generic, TypeVar T = TypeVar("T") class LRUCache(Generic[T]): """ Page Replacement Algorithm, Least Recently Used (LRU) Caching. >>> lru_cache: LRUCache[str | int] = LRUCache(4) >>> lru_cache.refer("A") >>> lru_cache.refer(2) >>> lru_cache.refer(3) >>> lru_cache LRUCache(4) => [3, 2, 'A'] >>> lru_cache.refer("A") >>> lru_cache LRUCache(4) => ['A', 3, 2] >>> lru_cache.refer(4) >>> lru_cache.refer(5) >>> lru_cache LRUCache(4) => [5, 4, 'A', 3] """ dq_store: deque[T] # Cache store of keys key_reference: set[T] # References of the keys in cache _MAX_CAPACITY: int = 10 # Maximum capacity of cache def __init__(self, n: int) -> None: """Creates an empty store and map for the keys. The LRUCache is set the size n. """ self.dq_store = deque() self.key_reference = set() if not n: LRUCache._MAX_CAPACITY = sys.maxsize elif n < 0: raise ValueError("n should be an integer greater than 0.") else: LRUCache._MAX_CAPACITY = n def refer(self, x: T) -> None: """ Looks for a page in the cache store and adds reference to the set. Remove the least recently used key if the store is full. Update store to reflect recent access. """ if x not in self.key_reference: if len(self.dq_store) == LRUCache._MAX_CAPACITY: last_element = self.dq_store.pop() self.key_reference.remove(last_element) else: self.dq_store.remove(x) self.dq_store.appendleft(x) self.key_reference.add(x) def display(self) -> None: """ Prints all the elements in the store. """ for k in self.dq_store: print(k) def __repr__(self) -> str: return f"LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store)}" if __name__ == "__main__": import doctest doctest.testmod() lru_cache: LRUCache[str | int] = LRUCache(4) lru_cache.refer("A") lru_cache.refer(2) lru_cache.refer(3) lru_cache.refer("A") lru_cache.refer(4) lru_cache.refer(5) lru_cache.display() print(lru_cache) assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: """ This solution is based on the pattern that the successive numbers in the series follow: 0+3,+2,+1,+3,+1,+2,+3. Returns the sum of all the multiples of 3 or 5 below n. >>> solution(3) 0 >>> solution(4) 3 >>> solution(10) 23 >>> solution(600) 83700 """ total = 0 num = 0 while 1: num += 3 if num >= n: break total += num num += 2 if num >= n: break total += num num += 1 if num >= n: break total += num num += 3 if num >= n: break total += num num += 1 if num >= n: break total += num num += 2 if num >= n: break total += num num += 3 if num >= n: break total += num return total if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 1: https://projecteuler.net/problem=1 Multiples of 3 and 5 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000. """ def solution(n: int = 1000) -> int: """ This solution is based on the pattern that the successive numbers in the series follow: 0+3,+2,+1,+3,+1,+2,+3. Returns the sum of all the multiples of 3 or 5 below n. >>> solution(3) 0 >>> solution(4) 3 >>> solution(10) 23 >>> solution(600) 83700 """ total = 0 num = 0 while 1: num += 3 if num >= n: break total += num num += 2 if num >= n: break total += num num += 1 if num >= n: break total += num num += 3 if num >= n: break total += num num += 1 if num >= n: break total += num num += 2 if num >= n: break total += num num += 3 if num >= n: break total += num return total if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Project Euler Problem 6: https://projecteuler.net/problem=6 Sum square difference The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640. Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum. """ def solution(n: int = 100) -> int: """ Returns the difference between the sum of the squares of the first n natural numbers and the square of the sum. >>> solution(10) 2640 >>> solution(15) 13160 >>> solution(20) 41230 >>> solution(50) 1582700 """ sum_of_squares = 0 sum_of_ints = 0 for i in range(1, n + 1): sum_of_squares += i**2 sum_of_ints += i return sum_of_ints**2 - sum_of_squares if __name__ == "__main__": print(f"{solution() = }")

""" Project Euler Problem 6: https://projecteuler.net/problem=6 Sum square difference The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 55^2 = 3025 Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640. Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum. """ def solution(n: int = 100) -> int: """ Returns the difference between the sum of the squares of the first n natural numbers and the square of the sum. >>> solution(10) 2640 >>> solution(15) 13160 >>> solution(20) 41230 >>> solution(50) 1582700 """ sum_of_squares = 0 sum_of_ints = 0 for i in range(1, n + 1): sum_of_squares += i**2 sum_of_ints += i return sum_of_ints**2 - sum_of_squares if __name__ == "__main__": print(f"{solution() = }")

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

# A naive recursive implementation of 0-1 Knapsack Problem This overview is taken from: https://en.wikipedia.org/wiki/Knapsack_problem --- ## Overview The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897 The name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. --- ## Documentation This module uses docstrings to enable the use of Python's in-built `help(...)` function. For instance, try `help(Vector)`, `help(unit_basis_vector)`, and `help(CLASSNAME.METHODNAME)`. --- ## Usage Import the module `knapsack.py` from the **.** directory into your project. --- ## Tests `.` contains Python unit tests which can be run with `python3 -m unittest -v`.

# A naive recursive implementation of 0-1 Knapsack Problem This overview is taken from: https://en.wikipedia.org/wiki/Knapsack_problem --- ## Overview The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897 The name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. --- ## Documentation This module uses docstrings to enable the use of Python's in-built `help(...)` function. For instance, try `help(Vector)`, `help(unit_basis_vector)`, and `help(CLASSNAME.METHODNAME)`. --- ## Usage Import the module `knapsack.py` from the **.** directory into your project. --- ## Tests `.` contains Python unit tests which can be run with `python3 -m unittest -v`.

