From 5990417ede8e3765bd0d9f07d46d82df01d69fa7 Mon Sep 17 00:00:00 2001 From: Ashish Daulatabad Date: Tue, 15 Nov 2022 10:22:58 +0530 Subject: [PATCH 01/12] Feat: Add Strassen's matrix multiplication --- DIRECTORY.md | 662 +++++++++--------- .../strassen_matrix_multiplication.cpp | 439 ++++++++++++ range_queries/sparse_table.cpp | 0 3 files changed, 770 insertions(+), 331 deletions(-) create mode 100644 divide_and_conquer/strassen_matrix_multiplication.cpp mode change 100755 => 100644 range_queries/sparse_table.cpp diff --git a/DIRECTORY.md b/DIRECTORY.md index 2faa8e47d05..5ea0f928ce4 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -1,378 +1,378 @@ ## Backtracking - * [Graph Coloring](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/graph_coloring.cpp) - * [Knight Tour](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/knight_tour.cpp) - * [Magic Sequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/magic_sequence.cpp) - * [Minimax](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/minimax.cpp) - * [N Queens](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens.cpp) - * [N Queens All Solution Optimised](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens_all_solution_optimised.cpp) - * [Nqueen Print All Solutions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/nqueen_print_all_solutions.cpp) - * [Rat Maze](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/rat_maze.cpp) - * [Subarray Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subarray_sum.cpp) - * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subset_sum.cpp) - * [Sudoku Solver](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solver.cpp) - * [Wildcard Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/wildcard_matching.cpp) + * [Graph Coloring](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/graph_coloring.cpp) + * [Knight Tour](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/knight_tour.cpp) + * [Magic Sequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/magic_sequence.cpp) + * [Minimax](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/minimax.cpp) + * [N Queens](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/n_queens.cpp) + * [N Queens All Solution Optimised](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/n_queens_all_solution_optimised.cpp) + * [Nqueen Print All Solutions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/nqueen_print_all_solutions.cpp) + * [Rat Maze](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/rat_maze.cpp) + * [Subarray Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/subarray_sum.cpp) + * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/subset_sum.cpp) + * [Sudoku Solver](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/sudoku_solver.cpp) + * [Wildcard Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/wildcard_matching.cpp) ## Bit Manipulation - * [Count Bits Flip](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_bits_flip.cpp) - * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_set_bits.cpp) - * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp) - * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/hamming_distance.cpp) - * [Set Kth Bit](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/set_kth_bit.cpp) + * [Count Bits Flip](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_bits_flip.cpp) + * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_set_bits.cpp) + * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp) + * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/hamming_distance.cpp) + * [Set Kth Bit](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/set_kth_bit.cpp) ## Ciphers - * [A1Z26 Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/a1z26_cipher.cpp) - * [Atbash Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/atbash_cipher.cpp) - * [Base64 Encoding](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/base64_encoding.cpp) - * [Caesar Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/caesar_cipher.cpp) - * [Elliptic Curve Key Exchange](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/elliptic_curve_key_exchange.cpp) - * [Hill Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/hill_cipher.cpp) - * [Morse Code](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/morse_code.cpp) - * [Uint128 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/uint128_t.hpp) - * [Uint256 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/uint256_t.hpp) - * [Vigenere Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/vigenere_cipher.cpp) - * [Xor Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/xor_cipher.cpp) + * [A1Z26 Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/a1z26_cipher.cpp) + * [Atbash Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/atbash_cipher.cpp) + * [Base64 Encoding](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/base64_encoding.cpp) + * [Caesar Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/caesar_cipher.cpp) + * [Elliptic Curve Key Exchange](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/elliptic_curve_key_exchange.cpp) + * [Hill Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/hill_cipher.cpp) + * [Morse Code](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/morse_code.cpp) + * [Uint128 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/uint128_t.hpp) + * [Uint256 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/uint256_t.hpp) + * [Vigenere Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/vigenere_cipher.cpp) + * [Xor Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/xor_cipher.cpp) ## Cpu Scheduling Algorithms - * [Fcfs Scheduling](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/cpu_scheduling_algorithms/fcfs_scheduling.cpp) + * [Fcfs Scheduling](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/cpu_scheduling_algorithms/fcfs_scheduling.cpp) ## Data Structures - * [Avltree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/avltree.cpp) - * [Binary Search Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binary_search_tree.cpp) - * [Binary Search Tree2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binary_search_tree2.cpp) - * [Binaryheap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binaryheap.cpp) - * [Bloom Filter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/bloom_filter.cpp) - * [Circular Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/circular_queue_using_linked_list.cpp) + * [Avltree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/avltree.cpp) + * [Binary Search Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/binary_search_tree.cpp) + * [Binary Search Tree2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/binary_search_tree2.cpp) + * [Binaryheap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/binaryheap.cpp) + * [Bloom Filter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/bloom_filter.cpp) + * [Circular Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/circular_queue_using_linked_list.cpp) * Cll - * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/cll.cpp) - * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/cll.h) - * [Main Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/main_cll.cpp) - * [Disjoint Set](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/disjoint_set.cpp) - * [Doubly Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/doubly_linked_list.cpp) - * [Dsu Path Compression](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/dsu_path_compression.cpp) - * [Dsu Union Rank](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/dsu_union_rank.cpp) - * [Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linked_list.cpp) - * [Linkedlist Implentation Usingarray](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linkedlist_implentation_usingarray.cpp) - * [List Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/list_array.cpp) - * [Morrisinorder](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/morrisinorder.cpp) - * [Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue.h) - * [Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_array.cpp) - * [Queue Using Array2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_array2.cpp) - * [Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_linked_list.cpp) - * [Queue Using Linkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_linkedlist.cpp) - * [Queue Using Two Stacks](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_two_stacks.cpp) - * [Rb Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/rb_tree.cpp) - * [Reverse A Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/reverse_a_linked_list.cpp) - * [Skip List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/skip_list.cpp) - * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/sparse_table.cpp) - * [Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack.h) - * [Stack Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_array.cpp) - * [Stack Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_linked_list.cpp) - * [Stack Using Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_queue.cpp) - * [Test Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_queue.cpp) - * [Test Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_stack.cpp) - * [Test Stack Students](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_stack_students.cpp) - * [Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/tree.cpp) - * [Tree 234](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/tree_234.cpp) - * [Trie Modern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_modern.cpp) - * [Trie Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_tree.cpp) - * [Trie Using Hashmap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_using_hashmap.cpp) + * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/cll/cll.cpp) + * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/cll/cll.h) + * [Main Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/cll/main_cll.cpp) + * [Disjoint Set](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/disjoint_set.cpp) + * [Doubly Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/doubly_linked_list.cpp) + * [Dsu Path Compression](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/dsu_path_compression.cpp) + * [Dsu Union Rank](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/dsu_union_rank.cpp) + * [Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/linked_list.cpp) + * [Linkedlist Implentation Usingarray](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/linkedlist_implentation_usingarray.cpp) + * [List Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/list_array.cpp) + * [Morrisinorder](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/morrisinorder.cpp) + * [Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue.h) + * [Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_array.cpp) + * [Queue Using Array2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_array2.cpp) + * [Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_linked_list.cpp) + * [Queue Using Linkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_linkedlist.cpp) + * [Queue Using Two Stacks](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_two_stacks.cpp) + * [Rb Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/rb_tree.cpp) + * [Reverse A Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/reverse_a_linked_list.cpp) + * [Skip List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/skip_list.cpp) + * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/sparse_table.cpp) + * [Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack.h) + * [Stack Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack_using_array.cpp) + * [Stack Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack_using_linked_list.cpp) + * [Stack Using Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack_using_queue.cpp) + * [Test Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/test_queue.cpp) + * [Test Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/test_stack.cpp) + * [Test Stack Students](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/test_stack_students.cpp) + * [Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/tree.cpp) + * [Tree 234](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/tree_234.cpp) + * [Trie Modern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/trie_modern.cpp) + * [Trie Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/trie_tree.cpp) + * [Trie Using Hashmap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/trie_using_hashmap.cpp) ## Divide And Conquer - * [Karatsuba Algorithm For Fast Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp) + * [Karatsuba Algorithm For Fast Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp) ## Dynamic Programming - * [0 1 Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/0_1_knapsack.cpp) - * [Abbreviation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/abbreviation.cpp) - * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/armstrong_number.cpp) - * [Bellman Ford](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/bellman_ford.cpp) - * [Catalan Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/catalan_numbers.cpp) - * [Coin