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

#!/usr/bin/env python3 """ Build quantum teleportation circuit using three quantum bits and 1 classical bit. The main idea is to send one qubit from Alice to Bob using the entanglement properties. This experiment run in IBM Q simulator with 1000 shots. . References: https://en.wikipedia.org/wiki/Quantum_teleportation https://qiskit.org/textbook/ch-algorithms/teleportation.html """ import numpy as np import qiskit from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute def quantum_teleportation( theta: float = np.pi / 2, phi: float = np.pi / 2, lam: float = np.pi / 2 ) -> qiskit.result.counts.Counts: """ # >>> quantum_teleportation() #{'00': 500, '11': 500} # ideally # ┌─────────────────┐ ┌───┐ #qr_0: ┤ U(π/2,π/2,π/2) ├───────■──┤ H ├─■───────── # └──────┬───┬──────┘ ┌─┴─┐└───┘ │ #qr_1: ───────┤ H ├─────────■──┤ X ├──────┼───■───── # └───┘ ┌─┴─┐└───┘ │ ┌─┴─┐┌─┐ #qr_2: ───────────────────┤ X ├───────────■─┤ X ├┤M├ # └───┘ └───┘└╥┘ #cr: 1/═══════════════════════════════════════════╩═ Args: theta (float): Single qubit rotation U Gate theta parameter. Default to np.pi/2 phi (float): Single qubit rotation U Gate phi parameter. Default to np.pi/2 lam (float): Single qubit rotation U Gate lam parameter. Default to np.pi/2 Returns: qiskit.result.counts.Counts: Teleported qubit counts. """ qr = QuantumRegister(3, "qr") # Define the number of quantum bits cr = ClassicalRegister(1, "cr") # Define the number of classical bits quantum_circuit = QuantumCircuit(qr, cr) # Define the quantum circuit. # Build the circuit quantum_circuit.u(theta, phi, lam, 0) # Quantum State to teleport quantum_circuit.h(1) # add hadamard gate quantum_circuit.cx( 1, 2 ) # add control gate with qubit 1 as control and 2 as target. quantum_circuit.cx(0, 1) quantum_circuit.h(0) quantum_circuit.cz(0, 2) # add control z gate. quantum_circuit.cx(1, 2) quantum_circuit.measure([2], [0]) # measure the qubit. # Simulate the circuit using qasm simulator backend = Aer.get_backend("aer_simulator") job = execute(quantum_circuit, backend, shots=1000) return job.result().get_counts(quantum_circuit) if __name__ == "__main__": print( "Total count for teleported state is: " f"{quantum_teleportation(np.pi/2, np.pi/2, np.pi/2)}" )

#!/usr/bin/env python3 """ Build quantum teleportation circuit using three quantum bits and 1 classical bit. The main idea is to send one qubit from Alice to Bob using the entanglement properties. This experiment run in IBM Q simulator with 1000 shots. . References: https://en.wikipedia.org/wiki/Quantum_teleportation https://qiskit.org/textbook/ch-algorithms/teleportation.html """ import numpy as np import qiskit from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute def quantum_teleportation( theta: float = np.pi / 2, phi: float = np.pi / 2, lam: float = np.pi / 2 ) -> qiskit.result.counts.Counts: """ # >>> quantum_teleportation() #{'00': 500, '11': 500} # ideally # ┌─────────────────┐ ┌───┐ #qr_0: ┤ U(π/2,π/2,π/2) ├───────■──┤ H ├─■───────── # └──────┬───┬──────┘ ┌─┴─┐└───┘ │ #qr_1: ───────┤ H ├─────────■──┤ X ├──────┼───■───── # └───┘ ┌─┴─┐└───┘ │ ┌─┴─┐┌─┐ #qr_2: ───────────────────┤ X ├───────────■─┤ X ├┤M├ # └───┘ └───┘└╥┘ #cr: 1/═══════════════════════════════════════════╩═ Args: theta (float): Single qubit rotation U Gate theta parameter. Default to np.pi/2 phi (float): Single qubit rotation U Gate phi parameter. Default to np.pi/2 lam (float): Single qubit rotation U Gate lam parameter. Default to np.pi/2 Returns: qiskit.result.counts.Counts: Teleported qubit counts. """ qr = QuantumRegister(3, "qr") # Define the number of quantum bits cr = ClassicalRegister(1, "cr") # Define the number of classical bits quantum_circuit = QuantumCircuit(qr, cr) # Define the quantum circuit. # Build the circuit quantum_circuit.u(theta, phi, lam, 0) # Quantum State to teleport quantum_circuit.h(1) # add hadamard gate quantum_circuit.cx( 1, 2 ) # add control gate with qubit 1 as control and 2 as target. quantum_circuit.cx(0, 1) quantum_circuit.h(0) quantum_circuit.cz(0, 2) # add control z gate. quantum_circuit.cx(1, 2) quantum_circuit.measure([2], [0]) # measure the qubit. # Simulate the circuit using qasm simulator backend = Aer.get_backend("aer_simulator") job = execute(quantum_circuit, backend, shots=1000) return job.result().get_counts(quantum_circuit) if __name__ == "__main__": print( "Total count for teleported state is: " f"{quantum_teleportation(np.pi/2, np.pi/2, np.pi/2)}" )

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Program to encode and decode Baconian or Bacon's Cipher Wikipedia reference : https://en.wikipedia.org/wiki/Bacon%27s_cipher """ encode_dict = { "a": "AAAAA", "b": "AAAAB", "c": "AAABA", "d": "AAABB", "e": "AABAA", "f": "AABAB", "g": "AABBA", "h": "AABBB", "i": "ABAAA", "j": "BBBAA", "k": "ABAAB", "l": "ABABA", "m": "ABABB", "n": "ABBAA", "o": "ABBAB", "p": "ABBBA", "q": "ABBBB", "r": "BAAAA", "s": "BAAAB", "t": "BAABA", "u": "BAABB", "v": "BBBAB", "w": "BABAA", "x": "BABAB", "y": "BABBA", "z": "BABBB", " ": " ", } decode_dict = {value: key for key, value in encode_dict.items()} def encode(word: str) -> str: """ Encodes to Baconian cipher >>> encode("hello") 'AABBBAABAAABABAABABAABBAB' >>> encode("hello world") 'AABBBAABAAABABAABABAABBAB BABAAABBABBAAAAABABAAAABB' >>> encode("hello world!") Traceback (most recent call last): ... Exception: encode() accepts only letters of the alphabet and spaces """ encoded = "" for letter in word.lower(): if letter.isalpha() or letter == " ": encoded += encode_dict[letter] else: raise Exception("encode() accepts only letters of the alphabet and spaces") return encoded def decode(coded: str) -> str: """ Decodes from Baconian cipher >>> decode("AABBBAABAAABABAABABAABBAB BABAAABBABBAAAAABABAAAABB") 'hello world' >>> decode("AABBBAABAAABABAABABAABBAB") 'hello' >>> decode("AABBBAABAAABABAABABAABBAB BABAAABBABBAAAAABABAAAABB!") Traceback (most recent call last): ... Exception: decode() accepts only 'A', 'B' and spaces """ if set(coded) - {"A", "B", " "} != set(): raise Exception("decode() accepts only 'A', 'B' and spaces") decoded = "" for word in coded.split(): while len(word) != 0: decoded += decode_dict[word[:5]] word = word[5:] decoded += " " return decoded.strip() if __name__ == "__main__": from doctest import testmod testmod()

""" Program to encode and decode Baconian or Bacon's Cipher Wikipedia reference : https://en.wikipedia.org/wiki/Bacon%27s_cipher """ encode_dict = { "a": "AAAAA", "b": "AAAAB", "c": "AAABA", "d": "AAABB", "e": "AABAA", "f": "AABAB", "g": "AABBA", "h": "AABBB", "i": "ABAAA", "j": "BBBAA", "k": "ABAAB", "l": "ABABA", "m": "ABABB", "n": "ABBAA", "o": "ABBAB", "p": "ABBBA", "q": "ABBBB", "r": "BAAAA", "s": "BAAAB", "t": "BAABA", "u": "BAABB", "v": "BBBAB", "w": "BABAA", "x": "BABAB", "y": "BABBA", "z": "BABBB", " ": " ", } decode_dict = {value: key for key, value in encode_dict.items()} def encode(word: str) -> str: """ Encodes to Baconian cipher >>> encode("hello") 'AABBBAABAAABABAABABAABBAB' >>> encode("hello world") 'AABBBAABAAABABAABABAABBAB BABAAABBABBAAAAABABAAAABB' >>> encode("hello world!") Traceback (most recent call last): ... Exception: encode() accepts only letters of the alphabet and spaces """ encoded = "" for letter in word.lower(): if letter.isalpha() or letter == " ": encoded += encode_dict[letter] else: raise Exception("encode() accepts only letters of the alphabet and spaces") return encoded def decode(coded: str) -> str: """ Decodes from Baconian cipher >>> decode("AABBBAABAAABABAABABAABBAB BABAAABBABBAAAAABABAAAABB") 'hello world' >>> decode("AABBBAABAAABABAABABAABBAB") 'hello' >>> decode("AABBBAABAAABABAABABAABBAB BABAAABBABBAAAAABABAAAABB!") Traceback (most recent call last): ... Exception: decode() accepts only 'A', 'B' and spaces """ if set(coded) - {"A", "B", " "} != set(): raise Exception("decode() accepts only 'A', 'B' and spaces") decoded = "" for word in coded.split(): while len(word) != 0: decoded += decode_dict[word[:5]] word = word[5:] decoded += " " return decoded.strip() if __name__ == "__main__": from doctest import testmod testmod()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

# https://www.tutorialspoint.com/python3/bitwise_operators_example.htm def binary_and(a: int, b: int) -> str: """ Take in 2 integers, convert them to binary, return a binary number that is the result of a binary and operation on the integers provided. >>> binary_and(25, 32) '0b000000' >>> binary_and(37, 50) '0b100000' >>> binary_and(21, 30) '0b10100' >>> binary_and(58, 73) '0b0001000' >>> binary_and(0, 255) '0b00000000' >>> binary_and(256, 256) '0b100000000' >>> binary_and(0, -1) Traceback (most recent call last): ... ValueError: the value of both inputs must be positive >>> binary_and(0, 1.1) Traceback (most recent call last): ... TypeError: 'float' object cannot be interpreted as an integer >>> binary_and("0", "1") Traceback (most recent call last): ... TypeError: '<' not supported between instances of 'str' and 'int' """ if a < 0 or b < 0: raise ValueError("the value of both inputs must be positive") a_binary = str(bin(a))[2:] # remove the leading "0b" b_binary = str(bin(b))[2:] # remove the leading "0b" max_len = max(len(a_binary), len(b_binary)) return "0b" + "".join( str(int(char_a == "1" and char_b == "1")) for char_a, char_b in zip(a_binary.zfill(max_len), b_binary.zfill(max_len)) ) if __name__ == "__main__": import doctest doctest.testmod()

# https://www.tutorialspoint.com/python3/bitwise_operators_example.htm def binary_and(a: int, b: int) -> str: """ Take in 2 integers, convert them to binary, return a binary number that is the result of a binary and operation on the integers provided. >>> binary_and(25, 32) '0b000000' >>> binary_and(37, 50) '0b100000' >>> binary_and(21, 30) '0b10100' >>> binary_and(58, 73) '0b0001000' >>> binary_and(0, 255) '0b00000000' >>> binary_and(256, 256) '0b100000000' >>> binary_and(0, -1) Traceback (most recent call last): ... ValueError: the value of both inputs must be positive >>> binary_and(0, 1.1) Traceback (most recent call last): ... TypeError: 'float' object cannot be interpreted as an integer >>> binary_and("0", "1") Traceback (most recent call last): ... TypeError: '<' not supported between instances of 'str' and 'int' """ if a < 0 or b < 0: raise ValueError("the value of both inputs must be positive") a_binary = str(bin(a))[2:] # remove the leading "0b" b_binary = str(bin(b))[2:] # remove the leading "0b" max_len = max(len(a_binary), len(b_binary)) return "0b" + "".join( str(int(char_a == "1" and char_b == "1")) for char_a, char_b in zip(a_binary.zfill(max_len), b_binary.zfill(max_len)) ) if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