Change](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/coin_change.cpp) - * [Coin Change Topdown](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/coin_change_topdown.cpp) - * [Cut Rod](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/cut_rod.cpp) - * [Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/edit_distance.cpp) - * [Egg Dropping Puzzle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/egg_dropping_puzzle.cpp) - * [Fibonacci Bottom Up](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/fibonacci_bottom_up.cpp) - * [Floyd Warshall](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/floyd_warshall.cpp) - * [House Robber](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/house_robber.cpp) - * [Kadane](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/kadane.cpp) - * [Kadane2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/kadane2.cpp) - * [Longest Common String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_common_string.cpp) - * [Longest Common Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_common_subsequence.cpp) - * [Longest Increasing Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence.cpp) - * [Longest Increasing Subsequence (Nlogn)](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp) - * [Longest Palindromic Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_palindromic_subsequence.cpp) - * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/matrix_chain_multiplication.cpp) - * [Minimum Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/minimum_edit_distance.cpp) - * [Palindrome Partitioning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/palindrome_partitioning.cpp) - * [Partition Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/partition_problem.cpp) - * [Searching Of Element In Dynamic Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/searching_of_element_in_dynamic_array.cpp) - * [Shortest Common Supersequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/shortest_common_supersequence.cpp) - * [Tree Height](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/tree_height.cpp) - * [Word Break](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/word_break.cpp) + * [0 1 Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/0_1_knapsack.cpp) + * [Abbreviation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/abbreviation.cpp) + * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/armstrong_number.cpp) + * [Bellman Ford](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/bellman_ford.cpp) + * [Catalan Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/catalan_numbers.cpp) + * [Coin Change](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/coin_change.cpp) + * [Coin Change Topdown](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/coin_change_topdown.cpp) + * [Cut Rod](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/cut_rod.cpp) + * [Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/edit_distance.cpp) + * [Egg Dropping Puzzle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/egg_dropping_puzzle.cpp) + * [Fibonacci Bottom Up](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/fibonacci_bottom_up.cpp) + * [Floyd Warshall](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/floyd_warshall.cpp) + * [House Robber](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/house_robber.cpp) + * [Kadane](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/kadane.cpp) + * [Kadane2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/kadane2.cpp) + * [Longest Common String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_common_string.cpp) + * [Longest Common Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_common_subsequence.cpp) + * [Longest Increasing Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_increasing_subsequence.cpp) + * [Longest Increasing Subsequence (Nlogn)](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp) + * [Longest Palindromic Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_palindromic_subsequence.cpp) + * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/matrix_chain_multiplication.cpp) + * [Minimum Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/minimum_edit_distance.cpp) + * [Palindrome Partitioning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/palindrome_partitioning.cpp) + * [Partition Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/partition_problem.cpp) + * [Searching Of Element In Dynamic Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/searching_of_element_in_dynamic_array.cpp) + * [Shortest Common Supersequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/shortest_common_supersequence.cpp) + * [Tree Height](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/tree_height.cpp) + * [Word Break](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/word_break.cpp) ## Geometry - * [Graham Scan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/graham_scan_algorithm.cpp) - * [Graham Scan Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/graham_scan_functions.hpp) - * [Jarvis Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/jarvis_algorithm.cpp) - * [Line Segment Intersection](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/line_segment_intersection.cpp) + * [Graham Scan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/graham_scan_algorithm.cpp) + * [Graham Scan Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/graham_scan_functions.hpp) + * [Jarvis Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/jarvis_algorithm.cpp) + * [Line Segment Intersection](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/line_segment_intersection.cpp) ## Graph - * [Bidirectional Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bidirectional_dijkstra.cpp) - * [Breadth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/breadth_first_search.cpp) - * [Bridge Finding With Tarjan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bridge_finding_with_tarjan_algorithm.cpp) - * [Connected Components](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components.cpp) - * [Connected Components With Dsu](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components_with_dsu.cpp) - * [Cycle Check Directed Graph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/cycle_check_directed_graph.cpp) - * [Depth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/depth_first_search.cpp) - * [Depth First Search With Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/depth_first_search_with_stack.cpp) - * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/dijkstra.cpp) - * [Hamiltons Cycle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/hamiltons_cycle.cpp) - * [Hopcroft Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/hopcroft_karp.cpp) - * [Is Graph Bipartite](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/is_graph_bipartite.cpp) - * [Is Graph Bipartite2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/is_graph_bipartite2.cpp) - * [Kosaraju](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/kosaraju.cpp) - * [Kruskal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/kruskal.cpp) - * [Lowest Common Ancestor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/lowest_common_ancestor.cpp) - * [Max Flow With Ford Fulkerson And Edmond Karp Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp) - * [Prim](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/prim.cpp) - * [Topological Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort.cpp) - * [Topological Sort By Kahns Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort_by_kahns_algo.cpp) - * [Travelling Salesman Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/travelling_salesman_problem.cpp) + * [Bidirectional Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/bidirectional_dijkstra.cpp) + * [Breadth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/breadth_first_search.cpp) + * [Bridge Finding With Tarjan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/bridge_finding_with_tarjan_algorithm.cpp) + * [Connected Components](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/connected_components.cpp) + * [Connected Components With Dsu](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/connected_components_with_dsu.cpp) + * [Cycle Check Directed Graph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/cycle_check_directed_graph.cpp) + * [Depth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/depth_first_search.cpp) + * [Depth First Search With Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/depth_first_search_with_stack.cpp) + * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/dijkstra.cpp) + * [Hamiltons Cycle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/hamiltons_cycle.cpp) + * [Hopcroft Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/hopcroft_karp.cpp) + * [Is Graph Bipartite](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/is_graph_bipartite.cpp) + * [Is Graph Bipartite2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/is_graph_bipartite2.cpp) + * [Kosaraju](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/kosaraju.cpp) + * [Kruskal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/kruskal.cpp) + * [Lowest Common Ancestor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/lowest_common_ancestor.cpp) + * [Max Flow With Ford Fulkerson And Edmond Karp Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp) + * [Prim](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/prim.cpp) + * [Topological Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/topological_sort.cpp) + * [Topological Sort By Kahns Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/topological_sort_by_kahns_algo.cpp) + * [Travelling Salesman Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/travelling_salesman_problem.cpp) ## Graphics - * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graphics/spirograph.cpp) + * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graphics/spirograph.cpp) ## Greedy Algorithms - * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/dijkstra.cpp) - * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/huffman.cpp) - * [Jumpgame](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/jumpgame.cpp) - * [Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/knapsack.cpp) - * [Kruskals Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/kruskals_minimum_spanning_tree.cpp) - * [Prims Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/prims_minimum_spanning_tree.cpp) + * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/dijkstra.cpp) + * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/huffman.cpp) + * [Jumpgame](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/jumpgame.cpp) + * [Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/knapsack.cpp) + * [Kruskals Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/kruskals_minimum_spanning_tree.cpp) + * [Prims Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/prims_minimum_spanning_tree.cpp) ## Hashing - * [Chaining](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/chaining.cpp) - * [Double Hash Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/double_hash_hash_table.cpp) - * [Linear Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/linear_probing_hash_table.cpp) - * [Md5](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/md5.cpp) - * [Quadratic Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/quadratic_probing_hash_table.cpp) - * [Sha1](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/sha1.cpp) + * [Chaining](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/chaining.cpp) + * [Double Hash Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/double_hash_hash_table.cpp) + * [Linear Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/linear_probing_hash_table.cpp) + * [Md5](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/md5.cpp) + * [Quadratic Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/quadratic_probing_hash_table.cpp) + * [Sha1](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/sha1.cpp) ## Machine Learning - * [A Star Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/a_star_search.cpp) - * [Adaline Learning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/adaline_learning.cpp) - * [Kohonen Som Topology](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/kohonen_som_topology.cpp) - * [Kohonen Som Trace](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/kohonen_som_trace.cpp) - * [Neural Network](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/neural_network.cpp) - * [Ordinary Least Squares Regressor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/ordinary_least_squares_regressor.cpp) - * [Vector Ops](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/vector_ops.hpp) + * [A Star Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/a_star_search.cpp) + * [Adaline Learning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/adaline_learning.cpp) + * [Kohonen Som Topology](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/kohonen_som_topology.cpp) + * [Kohonen Som Trace](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/kohonen_som_trace.cpp) + * [Neural Network](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/neural_network.cpp) + * [Ordinary