import numpy as np from numpy import ndarray from scipy.optimize import Bounds, LinearConstraint, minimize def norm_squared(vector: ndarray) -> float: """ Return the squared second norm of vector norm_squared(v) = sum(x * x for x in v) Args: vector (ndarray): input vector Returns: float: squared second norm of vector >>> norm_squared([1, 2]) 5 >>> norm_squared(np.asarray([1, 2])) 5 >>> norm_squared([0, 0]) 0 """ return np.dot(vector, vector) class SVC: """ Support Vector Classifier Args: kernel (str): kernel to use. Default: linear Possible choices: - linear regularization: constraint for soft margin (data not linearly separable) Default: unbound >>> SVC(kernel="asdf") Traceback (most recent call last): ... ValueError: Unknown kernel: asdf >>> SVC(kernel="rbf") Traceback (most recent call last): ... ValueError: rbf kernel requires gamma >>> SVC(kernel="rbf", gamma=-1) Traceback (most recent call last): ... ValueError: gamma must be > 0 """ def __init__( self, *, regularization: float = np.inf, kernel: str = "linear", gamma: float = 0.0, ) -> None: self.regularization = regularization self.gamma = gamma if kernel == "linear": self.kernel = self.__linear elif kernel == "rbf": if self.gamma == 0: raise ValueError("rbf kernel requires gamma") if not isinstance(self.gamma, (float, int)): raise ValueError("gamma must be float or int") if not self.gamma > 0: raise ValueError("gamma must be > 0") self.kernel = self.__rbf # in the future, there could be a default value like in sklearn # sklear: def_gamma = 1/(n_features * X.var()) (wiki) # previously it was 1/(n_features) else: msg = f"Unknown kernel: {kernel}" raise ValueError(msg) # kernels def __linear(self, vector1: ndarray, vector2: ndarray) -> float: """Linear kernel (as if no kernel used at all)""" return np.dot(vector1, vector2) def __rbf(self, vector1: ndarray, vector2: ndarray) -> float: """ RBF: Radial Basis Function Kernel Note: for more information see: https://en.wikipedia.org/wiki/Radial_basis_function_kernel Args: vector1 (ndarray): first vector vector2 (ndarray): second vector) Returns: float: exp(-(gamma * norm_squared(vector1 - vector2))) """ return np.exp(-(self.gamma * norm_squared(vector1 - vector2))) def fit(self, observations: list[ndarray], classes: ndarray) -> None: """ Fits the SVC with a set of observations. Args: observations (list[ndarray]): list of observations classes (ndarray): classification of each observation (in {1, -1}) """ self.observations = observations self.classes = classes # using Wolfe's Dual to calculate w. # Primal problem: minimize 1/2*norm_squared(w) # constraint: yn(w . xn + b) >= 1 # # With l a vector # Dual problem: maximize sum_n(ln) - # 1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm)) # constraint: self.C >= ln >= 0 # and sum_n(ln*yn) = 0 # Then we get w using w = sum_n(ln*yn*xn) # At the end we can get b ~= mean(yn - w . xn) # # Since we use kernels, we only need l_star to calculate b # and to classify observations (n,) = np.shape(classes) def to_minimize(candidate: ndarray) -> float: """ Opposite of the function to maximize Args: candidate (ndarray): candidate array to test Return: float: Wolfe's Dual result to minimize """ s = 0 (n,) = np.shape(candidate) for i in range(n): for j in range(n): s += ( candidate[i] * candidate[j] * classes[i] * classes[j] * self.kernel(observations[i], observations[j]) ) return 1 / 2 * s - sum(candidate) ly_contraint = LinearConstraint(classes, 0, 0) l_bounds = Bounds(0, self.regularization) l_star = minimize( to_minimize, np.ones(n), bounds=l_bounds, constraints=[ly_contraint] ).x self.optimum = l_star # calculating mean offset of separation plane to points s = 0 for i in range(n): for j in range(n): s += classes[i] - classes[i] * self.optimum[i] * self.kernel( observations[i], observations[j] ) self.offset = s / n def predict(self, observation: ndarray) -> int: """ Get the expected class of an observation Args: observation (Vector): observation Returns: int {1, -1}: expected class >>> xs = [ ... np.asarray([0, 1]), np.asarray([0, 2]), ... np.asarray([1, 1]), np.asarray([1, 2]) ... ] >>> y = np.asarray([1, 1, -1, -1]) >>> s = SVC() >>> s.fit(xs, y) >>> s.predict(np.asarray([0, 1])) 1 >>> s.predict(np.asarray([1, 1])) -1 >>> s.predict(np.asarray([2, 2])) -1 """ s = sum( self.optimum[n] * self.classes[n] * self.kernel(self.observations[n], observation) for n in range(len(self.classes)) ) return 1 if s + self.offset >= 0 else -1 if __name__ == "__main__": import doctest doctest.testmod()

import numpy as np from numpy import ndarray from scipy.optimize import Bounds, LinearConstraint, minimize def norm_squared(vector: ndarray) -> float: """ Return the squared second norm of vector norm_squared(v) = sum(x * x for x in v) Args: vector (ndarray): input vector Returns: float: squared second norm of vector >>> norm_squared([1, 2]) 5 >>> norm_squared(np.asarray([1, 2])) 5 >>> norm_squared([0, 0]) 0 """ return np.dot(vector, vector) class SVC: """ Support Vector Classifier Args: kernel (str): kernel to use. Default: linear Possible choices: - linear regularization: constraint for soft margin (data not linearly separable) Default: unbound >>> SVC(kernel="asdf") Traceback (most recent call last): ... ValueError: Unknown kernel: asdf >>> SVC(kernel="rbf") Traceback (most recent call last): ... ValueError: rbf kernel requires gamma >>> SVC(kernel="rbf", gamma=-1) Traceback (most recent call last): ... ValueError: gamma must be > 0 """ def __init__( self, *, regularization: float = np.inf, kernel: str = "linear", gamma: float = 0.0, ) -> None: self.regularization = regularization self.gamma = gamma if kernel == "linear": self.kernel = self.__linear elif kernel == "rbf": if self.gamma == 0: raise ValueError("rbf kernel requires gamma") if not isinstance(self.gamma, (float, int)): raise ValueError("gamma must be float or int") if not self.gamma > 0: raise ValueError("gamma must be > 0") self.kernel = self.__rbf # in the future, there could be a default value like in sklearn # sklear: def_gamma = 1/(n_features * X.var()) (wiki) # previously it was 1/(n_features) else: msg = f"Unknown kernel: {kernel}" raise ValueError(msg) # kernels def __linear(self, vector1: ndarray, vector2: ndarray) -> float: """Linear kernel (as if no kernel used at all)""" return np.dot(vector1, vector2) def __rbf(self, vector1: ndarray, vector2: ndarray) -> float: """ RBF: Radial Basis Function Kernel Note: for more information see: https://en.wikipedia.org/wiki/Radial_basis_function_kernel Args: vector1 (ndarray): first vector vector2 (ndarray): second vector) Returns: float: exp(-(gamma * norm_squared(vector1 - vector2))) """ return np.exp(-(self.gamma * norm_squared(vector1 - vector2))) def fit(self, observations: list[ndarray], classes: ndarray) -> None: """ Fits the SVC with a set of observations. Args: observations (list[ndarray]): list of observations classes (ndarray): classification of each observation (in {1, -1}) """ self.observations = observations self.classes = classes # using Wolfe's Dual to calculate w. # Primal problem: minimize 1/2*norm_squared(w) # constraint: yn(w . xn + b) >= 1 # # With l a vector # Dual problem: maximize sum_n(ln) - # 1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm)) # constraint: self.C >= ln >= 0 # and sum_n(ln*yn) = 0 # Then we get w using w = sum_n(ln*yn*xn) # At the end we can get b ~= mean(yn - w . xn) # # Since we use kernels, we only need l_star to calculate b # and to classify observations (n,) = np.shape(classes) def to_minimize(candidate: ndarray) -> float: """ Opposite of the function to maximize Args: candidate (ndarray): candidate array to test Return: float: Wolfe's Dual result to minimize """ s = 0 (n,) = np.shape(candidate) for i in range(n): for j in range(n): s += ( candidate[i] * candidate[j] * classes[i] * classes[j] * self.kernel(observations[i], observations[j]) ) return 1 / 2 * s - sum(candidate) ly_contraint = LinearConstraint(classes, 0, 0) l_bounds = Bounds(0, self.regularization) l_star = minimize( to_minimize, np.ones(n), bounds=l_bounds, constraints=[ly_contraint] ).x self.optimum = l_star # calculating mean offset of separation plane to points s = 0 for i in range(n): for j in range(n): s += classes[i] - classes[i] * self.optimum[i] * self.kernel( observations[i], observations[j] ) self.offset = s / n def predict(self, observation: ndarray) -> int: """ Get the expected class of an observation Args: observation (Vector): observation Returns: int {1, -1}: expected class >>> xs = [ ... np.asarray([0, 1]), np.asarray([0, 2]), ... np.asarray([1, 1]), np.asarray([1, 2]) ... ] >>> y = np.asarray([1, 1, -1, -1]) >>> s = SVC() >>> s.fit(xs, y) >>> s.predict(np.asarray([0, 1])) 1 >>> s.predict(np.asarray([1, 1])) -1 >>> s.predict(np.asarray([2, 2])) -1 """ s = sum( self.optimum[n] * self.classes[n] * self.kernel(self.observations[n], observation) for n in range(len(self.classes)) ) return 1 if s + self.offset >= 0 else -1 if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

from sklearn.neural_network import MLPClassifier X = [[0.0, 0.0], [1.0, 1.0], [1.0, 0.0], [0.0, 1.0]] y = [0, 1, 0, 0] clf = MLPClassifier( solver="lbfgs", alpha=1e-5, hidden_layer_sizes=(5, 2), random_state=1 ) clf.fit(X, y) test = [[0.0, 0.0], [0.0, 1.0], [1.0, 1.0]] Y = clf.predict(test) def wrapper(y): """ >>> wrapper(Y) [0, 0, 1] """ return list(y) if __name__ == "__main__": import doctest doctest.testmod()