Least Squares Regressor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/ordinary_least_squares_regressor.cpp) + * [Vector Ops](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/vector_ops.hpp) ## Math - * [Approximate Pi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/approximate_pi.cpp) - * [Area](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/area.cpp) - * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/armstrong_number.cpp) - * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp) - * [Binomial Calculate](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binomial_calculate.cpp) - * [Check Amicable Pair](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_amicable_pair.cpp) - * [Check Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_factorial.cpp) - * [Check Prime](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_prime.cpp) - * [Complex Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/complex_numbers.cpp) - * [Double Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/double_factorial.cpp) - * [Eulers Totient Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/eulers_totient_function.cpp) - * [Extended Euclid Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/extended_euclid_algorithm.cpp) - * [Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/factorial.cpp) - * [Fast Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fast_power.cpp) - * [Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci.cpp) - * [Fibonacci Fast](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_fast.cpp) - * [Fibonacci Large](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_large.cpp) - * [Fibonacci Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_matrix_exponentiation.cpp) - * [Fibonacci Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_sum.cpp) - * [Finding Number Of Digits In A Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/finding_number_of_digits_in_a_number.cpp) - * [Gcd Iterative Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_iterative_euclidean.cpp) - * [Gcd Of N Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_of_n_numbers.cpp) - * [Gcd Recursive Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_recursive_euclidean.cpp) - * [Integral Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/integral_approximation.cpp) - * [Integral Approximation2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/integral_approximation2.cpp) - * [Inv Sqrt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/inv_sqrt.cpp) - * [Large Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_factorial.cpp) - * [Large Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_number.h) - * [Largest Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/largest_power.cpp) - * [Lcm Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/lcm_sum.cpp) - * [Least Common Multiple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/least_common_multiple.cpp) - * [Linear Recurrence Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/linear_recurrence_matrix.cpp) - * [Magic Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/magic_number.cpp) - * [Miller Rabin](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/miller_rabin.cpp) - * [Modular Division](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_division.cpp) - * [Modular Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp) - * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp) - * [Modular Inverse Simple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_simple.cpp) - * [N Bonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_bonacci.cpp) - * [N Choose R](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_choose_r.cpp) - * [Ncr Modulo P](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/ncr_modulo_p.cpp) - * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp) - * [Perimeter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/perimeter.cpp) - * [Power For Huge Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_for_huge_numbers.cpp) - * [Power Of Two](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_of_two.cpp) - * [Prime Factorization](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_factorization.cpp) - * [Prime Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_numbers.cpp) - * [Primes Up To Billion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/primes_up_to_billion.cpp) - * [Realtime Stats](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/realtime_stats.cpp) - * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sieve_of_eratosthenes.cpp) - * [Sqrt Double](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sqrt_double.cpp) - * [String Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/string_fibonacci.cpp) - * [Sum Of Binomial Coefficient](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sum_of_binomial_coefficient.cpp) - * [Sum Of Digits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sum_of_digits.cpp) - * [Vector Cross Product](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/vector_cross_product.cpp) - * [Volume](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/volume.cpp) + * [Approximate Pi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/approximate_pi.cpp) + * [Area](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/area.cpp) + * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/armstrong_number.cpp) + * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/binary_exponent.cpp) + * [Binomial Calculate](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/binomial_calculate.cpp) + * [Check Amicable Pair](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_amicable_pair.cpp) + * [Check Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_factorial.cpp) + * [Check Prime](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_prime.cpp) + * [Complex Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/complex_numbers.cpp) + * [Double Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/double_factorial.cpp) + * [Eulers Totient Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/eulers_totient_function.cpp) + * [Extended Euclid Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/extended_euclid_algorithm.cpp) + * [Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/factorial.cpp) + * [Fast Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fast_power.cpp) + * [Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci.cpp) + * [Fibonacci Fast](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_fast.cpp) + * [Fibonacci Large](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_large.cpp) + * [Fibonacci Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_matrix_exponentiation.cpp) + * [Fibonacci Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_sum.cpp) + * [Finding Number Of Digits In A Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/finding_number_of_digits_in_a_number.cpp) + * [Gcd Iterative Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/gcd_iterative_euclidean.cpp) + * [Gcd Of N Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/gcd_of_n_numbers.cpp) + * [Gcd Recursive Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/gcd_recursive_euclidean.cpp) + * [Integral Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/integral_approximation.cpp) + * [Integral Approximation2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/integral_approximation2.cpp) + * [Inv Sqrt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/inv_sqrt.cpp) + * [Large Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/large_factorial.cpp) + * [Large Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/large_number.h) + * [Largest Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/largest_power.cpp) + * [Lcm Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/lcm_sum.cpp) + * [Least Common Multiple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/least_common_multiple.cpp) + * [Linear Recurrence Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/linear_recurrence_matrix.cpp) + * [Magic Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/magic_number.cpp) + * [Miller Rabin](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/miller_rabin.cpp) + * [Modular Division](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_division.cpp) + * [Modular Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_exponentiation.cpp) + * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_inverse_fermat_little_theorem.cpp) + * [Modular Inverse Simple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_inverse_simple.cpp) + * [N Bonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/n_bonacci.cpp) + * [N Choose R](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/n_choose_r.cpp) + * [Ncr Modulo P](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/ncr_modulo_p.cpp) + * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/number_of_positive_divisors.cpp) + * [Perimeter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/perimeter.cpp) + * [Power For Huge Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/power_for_huge_numbers.cpp) + * [Power Of Two](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/power_of_two.cpp) + * [Prime Factorization](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/prime_factorization.cpp) + * [Prime Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/prime_numbers.cpp) + * [Primes Up To Billion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/primes_up_to_billion.cpp) + * [Realtime Stats](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/realtime_stats.cpp) + * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sieve_of_eratosthenes.cpp) + * [Sqrt Double](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sqrt_double.cpp) + * [String Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/string_fibonacci.cpp) + * [Sum Of Binomial Coefficient](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sum_of_binomial_coefficient.cpp) + * [Sum Of Digits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sum_of_digits.cpp) + * [Vector Cross Product](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/vector_cross_product.cpp) + * [Volume](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/volume.cpp) ## Numerical Methods - * [Babylonian Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/babylonian_method.cpp) - * [Bisection Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/bisection_method.cpp) - * [Brent Method Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/brent_method_extrema.cpp) - * [Composite Simpson Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/composite_simpson_rule.cpp) - * [Durand Kerner Roots](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/durand_kerner_roots.cpp) - * [False Position](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/false_position.cpp) - * [Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/fast_fourier_transform.cpp) - * [Gaussian Elimination](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gaussian_elimination.cpp) - * [Golden Search Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/golden_search_extrema.cpp) - * [Gram Schmidt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gram_schmidt.cpp) - * [Inverse Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/inverse_fast_fourier_transform.cpp) - * [Lu Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decompose.cpp) - * [Lu Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decomposition.h) - * [Midpoint Integral Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/midpoint_integral_method.cpp) - * [Newton Raphson Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/newton_raphson_method.cpp) - * [Ode Forward Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_forward_euler.cpp) - * [Ode Midpoint Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_midpoint_euler.cpp) - * [Ode Semi Implicit Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_semi_implicit_euler.cpp) - * [Qr Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decompose.h) - * [Qr Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decomposition.cpp) - * [Qr Eigen Values](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_eigen_values.cpp) - * [Rungekutta](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/rungekutta.cpp) - * [Successive Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/successive_approximation.cpp) + * [Babylonian Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/babylonian_method.cpp) + * [Bisection Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/bisection_method.cpp) + * [Brent Method Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/brent_method_extrema.cpp) + * [Composite Simpson Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/composite_simpson_rule.cpp) + * [Durand Kerner Roots](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/durand_kerner_roots.cpp) + * [False Position](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/false_position.cpp) + * [Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/fast_fourier_transform.cpp) + * [Gaussian Elimination](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/gaussian_elimination.cpp) + * [Golden Search Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/golden_search_extrema.cpp) + * [Gram