from sklearn.neural_network import MLPClassifier X = [[0.0, 0.0], [1.0, 1.0], [1.0, 0.0], [0.0, 1.0]] y = [0, 1, 0, 0] clf = MLPClassifier( solver="lbfgs", alpha=1e-5, hidden_layer_sizes=(5, 2), random_state=1 ) clf.fit(X, y) test = [[0.0, 0.0], [0.0, 1.0], [1.0, 1.0]] Y = clf.predict(test) def wrapper(y): """ >>> wrapper(Y) [0, 0, 1] """ return list(y) if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" Testing here assumes that numpy and linalg is ALWAYS correct!!!! If running from PyCharm you can place the following line in "Additional Arguments" for the pytest run configuration -vv -m mat_ops -p no:cacheprovider """ import logging # standard libraries import sys import numpy as np import pytest # type: ignore # Custom/local libraries from matrix import matrix_operation as matop mat_a = [[12, 10], [3, 9]] mat_b = [[3, 4], [7, 4]] mat_c = [[3, 0, 2], [2, 0, -2], [0, 1, 1]] mat_d = [[3, 0, -2], [2, 0, 2], [0, 1, 1]] mat_e = [[3, 0, 2], [2, 0, -2], [0, 1, 1], [2, 0, -2]] mat_f = [1] mat_h = [2] logger = logging.getLogger() logger.level = logging.DEBUG stream_handler = logging.StreamHandler(sys.stdout) logger.addHandler(stream_handler) @pytest.mark.mat_ops() @pytest.mark.parametrize( ("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)] ) def test_addition(mat1, mat2): if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2): logger.info(f"\n\t{test_addition.__name__} returned integer") with pytest.raises(TypeError): matop.add(mat1, mat2) elif (np.array(mat1)).shape == (np.array(mat2)).shape: logger.info(f"\n\t{test_addition.__name__} with same matrix dims") act = (np.array(mat1) + np.array(mat2)).tolist() theo = matop.add(mat1, mat2) assert theo == act else: logger.info(f"\n\t{test_addition.__name__} with different matrix dims") with pytest.raises(ValueError): matop.add(mat1, mat2) @pytest.mark.mat_ops() @pytest.mark.parametrize( ("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)] ) def test_subtraction(mat1, mat2): if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2): logger.info(f"\n\t{test_subtraction.__name__} returned integer") with pytest.raises(TypeError): matop.subtract(mat1, mat2) elif (np.array(mat1)).shape == (np.array(mat2)).shape: logger.info(f"\n\t{test_subtraction.__name__} with same matrix dims") act = (np.array(mat1) - np.array(mat2)).tolist() theo = matop.subtract(mat1, mat2) assert theo == act else: logger.info(f"\n\t{test_subtraction.__name__} with different matrix dims") with pytest.raises(ValueError): assert matop.subtract(mat1, mat2) @pytest.mark.mat_ops() @pytest.mark.parametrize( ("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)] ) def test_multiplication(mat1, mat2): if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2): logger.info(f"\n\t{test_multiplication.__name__} returned integer") with pytest.raises(TypeError): matop.add(mat1, mat2) elif (np.array(mat1)).shape == (np.array(mat2)).shape: logger.info(f"\n\t{test_multiplication.__name__} meets dim requirements") act = (np.matmul(mat1, mat2)).tolist() theo = matop.multiply(mat1, mat2) assert theo == act else: logger.info( f"\n\t{test_multiplication.__name__} does not meet dim requirements" ) with pytest.raises(ValueError): assert matop.subtract(mat1, mat2) @pytest.mark.mat_ops() def test_scalar_multiply(): act = (3.5 * np.array(mat_a)).tolist() theo = matop.scalar_multiply(mat_a, 3.5) assert theo == act @pytest.mark.mat_ops() def test_identity(): act = (np.identity(5)).tolist() theo = matop.identity(5) assert theo == act @pytest.mark.mat_ops() @pytest.mark.parametrize("mat", [mat_a, mat_b, mat_c, mat_d, mat_e, mat_f]) def test_transpose(mat): if (np.array(mat)).shape < (2, 2): logger.info(f"\n\t{test_transpose.__name__} returned integer") with pytest.raises(TypeError): matop.transpose(mat) else: act = (np.transpose(mat)).tolist() theo = matop.transpose(mat, return_map=False) assert theo == act

""" Testing here assumes that numpy and linalg is ALWAYS correct!!!! If running from PyCharm you can place the following line in "Additional Arguments" for the pytest run configuration -vv -m mat_ops -p no:cacheprovider """ import logging # standard libraries import sys import numpy as np import pytest # type: ignore # Custom/local libraries from matrix import matrix_operation as matop mat_a = [[12, 10], [3, 9]] mat_b = [[3, 4], [7, 4]] mat_c = [[3, 0, 2], [2, 0, -2], [0, 1, 1]] mat_d = [[3, 0, -2], [2, 0, 2], [0, 1, 1]] mat_e = [[3, 0, 2], [2, 0, -2], [0, 1, 1], [2, 0, -2]] mat_f = [1] mat_h = [2] logger = logging.getLogger() logger.level = logging.DEBUG stream_handler = logging.StreamHandler(sys.stdout) logger.addHandler(stream_handler) @pytest.mark.mat_ops() @pytest.mark.parametrize( ("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)] ) def test_addition(mat1, mat2): if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2): logger.info(f"\n\t{test_addition.__name__} returned integer") with pytest.raises(TypeError): matop.add(mat1, mat2) elif (np.array(mat1)).shape == (np.array(mat2)).shape: logger.info(f"\n\t{test_addition.__name__} with same matrix dims") act = (np.array(mat1) + np.array(mat2)).tolist() theo = matop.add(mat1, mat2) assert theo == act else: logger.info(f"\n\t{test_addition.__name__} with different matrix dims") with pytest.raises(ValueError): matop.add(mat1, mat2) @pytest.mark.mat_ops() @pytest.mark.parametrize( ("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)] ) def test_subtraction(mat1, mat2): if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2): logger.info(f"\n\t{test_subtraction.__name__} returned integer") with pytest.raises(TypeError): matop.subtract(mat1, mat2) elif (np.array(mat1)).shape == (np.array(mat2)).shape: logger.info(f"\n\t{test_subtraction.__name__} with same matrix dims") act = (np.array(mat1) - np.array(mat2)).tolist() theo = matop.subtract(mat1, mat2) assert theo == act else: logger.info(f"\n\t{test_subtraction.__name__} with different matrix dims") with pytest.raises(ValueError): assert matop.subtract(mat1, mat2) @pytest.mark.mat_ops() @pytest.mark.parametrize( ("mat1", "mat2"), [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)] ) def test_multiplication(mat1, mat2): if (np.array(mat1)).shape < (2, 2) or (np.array(mat2)).shape < (2, 2): logger.info(f"\n\t{test_multiplication.__name__} returned integer") with pytest.raises(TypeError): matop.add(mat1, mat2) elif (np.array(mat1)).shape == (np.array(mat2)).shape: logger.info(f"\n\t{test_multiplication.__name__} meets dim requirements") act = (np.matmul(mat1, mat2)).tolist() theo = matop.multiply(mat1, mat2) assert theo == act else: logger.info( f"\n\t{test_multiplication.__name__} does not meet dim requirements" ) with pytest.raises(ValueError): assert matop.subtract(mat1, mat2) @pytest.mark.mat_ops() def test_scalar_multiply(): act = (3.5 * np.array(mat_a)).tolist() theo = matop.scalar_multiply(mat_a, 3.5) assert theo == act @pytest.mark.mat_ops() def test_identity(): act = (np.identity(5)).tolist() theo = matop.identity(5) assert theo == act @pytest.mark.mat_ops() @pytest.mark.parametrize("mat", [mat_a, mat_b, mat_c, mat_d, mat_e, mat_f]) def test_transpose(mat): if (np.array(mat)).shape < (2, 2): logger.info(f"\n\t{test_transpose.__name__} returned integer") with pytest.raises(TypeError): matop.transpose(mat) else: act = (np.transpose(mat)).tolist() theo = matop.transpose(mat, return_map=False) assert theo == act

TheAlgorithms/Python

Add tests without modifying code

### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

gio-puter

d73a4c2ee035698de437086230985574766f195b

0601b56173021fe96fb070d20085962b036e85c3

Add tests without modifying code. ### Describe your change: Contributes to #9943 Added doctest to maths/largest_of_very_large_numbers.py Added doctest to strings/words_patterns.py Added doctest to ciphers/onepad_cipher.py * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request. * [ ] Documentation change? ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" The Horn-Schunck method estimates the optical flow for every single pixel of a sequence of images. It works by assuming brightness constancy between two consecutive frames and smoothness in the optical flow. Useful resources: Wikipedia: https://en.wikipedia.org/wiki/Horn%E2%80%93Schunck_method Paper: http://image.diku.dk/imagecanon/material/HornSchunckOptical_Flow.pdf """ from typing import SupportsIndex import numpy as np from scipy.ndimage import convolve def warp( image: np.ndarray, horizontal_flow: np.ndarray, vertical_flow: np.ndarray ) -> np.ndarray: """ Warps the pixels of an image into a new image using the horizontal and vertical flows. Pixels that are warped from an invalid location are set to 0. Parameters: image: Grayscale image horizontal_flow: Horizontal flow vertical_flow: Vertical flow Returns: Warped image >>> warp(np.array([[0, 1, 2], [0, 3, 0], [2, 2, 2]]), \ np.array([[0, 1, -1], [-1, 0, 0], [1, 1, 1]]), \ np.array([[0, 0, 0], [0, 1, 0], [0, 0, 1]])) array([[0, 0, 0], [3, 1, 0], [0, 2, 3]]) """ flow = np.stack((horizontal_flow, vertical_flow), 2) # Create a grid of all pixel coordinates and subtract the flow to get the # target pixels coordinates grid = np.stack( np.meshgrid(np.arange(0, image.shape[1]), np.arange(0, image.shape[0])), 2 ) grid = np.round(grid - flow).astype(np.int32) # Find the locations outside of the original image invalid = (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]])) grid[invalid] = 0 warped = image[grid[:, :, 1], grid[:, :, 0]] # Set pixels at invalid locations to 0 warped[invalid[:, :, 0] | invalid[:, :, 1]] = 0 return warped def horn_schunck( image0: np.ndarray, image1: np.ndarray, num_iter: SupportsIndex, alpha: float | None = None, ) -> tuple[np.ndarray, np.ndarray]: """ This function performs the Horn-Schunck algorithm and returns the estimated optical flow. It is assumed that the input images are grayscale and normalized to be in [0, 1]. Parameters: image0: First image of the sequence image1: Second image of the sequence alpha: Regularization constant num_iter: Number of iterations performed Returns: estimated horizontal & vertical flow >>> np.round(horn_schunck(np.array([[0, 0, 2], [0, 0, 2]]), \ np.array([[0, 2, 0], [0, 2, 0]]), alpha=0.1, num_iter=110)).\ astype(np.int32) array([[[ 0, -1, -1], [ 0, -1, -1]], <BLANKLINE> [[ 0, 0, 0], [ 0, 0, 0]]], dtype=int32) """ if alpha is None: alpha = 0.1 # Initialize flow horizontal_flow = np.zeros_like(image0) vertical_flow = np.zeros_like(image0) # Prepare kernels for the calculation of the derivatives and the average velocity kernel_x = np.array([[-1, 1], [-1, 1]]) * 0.25 kernel_y = np.array([[-1, -1], [1, 1]]) * 0.25 kernel_t = np.array([[1, 1], [1, 1]]) * 0.25 kernel_laplacian = np.array( [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]] ) # Iteratively refine the flow for _ in range(num_iter): warped_image = warp(image0, horizontal_flow, vertical_flow) derivative_x = convolve(warped_image, kernel_x) + convolve(image1, kernel_x) derivative_y = convolve(warped_image, kernel_y) + convolve(image1, kernel_y) derivative_t = convolve(warped_image, kernel_t) + convolve(image1, -kernel_t) avg_horizontal_velocity = convolve(horizontal_flow, kernel_laplacian) avg_vertical_velocity = convolve(vertical_flow, kernel_laplacian) # This updates the flow as proposed in the paper (Step 12) update = ( derivative_x * avg_horizontal_velocity + derivative_y * avg_vertical_velocity + derivative_t ) update = update / (alpha**2 + derivative_x**2 + derivative_y**2) horizontal_flow = avg_horizontal_velocity - derivative_x * update vertical_flow = avg_vertical_velocity - derivative_y * update return horizontal_flow, vertical_flow if __name__ == "__main__": import doctest doctest.testmod()