Schmidt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/gram_schmidt.cpp) + * [Inverse Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/inverse_fast_fourier_transform.cpp) + * [Lu Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/lu_decompose.cpp) + * [Lu Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/lu_decomposition.h) + * [Midpoint Integral Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/midpoint_integral_method.cpp) + * [Newton Raphson Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/newton_raphson_method.cpp) + * [Ode Forward Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/ode_forward_euler.cpp) + * [Ode Midpoint Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/ode_midpoint_euler.cpp) + * [Ode Semi Implicit Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/ode_semi_implicit_euler.cpp) + * [Qr Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/qr_decompose.h) + * [Qr Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/qr_decomposition.cpp) + * [Qr Eigen Values](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/qr_eigen_values.cpp) + * [Rungekutta](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/rungekutta.cpp) + * [Successive Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/successive_approximation.cpp) ## Operations On Datastructures - * [Array Left Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/array_left_rotation.cpp) - * [Array Right Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/array_right_rotation.cpp) - * [Circular Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_linked_list.cpp) - * [Circular Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_queue_using_array.cpp) - * [Get Size Of Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/get_size_of_linked_list.cpp) - * [Inorder Successor Of Bst](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/inorder_successor_of_bst.cpp) - * [Intersection Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/intersection_of_two_arrays.cpp) - * [Reverse A Linked List Using Recusion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_a_linked_list_using_recusion.cpp) - * [Reverse Binary Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_binary_tree.cpp) - * [Selectionsortlinkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/selectionsortlinkedlist.cpp) - * [Trie Multiple Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/trie_multiple_search.cpp) - * [Union Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/union_of_two_arrays.cpp) + * [Array Left Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/array_left_rotation.cpp) + * [Array Right Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/array_right_rotation.cpp) + * [Circular Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/circular_linked_list.cpp) + * [Circular Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/circular_queue_using_array.cpp) + * [Get Size Of Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/get_size_of_linked_list.cpp) + * [Inorder Successor Of Bst](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/inorder_successor_of_bst.cpp) + * [Intersection Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/intersection_of_two_arrays.cpp) + * [Reverse A Linked List Using Recusion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/reverse_a_linked_list_using_recusion.cpp) + * [Reverse Binary Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/reverse_binary_tree.cpp) + * [Selectionsortlinkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/selectionsortlinkedlist.cpp) + * [Trie Multiple Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/trie_multiple_search.cpp) + * [Union Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/union_of_two_arrays.cpp) ## Others - * [Buzz Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/buzz_number.cpp) - * [Decimal To Binary](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_binary.cpp) - * [Decimal To Hexadecimal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_hexadecimal.cpp) - * [Decimal To Roman Numeral](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_roman_numeral.cpp) - * [Easter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/easter.cpp) - * [Fast Integer Input](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/fast_integer_input.cpp) - * [Happy Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/happy_number.cpp) - * [Iterative Tree Traversals](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/iterative_tree_traversals.cpp) - * [Kadanes3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/kadanes3.cpp) - * [Lru Cache](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/lru_cache.cpp) - * [Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/matrix_exponentiation.cpp) - * [Palindrome Of Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/palindrome_of_number.cpp) - * [Paranthesis Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/paranthesis_matching.cpp) - * [Pascal Triangle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/pascal_triangle.cpp) - * [Postfix Evaluation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/postfix_evaluation.cpp) - * [Primality Test](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/primality_test.cpp) - * [Recursive Tree Traversal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/recursive_tree_traversal.cpp) - * [Smallest Circle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/smallest_circle.cpp) - * [Sparse Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/sparse_matrix.cpp) - * [Spiral Print](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/spiral_print.cpp) - * [Stairs Pattern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/stairs_pattern.cpp) - * [Tower Of Hanoi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/tower_of_hanoi.cpp) - * [Vector Important Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/vector_important_functions.cpp) + * [Buzz Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/buzz_number.cpp) + * [Decimal To Binary](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/decimal_to_binary.cpp) + * [Decimal To Hexadecimal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/decimal_to_hexadecimal.cpp) + * [Decimal To Roman Numeral](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/decimal_to_roman_numeral.cpp) + * [Easter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/easter.cpp) + * [Fast Integer Input](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/fast_integer_input.cpp) + * [Happy Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/happy_number.cpp) + * [Iterative Tree Traversals](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/iterative_tree_traversals.cpp) + * [Kadanes3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/kadanes3.cpp) + * [Lru Cache](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/lru_cache.cpp) + * [Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/matrix_exponentiation.cpp) + * [Palindrome Of Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/palindrome_of_number.cpp) + * [Paranthesis Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/paranthesis_matching.cpp) + * [Pascal Triangle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/pascal_triangle.cpp) + * [Postfix Evaluation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/postfix_evaluation.cpp) + * [Primality Test](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/primality_test.cpp) + * [Recursive Tree Traversal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/recursive_tree_traversal.cpp) + * [Smallest Circle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/smallest_circle.cpp) + * [Sparse Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/sparse_matrix.cpp) + * [Spiral Print](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/spiral_print.cpp) + * [Stairs Pattern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/stairs_pattern.cpp) + * [Tower Of Hanoi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/tower_of_hanoi.cpp) + * [Vector Important Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/vector_important_functions.cpp) ## Physics - * [Ground To Ground Projectile Motion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/physics/ground_to_ground_projectile_motion.cpp) + * [Ground To Ground Projectile Motion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/physics/ground_to_ground_projectile_motion.cpp) ## Probability - * [Addition Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/addition_rule.cpp) - * [Bayes Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/bayes_theorem.cpp) - * [Binomial Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/binomial_dist.cpp) - * [Geometric Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/geometric_dist.cpp) - * [Poisson Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/poisson_dist.cpp) - * [Windowed Median](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/windowed_median.cpp) + * [Addition Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/addition_rule.cpp) + * [Bayes Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/bayes_theorem.cpp) + * [Binomial Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/binomial_dist.cpp) + * [Geometric Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/geometric_dist.cpp) + * [Poisson Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/poisson_dist.cpp) + * [Windowed Median](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/windowed_median.cpp) ## Range Queries - * [Fenwick Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/fenwick_tree.cpp) - * [Heavy Light Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/heavy_light_decomposition.cpp) - * [Mo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/mo.cpp) - * [Persistent Seg Tree Lazy Prop](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/persistent_seg_tree_lazy_prop.cpp) - * [Prefix Sum Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/prefix_sum_array.cpp) - * [Segtree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/segtree.cpp) - * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/sparse_table.cpp) + * [Fenwick Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/fenwick_tree.cpp) + * [Heavy Light Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/heavy_light_decomposition.cpp) + * [Mo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/mo.cpp) + * [Persistent Seg Tree Lazy Prop](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/persistent_seg_tree_lazy_prop.cpp) + * [Prefix Sum Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/prefix_sum_array.cpp) + * [Segtree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/segtree.cpp) + * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/sparse_table.cpp) ## Search - * [Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/binary_search.cpp) - * [Exponential Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/exponential_search.cpp) - * [Fibonacci Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/fibonacci_search.cpp) - * [Floyd Cycle Detection Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/floyd_cycle_detection_algo.cpp) - * [Hash Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/hash_search.cpp) - * [Interpolation Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/interpolation_search.cpp) - * [Interpolation Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/interpolation_search2.cpp) - * [Jump Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/jump_search.cpp) - * [Linear Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/linear_search.cpp) - * [Median Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/median_search.cpp) - * [Median Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/median_search2.cpp) - * [Saddleback Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/saddleback_search.cpp) - * [Sublist Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/sublist_search.cpp) - * [Ternary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/ternary_search.cpp) - * [Text Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/text_search.cpp) + * [Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/binary_search.cpp) + * [Exponential Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/exponential_search.cpp) + * [Fibonacci Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/fibonacci_search.cpp) + * [Floyd Cycle Detection Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/floyd_cycle_detection_algo.cpp) + * [Hash Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/hash_search.cpp) + * [Interpolation Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/interpolation_search.cpp) + * [Interpolation Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/interpolation_search2.cpp) + * [Jump Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/jump_search.cpp) + * [Linear Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/linear_search.cpp) + * [Median Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/median_search.cpp) + * [Median Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/median_search2.cpp) + * [Saddleback Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/saddleback_search.cpp) + * [Sublist Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/sublist_search.cpp) + * [Ternary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/ternary_search.cpp) + * [Text Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/text_search.cpp) ## Sorting - * [Bead Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bead_sort.cpp) - * [Binary Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/binary_insertion_sort.cpp) - * [Bitonic Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bitonic_sort.cpp) - * [Bogo Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bogo_sort.cpp) - * [Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bubble_sort.cpp) - * [Bucket Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bucket_sort.cpp) - * [Cocktail Selection Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/cocktail_selection_sort.cpp) - * [Comb Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/comb_sort.cpp) - * [Count Inversions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/count_inversions.cpp) - * [Counting Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort.cpp) - * [Counting Sort String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort_string.cpp) - * [Cycle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/cycle_sort.cpp) - * [Dnf Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/dnf_sort.cpp) - * [Gnome Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/gnome_sort.cpp) - * [Heap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/heap_sort.cpp) - * [Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/insertion_sort.cpp) - * [Library Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/library_sort.cpp) - * [Merge Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/merge_insertion_sort.cpp) - * [Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/merge_sort.cpp) - * [Non Recursive Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/non_recursive_merge_sort.cpp) - * [Numeric String Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/numeric_string_sort.cpp) - * [Odd Even Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/odd_even_sort.cpp) - * [Pancake Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/pancake_sort.cpp) - * [Pigeonhole Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/pigeonhole_sort.cpp) - * [Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/quick_sort.cpp) - * [Quick Sort 3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/quick_sort_3.cpp) - * [Radix Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort.cpp) - * [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort2.cpp) - * [Random Pivot Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/random_pivot_quick_sort.cpp) - * [Recursive Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/recursive_bubble_sort.cpp) - * [Selection Sort Iterative](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort_iterative.cpp) - * [Selection Sort Recursive](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort_recursive.cpp) - * [Shell Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort.cpp) - * [Shell Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort2.cpp) - * [Slow Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/slow_sort.cpp) - * [Strand Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/strand_sort.cpp) - * [Swap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/swap_sort.cpp) - * [Tim Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/tim_sort.cpp) - * [Wave Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/wave_sort.cpp) - * [Wiggle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/wiggle_sort.cpp) + * [Bead Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bead_sort.cpp) + * [Binary Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/binary_insertion_sort.cpp) + * [Bitonic Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bitonic_sort.cpp) + * [Bogo Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bogo_sort.cpp) + * [Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bubble_sort.cpp) + * [Bucket Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bucket_sort.cpp) + * [Cocktail Selection Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/cocktail_selection_sort.cpp) + * [Comb Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/comb_sort.cpp) + * [Count Inversions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/count_inversions.cpp) + * [Counting Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/counting_sort.cpp) + * [Counting Sort String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/counting_sort_string.cpp) + * [Cycle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/cycle_sort.cpp) + * [Dnf Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/dnf_sort.cpp) + * [Gnome Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/gnome_sort.cpp) + * [Heap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/heap_sort.cpp) + * [Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/insertion_sort.cpp) + * [Library Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/library_sort.cpp) + * [Merge Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/merge_insertion_sort.cpp) + * [Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/merge_sort.cpp) + * [Non Recursive Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/non_recursive_merge_sort.cpp) + * [Numeric String Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/numeric_string_sort.cpp) + * [Odd Even Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/odd_even_sort.cpp) + * [Pancake Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/pancake_sort.cpp) + * [Pigeonhole Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/pigeonhole_sort.cpp) + * [Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort.cpp) + * [Quick Sort 3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort_3.cpp) + * [Radix Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/radix_sort.cpp) + * [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/radix_sort2.cpp) + * [Random Pivot Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/random_pivot_quick_sort.cpp) + * [Recursive Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/recursive_bubble_sort.cpp) + * [Selection Sort Iterative](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/selection_sort_iterative.cpp) + * [Selection Sort Recursive](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/selection_sort_recursive.cpp) + * [Shell Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/shell_sort.cpp) + * [Shell Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/shell_sort2.cpp) + * [Slow Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/slow_sort.cpp) + * [Strand Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/strand_sort.cpp) + * [Swap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/swap_sort.cpp) + * [Tim Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/tim_sort.cpp) + * [Wave Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/wave_sort.cpp) + * [Wiggle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/wiggle_sort.cpp) ## Strings - * [Brute Force String Searching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/brute_force_string_searching.cpp) - * [Horspool](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/horspool.cpp) - * [Knuth Morris Pratt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/knuth_morris_pratt.cpp) - * [Manacher Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp) - * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp) - * [Z Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/z_function.cpp) + * [Brute Force String Searching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/brute_force_string_searching.cpp) + * [Horspool](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/horspool.cpp) + * [Knuth Morris Pratt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/knuth_morris_pratt.cpp) + * [Manacher Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/manacher_algorithm.cpp) + * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/rabin_karp.cpp) + * [Z Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/z_function.cpp) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp new file mode 100644 index 00000000000..1171f84513b --- /dev/null +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -0,0 +1,439 @@ +#include +#include +#include +#include +#include + +/// Complement of 0 is a max integer. +#define MAX_SIZE ~0ULL +/** + * @brief Matrix class. + */ +template ::value || std::is_floating_point::value, + bool>::type> +class Matrix { + std::vector> _mat; + + public: + /** + * @brief Constructor + * @tparam Integer ensuring integers are being evaluated and not other + * data types. + * @param size denoting the size of Matrix as size x size + */ + template ::value, Integer>::type> + Matrix(const Integer size) { + for (size_t i = 0; i < size; ++i) { + _mat.emplace_back(std::vector(size, 0)); + } + } + + /** + * @brief Constructor + * @tparam Integer ensuring integers are being evaluated and not other + * data types. + * @param rows denoting the total rows of Matrix + * @param cols denoting the total elements in each row of Matrix + */ + template ::value, Integer>::type> + Matrix(const Integer rows, const Integer cols) { + for (size_t i = 0; i < rows; ++i) { + _mat.emplace_back(std::vector(cols, 0)); + } + } + + /** + * @brief Get the matrix shape + * @returns pair of integer denoting total rows and columns + */ + inline std::pair size() const { + return {_mat.size(), _mat[0].size()}; + } + + /** + * @brief returns the address of the element at ith place + * (here ith row of the matrix) + * @tparam Integer any valid integer + * @param index index which is requested + * @returns the address of the element (here ith row or array) + */ + template ::value, Integer>::type> + inline std::vector &operator[](const Integer index) { + return _mat[index]; + } + + /** + * @brief Creates a new matrix and returns a part of it. + * @param row_start start of the row + * @param row_end end of the row + * @param col_start start of the col + * @param col_end end of the column + * @returns A slice of (row_end - row_start) x (col_end - col_start) size of + * array starting from row_start row and col_start column + */ + Matrix slice(const size_t row_start, const size_t row_end = MAX_SIZE, + const size_t col_start = MAX_SIZE, + const size_t col_end = MAX_SIZE) const { + const size_t h_size = + (row_end != MAX_SIZE ? row_end : _mat.size()) - row_start; + const size_t v_size = (col_end != MAX_SIZE ? col_end : _mat[0].size()) - + (col_start != MAX_SIZE ? col_start : 0); + Matrix result = Matrix(h_size, v_size); + + const size_t v_start = (col_start != MAX_SIZE ? col_start : 0); + for (size_t i = 0; i < h_size; ++i) { + for (size_t j = 0; j < v_size; ++j) { + result._mat[i][j] = _mat[i + row_start][j + v_start]; + } + } + return result; + } + + /** + * @brief Horizontally stack the matrix (one after the other) + * @tparam Number any type of number + * @param other the other matrix: note that this array is not modified + * @returns void, but modifies the current array + */ + template ::value || + std::is_floating_point::value, + Number>::type> + void h_stack(const Matrix &other) { + assert(_mat.size() == other._mat.size()); + for (size_t i = 0; i < other._mat.size(); ++i) { + for (size_t j = 0; j < other._mat[i].size(); ++j) { + _mat[i].push_back(other._mat[i][j]); + } + } + } + + /** + * @brief Horizontally stack the matrix (current matrix above the other) + * @tparam Number any type of number (Integer or floating point) + * @param other the other matrix: note that this array is not modified + * @returns void, but modifies the current array + */ + template ::value || + std::is_floating_point::value, + Number>::type> + void v_stack(const Matrix &other) { + assert(_mat[0].size() == other._mat[0].size()); + for (size_t i = 0; i < other._mat.size(); ++i) { + _mat.emplace_back(std::vector(other._mat[i].size())); + for (size_t j = 0; j < other._mat[i].size(); ++j) { + _mat.back()[j] = other._mat[i][j]; + } + } + } + + /** + * @brief Add two matrices and returns a new matrix + * @tparam Number any real value to add + * @param other Other matrix to add to this + * @returns new matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix operator+(const Matrix &other) const { + assert(this->size() == other.size()); + Matrix C = Matrix(_mat.size(), _mat[0].size()); + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + C._mat[i][j] = _mat[i][j] + other._mat[i][j]; + } + } + return C; + } + + /** + * @brief Add another matrices to current matrix + * @tparam Number any real value to add + * @param other Other matrix to add to this + * @returns reference of current matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix &operator+=(const Matrix &other) const { + assert(this->size() == other.size()); + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + _mat[i][j] += other._mat[i][j]; + } + } + return this; + } + + /** + * @brief Subtract two matrices and returns a new matrix + * @tparam Number any real value to multiply + * @param other Other matrix to subtract to this + * @returns new matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix operator-(const Matrix &other) const { + assert(this->size() == other.size()); + Matrix C = Matrix(_mat.size(), _mat[0].size()); + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + C._mat[i][j] = _mat[i][j] - other._mat[i][j]; + } + } + return C; + } + + /** + * @brief Subtract another matrices to current matrix + * @tparam Number any real value to Subtract + * @param other Other matrix to Subtract to this + * @returns reference of current matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix &operator-=(const Matrix &other) const { + assert(this->size() == other.size()); + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + _mat[i][j] -= other._mat[i][j]; + } + } + return this; + } + + /** + * @brief Multiply two matrices and returns a new matrix + * @tparam Number any real value to multiply + * @param other Other matrix to multiply to this + * @returns new matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + inline Matrix operator*(const Matrix &other) const { + assert(_mat[0].size() == other._mat.size()); + auto [row, col] = this->size(); + // Main condition for applying strassen's method: + // 1: matrix should be a square matrix + // 2: matrix should be of even size (mat.size() % 2 == 0) + return (row == col && (row & 1) == 0) + ? this->strassens_multiplication(other) + : this->naive_multiplication(other); + } + + /** + * @brief Multiply matrix with a number and returns a new matrix + * @tparam Number any real value to multiply + * @param other Other real number to multiply to current matrix + * @returns new matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + inline Matrix operator*(const Number other) const { + Matrix C = Matrix(_mat.size(), _mat[0].size()); + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + C._mat[i][j] = _mat[i][j] * other; + } + } + return C; + } + + /** + * @brief Multiply a number to current matrix + * @tparam Number any real value to multiply + * @param other Other matrix to multiply to this + * @returns reference of current matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix &operator*=(const Number other) const { + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + _mat[i][j] *= other; + } + } + return this; + } + + /** + * @brief Naive multiplication performed on this + * @tparam Number any real value to multiply + * @param other Other matrix to multiply to this + * @returns new matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix naive_multiplication(const Matrix &other) const { + Matrix C = Matrix(_mat.size(), other._mat[0].size()); + + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < other._mat[0].size(); ++j) { + for (size_t k = 0; k < _mat[0].size(); ++k) { + C._mat[i][j] += _mat[i][k] * other._mat[k][j]; + } + } + } + return C; + } + + /** + * @brief Strassens method of multiplying two matrices + * References: https://en.wikipedia.org/wiki/Strassen_algorithm + * @tparam Number any real value to multiply + * @param other Other matrix to multiply to this + * @returns new matrix + */ + template ::value || + std::is_floating_point::value, + bool>::type> + Matrix strassens_multiplication(const Matrix &other) const { + const size_t size = _mat.size(); + // Base case: when a matrix is small enough for faster naive + // multiplication, or the matrix is of odd size, then go with the naive + // multiplication route; + // else; go with the strassen's method. + if (size <= 128ULL || (size & 1ULL)) { + return this->naive_multiplication(other); + } else { + const Matrix + A = this->slice(0ULL, size >> 1, 0ULL, size >> 1), + B = this->slice(0ULL, size >> 1, size >> 1, size), + C = this->slice(size >> 1, size, 0ULL, size >> 1), + D = this->slice(size >> 1, size, size >> 1, size), + E = other.slice(0ULL, size >> 1, 0ULL, size >> 1), + F = other.slice(0ULL, size >> 1, size >> 1, size), + G = other.slice(size >> 1, size, 0ULL, size >> 1), + H = other.slice(size >> 1, size, size >> 1, size); + + Matrix P1 = A.strassens_multiplication(F - H); + Matrix P2 = (A + B).strassens_multiplication(H); + Matrix P3 = (C + D).strassens_multiplication(E); + Matrix P4 = D.strassens_multiplication(G - E); + Matrix P5 = (A + D).strassens_multiplication(E + H); + Matrix P6 = (B - D).strassens_multiplication(G + H); + Matrix P7 = (A - C).strassens_multiplication(E + F); + + // Building final matrix C11 would be + // [ | ] + // [ C11 | C12 ] + // C = [ ____ | ____ ] + // [ | ] + // [ C21 | C22 ] + // [ | ] + + Matrix C11 = P5 + P4 - P2 + P6; + Matrix C12 = P1 + P2; + Matrix C21 = P3 + P4; + Matrix C22 = P1 + P5 - P3 - P7; + + C21.h_stack(C22); + C11.h_stack(C12); + C11.v_stack(C21); + + return C11; + } + } + + /** + * @brief Compares two matrices if each of them are equal or not + * @param other other matrix to compare + * @returns whether they are equal or not + */ + bool operator==(const Matrix &other) const { + if (_mat.size() != other._mat.size() || + _mat[0].size() != other._mat[0].size()) { + return false; + } + for (size_t i = 0; i < _mat.size(); ++i) { + for (size_t j = 0; j < _mat[i].size(); ++j) { + if (_mat[i][j] != other._mat[i][j]) { + return false; + } + } + } + return true; + } + + friend std::ostream &operator<<(std::ostream &out, const Matrix &mat) { + for (auto &row : mat._mat) { + for (auto &elem : row) { + out << elem << " "; + } + out << "\n"; + } + return out << "\n"; + } +}; + +/** + * @brief Method for testing current implementation + */ +void test() { + const size_t s = 1024; + auto matrix_demo = Matrix(s, s); + auto [row, col] = matrix_demo.size(); + for (size_t i = 0; i < row; ++i) { + for (size_t j = 0; j < col; ++j) { + matrix_demo[i][j] = i + j; + } + } + + auto matrix_demo2 = Matrix(s, s); + std::tie(row, col) = matrix_demo2.size(); + for (size_t i = 0; i < row; ++i) { + for (size_t j = 0; j < col; ++j) { + matrix_demo2[i][j] = 2 + i + j; + } + } + + auto start = std::chrono::system_clock::now(); + auto Mat3 = matrix_demo2 * matrix_demo; + auto end = std::chrono::system_clock::now(); + + std::chrono::duration time = (end - start); + std::cout << "Strassen time: " << time.count() << "s" << std::endl; + + start = std::chrono::system_clock::now(); + auto conf = matrix_demo2.naive_multiplication(matrix_demo); + end = std::chrono::system_clock::now(); + + time = end - start; + std::cout << "Normal time: " << time.count() << "s" << std::endl; + + // std::cout << Mat3 << conf << std::endl; + assert(Mat3 == conf); +} + +/** + * @brief main function + */ +int main() { + test(); + return 0; +} diff --git a/range_queries/sparse_table.cpp b/range_queries/sparse_table.cpp old mode 100755 new mode 100644 From dfb61dfa0f5dd4992a35456b86cbedad13fabe58 Mon Sep 17 00:00:00 2001 From: David Date: Tue, 15 Nov 2022 04:59:08 +0000 Subject: [PATCH 02/12] updating DIRECTORY.md --- DIRECTORY.md | 662 +++++++++++++++++++++++++-------------------------- 1 file changed, 331 insertions(+), 331 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index 2faa8e47d05..5ea0f928ce4 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -1,378 +1,378 @@ ## Backtracking - * [Graph Coloring](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/graph_coloring.cpp) - * [Knight Tour](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/knight_tour.cpp) - * [Magic Sequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/magic_sequence.cpp) - * [Minimax](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/minimax.cpp) - * [N Queens](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens.cpp) - * [N Queens All Solution Optimised](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens_all_solution_optimised.cpp) - * [Nqueen Print All Solutions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/nqueen_print_all_solutions.cpp) - * [Rat Maze](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/rat_maze.cpp) - * [Subarray Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subarray_sum.cpp) - * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subset_sum.cpp) - * [Sudoku Solver](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solver.cpp) - * [Wildcard Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/wildcard_matching.cpp) + * [Graph Coloring](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/graph_coloring.cpp) + * [Knight Tour](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/knight_tour.cpp) + * [Magic Sequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/magic_sequence.cpp) + * [Minimax](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/minimax.cpp) + * [N Queens](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/n_queens.cpp) + * [N Queens All Solution Optimised](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/n_queens_all_solution_optimised.cpp) + * [Nqueen Print All Solutions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/nqueen_print_all_solutions.cpp) + * [Rat Maze](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/rat_maze.cpp) + * [Subarray Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/subarray_sum.cpp) + * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/subset_sum.cpp) + * [Sudoku Solver](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/sudoku_solver.cpp) + * [Wildcard Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/backtracking/wildcard_matching.cpp) ## Bit Manipulation - * [Count Bits Flip](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_bits_flip.cpp) - * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_set_bits.cpp) - * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp) - * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/hamming_distance.cpp) - * [Set Kth Bit](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/set_kth_bit.cpp) + * [Count Bits Flip](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_bits_flip.cpp) + * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_set_bits.cpp) + * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp) + * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/hamming_distance.cpp) + * [Set Kth Bit](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/set_kth_bit.cpp) ## Ciphers - * [A1Z26 Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/a1z26_cipher.cpp) - * [Atbash Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/atbash_cipher.cpp) - * [Base64 Encoding](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/base64_encoding.cpp) - * [Caesar Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/caesar_cipher.cpp) - * [Elliptic Curve Key Exchange](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/elliptic_curve_key_exchange.cpp) - * [Hill Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/hill_cipher.cpp) - * [Morse Code](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/morse_code.cpp) - * [Uint128 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/uint128_t.hpp) - * [Uint256 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/uint256_t.hpp) - * [Vigenere Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/vigenere_cipher.cpp) - * [Xor Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/ciphers/xor_cipher.cpp) + * [A1Z26 Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/a1z26_cipher.cpp) + * [Atbash Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/atbash_cipher.cpp) + * [Base64 Encoding](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/base64_encoding.cpp) + * [Caesar Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/caesar_cipher.cpp) + * [Elliptic Curve Key Exchange](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/elliptic_curve_key_exchange.cpp) + * [Hill Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/hill_cipher.cpp) + * [Morse Code](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/morse_code.cpp) + * [Uint128 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/uint128_t.hpp) + * [Uint256 T](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/uint256_t.hpp) + * [Vigenere Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/vigenere_cipher.cpp) + * [Xor Cipher](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/ciphers/xor_cipher.cpp) ## Cpu Scheduling Algorithms - * [Fcfs Scheduling](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/cpu_scheduling_algorithms/fcfs_scheduling.cpp) + * [Fcfs Scheduling](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/cpu_scheduling_algorithms/fcfs_scheduling.cpp) ## Data Structures - * [Avltree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/avltree.cpp) - * [Binary Search Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binary_search_tree.cpp) - * [Binary Search Tree2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binary_search_tree2.cpp) - * [Binaryheap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/binaryheap.cpp) - * [Bloom Filter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/bloom_filter.cpp) - * [Circular Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/circular_queue_using_linked_list.cpp) + * [Avltree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/avltree.cpp) + * [Binary Search Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/binary_search_tree.cpp) + * [Binary Search Tree2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/binary_search_tree2.cpp) + * [Binaryheap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/binaryheap.cpp) + * [Bloom Filter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/bloom_filter.cpp) + * [Circular Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/circular_queue_using_linked_list.cpp) * Cll - * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/cll.cpp) - * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/cll.h) - * [Main Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/cll/main_cll.cpp) - * [Disjoint Set](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/disjoint_set.cpp) - * [Doubly Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/doubly_linked_list.cpp) - * [Dsu Path Compression](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/dsu_path_compression.cpp) - * [Dsu Union Rank](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/dsu_union_rank.cpp) - * [Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linked_list.cpp) - * [Linkedlist Implentation Usingarray](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/linkedlist_implentation_usingarray.cpp) - * [List Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/list_array.cpp) - * [Morrisinorder](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/morrisinorder.cpp) - * [Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue.h) - * [Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_array.cpp) - * [Queue Using Array2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_array2.cpp) - * [Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_linked_list.cpp) - * [Queue Using Linkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_linkedlist.cpp) - * [Queue Using Two Stacks](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/queue_using_two_stacks.cpp) - * [Rb Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/rb_tree.cpp) - * [Reverse A Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/reverse_a_linked_list.cpp) - * [Skip List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/skip_list.cpp) - * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/sparse_table.cpp) - * [Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack.h) - * [Stack Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_array.cpp) - * [Stack Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_linked_list.cpp) - * [Stack Using Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/stack_using_queue.cpp) - * [Test Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_queue.cpp) - * [Test Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_stack.cpp) - * [Test Stack Students](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/test_stack_students.cpp) - * [Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/tree.cpp) - * [Tree 234](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/tree_234.cpp) - * [Trie Modern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_modern.cpp) - * [Trie Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_tree.cpp) - * [Trie Using Hashmap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_using_hashmap.cpp) + * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/cll/cll.cpp) + * [Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/cll/cll.h) + * [Main Cll](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/cll/main_cll.cpp) + * [Disjoint Set](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/disjoint_set.cpp) + * [Doubly Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/doubly_linked_list.cpp) + * [Dsu Path Compression](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/dsu_path_compression.cpp) + * [Dsu Union Rank](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/dsu_union_rank.cpp) + * [Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/linked_list.cpp) + * [Linkedlist Implentation Usingarray](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/linkedlist_implentation_usingarray.cpp) + * [List Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/list_array.cpp) + * [Morrisinorder](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/morrisinorder.cpp) + * [Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue.h) + * [Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_array.cpp) + * [Queue Using Array2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_array2.cpp) + * [Queue Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_linked_list.cpp) + * [Queue Using Linkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_linkedlist.cpp) + * [Queue Using Two Stacks](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/queue_using_two_stacks.cpp) + * [Rb Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/rb_tree.cpp) + * [Reverse A Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/reverse_a_linked_list.cpp) + * [Skip List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/skip_list.cpp) + * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/sparse_table.cpp) + * [Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack.h) + * [Stack Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack_using_array.cpp) + * [Stack Using Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack_using_linked_list.cpp) + * [Stack Using Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/stack_using_queue.cpp) + * [Test Queue](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/test_queue.cpp) + * [Test Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/test_stack.cpp) + * [Test Stack Students](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/test_stack_students.cpp) + * [Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/tree.cpp) + * [Tree 234](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/tree_234.cpp) + * [Trie Modern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/trie_modern.cpp) + * [Trie Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/trie_tree.cpp) + * [Trie Using Hashmap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/data_structures/trie_using_hashmap.cpp) ## Divide And Conquer - * [Karatsuba Algorithm For Fast Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp) + * [Karatsuba Algorithm For Fast Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp) ## Dynamic Programming - * [0 1 Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/0_1_knapsack.cpp) - * [Abbreviation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/abbreviation.cpp) - * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/armstrong_number.cpp) - * [Bellman Ford](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/bellman_ford.cpp) - * [Catalan Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/catalan_numbers.cpp) - * [Coin Change](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/coin_change.cpp) - * [Coin Change Topdown](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/coin_change_topdown.cpp) - * [Cut Rod](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/cut_rod.cpp) - * [Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/edit_distance.cpp) - * [Egg Dropping Puzzle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/egg_dropping_puzzle.cpp) - * [Fibonacci Bottom Up](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/fibonacci_bottom_up.cpp) - * [Floyd Warshall](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/floyd_warshall.cpp) - * [House Robber](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/house_robber.cpp) - * [Kadane](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/kadane.cpp) - * [Kadane2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/kadane2.cpp) - * [Longest Common String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_common_string.cpp) - * [Longest Common Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_common_subsequence.cpp) - * [Longest Increasing Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence.cpp) - * [Longest Increasing Subsequence (Nlogn)](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp) - * [Longest Palindromic Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/longest_palindromic_subsequence.cpp) - * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/matrix_chain_multiplication.cpp) - * [Minimum Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/minimum_edit_distance.cpp) - * [Palindrome Partitioning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/palindrome_partitioning.cpp) - * [Partition Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/partition_problem.cpp) - * [Searching Of Element In Dynamic Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/searching_of_element_in_dynamic_array.cpp) - * [Shortest Common Supersequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/shortest_common_supersequence.cpp) - * [Tree Height](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/tree_height.cpp) - * [Word Break](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/word_break.cpp) + * [0 1 Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/0_1_knapsack.cpp) + * [Abbreviation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/abbreviation.cpp) + * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/armstrong_number.cpp) + * [Bellman Ford](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/bellman_ford.cpp) + * [Catalan Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/catalan_numbers.cpp) + * [Coin Change](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/coin_change.cpp) + * [Coin Change Topdown](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/coin_change_topdown.cpp) + * [Cut Rod](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/cut_rod.cpp) + * [Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/edit_distance.cpp) + * [Egg Dropping Puzzle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/egg_dropping_puzzle.cpp) + * [Fibonacci Bottom Up](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/fibonacci_bottom_up.cpp) + * [Floyd Warshall](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/floyd_warshall.cpp) + * [House Robber](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/house_robber.cpp) + * [Kadane](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/kadane.cpp) + * [Kadane2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/kadane2.cpp) + * [Longest Common String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_common_string.cpp) + * [Longest Common Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_common_subsequence.cpp) + * [Longest Increasing Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_increasing_subsequence.cpp) + * [Longest Increasing Subsequence (Nlogn)](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp) + * [Longest Palindromic Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_palindromic_subsequence.cpp) + * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/matrix_chain_multiplication.cpp) + * [Minimum Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/minimum_edit_distance.cpp) + * [Palindrome Partitioning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/palindrome_partitioning.cpp) + * [Partition Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/partition_problem.cpp) + * [Searching Of Element In Dynamic Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/searching_of_element_in_dynamic_array.cpp) + * [Shortest Common Supersequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/shortest_common_supersequence.cpp) + * [Tree Height](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/tree_height.cpp) + * [Word Break](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/word_break.cpp) ## Geometry - * [Graham Scan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/graham_scan_algorithm.cpp) - * [Graham Scan Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/graham_scan_functions.hpp) - * [Jarvis Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/jarvis_algorithm.cpp) - * [Line Segment Intersection](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/line_segment_intersection.cpp) + * [Graham Scan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/graham_scan_algorithm.cpp) + * [Graham Scan Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/graham_scan_functions.hpp) + * [Jarvis Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/jarvis_algorithm.cpp) + * [Line Segment Intersection](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/geometry/line_segment_intersection.cpp) ## Graph - * [Bidirectional Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bidirectional_dijkstra.cpp) - * [Breadth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/breadth_first_search.cpp) - * [Bridge Finding With Tarjan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/bridge_finding_with_tarjan_algorithm.cpp) - * [Connected Components](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components.cpp) - * [Connected Components With Dsu](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/connected_components_with_dsu.cpp) - * [Cycle Check Directed Graph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/cycle_check_directed_graph.cpp) - * [Depth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/depth_first_search.cpp) - * [Depth First Search With Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/depth_first_search_with_stack.cpp) - * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/dijkstra.cpp) - * [Hamiltons Cycle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/hamiltons_cycle.cpp) - * [Hopcroft Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/hopcroft_karp.cpp) - * [Is Graph Bipartite](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/is_graph_bipartite.cpp) - * [Is Graph