""" The Horn-Schunck method estimates the optical flow for every single pixel of a sequence of images. It works by assuming brightness constancy between two consecutive frames and smoothness in the optical flow. Useful resources: Wikipedia: https://en.wikipedia.org/wiki/Horn%E2%80%93Schunck_method Paper: http://image.diku.dk/imagecanon/material/HornSchunckOptical_Flow.pdf """ from typing import SupportsIndex import numpy as np from scipy.ndimage import convolve def warp( image: np.ndarray, horizontal_flow: np.ndarray, vertical_flow: np.ndarray ) -> np.ndarray: """ Warps the pixels of an image into a new image using the horizontal and vertical flows. Pixels that are warped from an invalid location are set to 0. Parameters: image: Grayscale image horizontal_flow: Horizontal flow vertical_flow: Vertical flow Returns: Warped image >>> warp(np.array([[0, 1, 2], [0, 3, 0], [2, 2, 2]]), \ np.array([[0, 1, -1], [-1, 0, 0], [1, 1, 1]]), \ np.array([[0, 0, 0], [0, 1, 0], [0, 0, 1]])) array([[0, 0, 0], [3, 1, 0], [0, 2, 3]]) """ flow = np.stack((horizontal_flow, vertical_flow), 2) # Create a grid of all pixel coordinates and subtract the flow to get the # target pixels coordinates grid = np.stack( np.meshgrid(np.arange(0, image.shape[1]), np.arange(0, image.shape[0])), 2 ) grid = np.round(grid - flow).astype(np.int32) # Find the locations outside of the original image invalid = (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]])) grid[invalid] = 0 warped = image[grid[:, :, 1], grid[:, :, 0]] # Set pixels at invalid locations to 0 warped[invalid[:, :, 0] | invalid[:, :, 1]] = 0 return warped def horn_schunck( image0: np.ndarray, image1: np.ndarray, num_iter: SupportsIndex, alpha: float | None = None, ) -> tuple[np.ndarray, np.ndarray]: """ This function performs the Horn-Schunck algorithm and returns the estimated optical flow. It is assumed that the input images are grayscale and normalized to be in [0, 1]. Parameters: image0: First image of the sequence image1: Second image of the sequence alpha: Regularization constant num_iter: Number of iterations performed Returns: estimated horizontal & vertical flow >>> np.round(horn_schunck(np.array([[0, 0, 2], [0, 0, 2]]), \ np.array([[0, 2, 0], [0, 2, 0]]), alpha=0.1, num_iter=110)).\ astype(np.int32) array([[[ 0, -1, -1], [ 0, -1, -1]], <BLANKLINE> [[ 0, 0, 0], [ 0, 0, 0]]], dtype=int32) """ if alpha is None: alpha = 0.1 # Initialize flow horizontal_flow = np.zeros_like(image0) vertical_flow = np.zeros_like(image0) # Prepare kernels for the calculation of the derivatives and the average velocity kernel_x = np.array([[-1, 1], [-1, 1]]) * 0.25 kernel_y = np.array([[-1, -1], [1, 1]]) * 0.25 kernel_t = np.array([[1, 1], [1, 1]]) * 0.25 kernel_laplacian = np.array( [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]] ) # Iteratively refine the flow for _ in range(num_iter): warped_image = warp(image0, horizontal_flow, vertical_flow) derivative_x = convolve(warped_image, kernel_x) + convolve(image1, kernel_x) derivative_y = convolve(warped_image, kernel_y) + convolve(image1, kernel_y) derivative_t = convolve(warped_image, kernel_t) + convolve(image1, -kernel_t) avg_horizontal_velocity = convolve(horizontal_flow, kernel_laplacian) avg_vertical_velocity = convolve(vertical_flow, kernel_laplacian) # This updates the flow as proposed in the paper (Step 12) update = ( derivative_x * avg_horizontal_velocity + derivative_y * avg_vertical_velocity + derivative_t ) update = update / (alpha**2 + derivative_x**2 + derivative_y**2) horizontal_flow = avg_horizontal_velocity - derivative_x * update vertical_flow = avg_vertical_velocity - derivative_y * update return horizontal_flow, vertical_flow if __name__ == "__main__": import doctest doctest.testmod()

TheAlgorithms/Python

Converted tests into doctests

### Describe your change: Turned tests into doctests in the Boolean Algebra section for consistency and as an improved way of testing. * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [ ] Documentation change? * [x] Changed code ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [x] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

AksharGoyal

cc0405d05cb4c5009e8bf826e3f641c427ba70d5

f4ff73b1bdaa4349315beaf44e093c59f6c87fd3

Converted tests into doctests. ### Describe your change: Turned tests into doctests in the Boolean Algebra section for consistency and as an improved way of testing. * [ ] Add an algorithm? * [ ] Fix a bug or typo in an existing algorithm? * [ ] Documentation change? * [x] Changed code ### Checklist: * [x] I have read [CONTRIBUTING.md](https://github.com/TheAlgorithms/Python/blob/master/CONTRIBUTING.md). * [x] This pull request is all my own work -- I have not plagiarized. * [x] I know that pull requests will not be merged if they fail the automated tests. * [x] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms. * [x] All new Python files are placed inside an existing directory. * [x] All filenames are in all lowercase characters with no spaces or dashes. * [x] All functions and variable names follow Python naming conventions. * [x] All function parameters and return values are annotated with Python [type hints](https://docs.python.org/3/library/typing.html). * [x] All functions have [doctests](https://docs.python.org/3/library/doctest.html) that pass the automated testing. * [x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation. * [x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a [closing keyword](https://docs.github.com/en/issues/tracking-your-work-with-issues/linking-a-pull-request-to-an-issue): "Fixes #ISSUE-NUMBER".

""" An AND Gate is a logic gate in boolean algebra which results to 1 (True) if both the inputs are 1, and 0 (False) otherwise. Following is the truth table of an AND Gate: ------------------------------ | Input 1 | Input 2 | Output | ------------------------------ | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | ------------------------------ Refer - https://www.geeksforgeeks.org/logic-gates-in-python/ """ def and_gate(input_1: int, input_2: int) -> int: """ Calculate AND of the input values >>> and_gate(0, 0) 0 >>> and_gate(0, 1) 0 >>> and_gate(1, 0) 0 >>> and_gate(1, 1) 1 """ return int((input_1, input_2).count(0) == 0) def test_and_gate() -> None: """ Tests the and_gate function """ assert and_gate(0, 0) == 0 assert and_gate(0, 1) == 0 assert and_gate(1, 0) == 0 assert and_gate(1, 1) == 1 if __name__ == "__main__": test_and_gate() print(and_gate(1, 0)) print(and_gate(0, 0)) print(and_gate(0, 1)) print(and_gate(1, 1))

""" An AND Gate is a logic gate in boolean algebra which results to 1 (True) if both the inputs are 1, and 0 (False) otherwise. Following is the truth table of an AND Gate: ------------------------------ | Input 1 | Input 2 | Output | ------------------------------ | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | ------------------------------ Refer - https://www.geeksforgeeks.org/logic-gates-in-python/ """ def and_gate(input_1: int, input_2: int) -> int: """ Calculate AND of the input values >>> and_gate(0, 0) 0 >>> and_gate(0, 1) 0 >>> and_gate(1, 0) 0 >>> and_gate(1, 1) 1 """ return int((input_1, input_2).count(0) == 0) if __name__ == "__main__": import doctest doctest.testmod()