Bipartite2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/is_graph_bipartite2.cpp) - * [Kosaraju](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/kosaraju.cpp) - * [Kruskal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/kruskal.cpp) - * [Lowest Common Ancestor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/lowest_common_ancestor.cpp) - * [Max Flow With Ford Fulkerson And Edmond Karp Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp) - * [Prim](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/prim.cpp) - * [Topological Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort.cpp) - * [Topological Sort By Kahns Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort_by_kahns_algo.cpp) - * [Travelling Salesman Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/travelling_salesman_problem.cpp) + * [Bidirectional Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/bidirectional_dijkstra.cpp) + * [Breadth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/breadth_first_search.cpp) + * [Bridge Finding With Tarjan Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/bridge_finding_with_tarjan_algorithm.cpp) + * [Connected Components](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/connected_components.cpp) + * [Connected Components With Dsu](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/connected_components_with_dsu.cpp) + * [Cycle Check Directed Graph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/cycle_check_directed_graph.cpp) + * [Depth First Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/depth_first_search.cpp) + * [Depth First Search With Stack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/depth_first_search_with_stack.cpp) + * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/dijkstra.cpp) + * [Hamiltons Cycle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/hamiltons_cycle.cpp) + * [Hopcroft Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/hopcroft_karp.cpp) + * [Is Graph Bipartite](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/is_graph_bipartite.cpp) + * [Is Graph Bipartite2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/is_graph_bipartite2.cpp) + * [Kosaraju](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/kosaraju.cpp) + * [Kruskal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/kruskal.cpp) + * [Lowest Common Ancestor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/lowest_common_ancestor.cpp) + * [Max Flow With Ford Fulkerson And Edmond Karp Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp) + * [Prim](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/prim.cpp) + * [Topological Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/topological_sort.cpp) + * [Topological Sort By Kahns Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/topological_sort_by_kahns_algo.cpp) + * [Travelling Salesman Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graph/travelling_salesman_problem.cpp) ## Graphics - * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graphics/spirograph.cpp) + * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graphics/spirograph.cpp) ## Greedy Algorithms - * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/dijkstra.cpp) - * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/huffman.cpp) - * [Jumpgame](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/jumpgame.cpp) - * [Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/knapsack.cpp) - * [Kruskals Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/kruskals_minimum_spanning_tree.cpp) - * [Prims Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/greedy_algorithms/prims_minimum_spanning_tree.cpp) + * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/dijkstra.cpp) + * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/huffman.cpp) + * [Jumpgame](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/jumpgame.cpp) + * [Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/knapsack.cpp) + * [Kruskals Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/kruskals_minimum_spanning_tree.cpp) + * [Prims Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/prims_minimum_spanning_tree.cpp) ## Hashing - * [Chaining](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/chaining.cpp) - * [Double Hash Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/double_hash_hash_table.cpp) - * [Linear Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/linear_probing_hash_table.cpp) - * [Md5](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/md5.cpp) - * [Quadratic Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/quadratic_probing_hash_table.cpp) - * [Sha1](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/hashing/sha1.cpp) + * [Chaining](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/chaining.cpp) + * [Double Hash Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/double_hash_hash_table.cpp) + * [Linear Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/linear_probing_hash_table.cpp) + * [Md5](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/md5.cpp) + * [Quadratic Probing Hash Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/quadratic_probing_hash_table.cpp) + * [Sha1](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/hashing/sha1.cpp) ## Machine Learning - * [A Star Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/a_star_search.cpp) - * [Adaline Learning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/adaline_learning.cpp) - * [Kohonen Som Topology](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/kohonen_som_topology.cpp) - * [Kohonen Som Trace](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/kohonen_som_trace.cpp) - * [Neural Network](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/neural_network.cpp) - * [Ordinary Least Squares Regressor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/ordinary_least_squares_regressor.cpp) - * [Vector Ops](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/machine_learning/vector_ops.hpp) + * [A Star Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/a_star_search.cpp) + * [Adaline Learning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/adaline_learning.cpp) + * [Kohonen Som Topology](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/kohonen_som_topology.cpp) + * [Kohonen Som Trace](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/kohonen_som_trace.cpp) + * [Neural Network](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/neural_network.cpp) + * [Ordinary Least Squares Regressor](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/ordinary_least_squares_regressor.cpp) + * [Vector Ops](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/vector_ops.hpp) ## Math - * [Approximate Pi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/approximate_pi.cpp) - * [Area](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/area.cpp) - * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/armstrong_number.cpp) - * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp) - * [Binomial Calculate](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binomial_calculate.cpp) - * [Check Amicable Pair](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_amicable_pair.cpp) - * [Check Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_factorial.cpp) - * [Check Prime](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_prime.cpp) - * [Complex Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/complex_numbers.cpp) - * [Double Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/double_factorial.cpp) - * [Eulers Totient Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/eulers_totient_function.cpp) - * [Extended Euclid Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/extended_euclid_algorithm.cpp) - * [Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/factorial.cpp) - * [Fast Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fast_power.cpp) - * [Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci.cpp) - * [Fibonacci Fast](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_fast.cpp) - * [Fibonacci Large](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_large.cpp) - * [Fibonacci Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_matrix_exponentiation.cpp) - * [Fibonacci Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/fibonacci_sum.cpp) - * [Finding Number Of Digits In A Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/finding_number_of_digits_in_a_number.cpp) - * [Gcd Iterative Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_iterative_euclidean.cpp) - * [Gcd Of N Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_of_n_numbers.cpp) - * [Gcd Recursive Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_recursive_euclidean.cpp) - * [Integral Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/integral_approximation.cpp) - * [Integral Approximation2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/integral_approximation2.cpp) - * [Inv Sqrt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/inv_sqrt.cpp) - * [Large Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_factorial.cpp) - * [Large Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_number.h) - * [Largest Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/largest_power.cpp) - * [Lcm Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/lcm_sum.cpp) - * [Least Common Multiple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/least_common_multiple.cpp) - * [Linear Recurrence Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/linear_recurrence_matrix.cpp) - * [Magic Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/magic_number.cpp) - * [Miller Rabin](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/miller_rabin.cpp) - * [Modular Division](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_division.cpp) - * [Modular Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp) - * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp) - * [Modular Inverse Simple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_simple.cpp) - * [N Bonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_bonacci.cpp) - * [N Choose R](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_choose_r.cpp) - * [Ncr Modulo P](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/ncr_modulo_p.cpp) - * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp) - * [Perimeter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/perimeter.cpp) - * [Power For Huge Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_for_huge_numbers.cpp) - * [Power Of Two](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/power_of_two.cpp) - * [Prime Factorization](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_factorization.cpp) - * [Prime Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/prime_numbers.cpp) - * [Primes Up To Billion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/primes_up_to_billion.cpp) - * [Realtime Stats](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/realtime_stats.cpp) - * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sieve_of_eratosthenes.cpp) - * [Sqrt Double](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sqrt_double.cpp) - * [String Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/string_fibonacci.cpp) - * [Sum Of Binomial Coefficient](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sum_of_binomial_coefficient.cpp) - * [Sum Of Digits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sum_of_digits.cpp) - * [Vector Cross Product](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/vector_cross_product.cpp) - * [Volume](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/volume.cpp) + * [Approximate Pi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/approximate_pi.cpp) + * [Area](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/area.cpp) + * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/armstrong_number.cpp) + * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/binary_exponent.cpp) + * [Binomial Calculate](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/binomial_calculate.cpp) + * [Check Amicable Pair](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_amicable_pair.cpp) + * [Check Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_factorial.cpp) + * [Check Prime](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/check_prime.cpp) + * [Complex Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/complex_numbers.cpp) + * [Double Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/double_factorial.cpp) + * [Eulers Totient Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/eulers_totient_function.cpp) + * [Extended Euclid Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/extended_euclid_algorithm.cpp) + * [Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/factorial.cpp) + * [Fast Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fast_power.cpp) + * [Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci.cpp) + * [Fibonacci Fast](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_fast.cpp) + * [Fibonacci Large](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_large.cpp) + * [Fibonacci Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_matrix_exponentiation.cpp) + * [Fibonacci Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/fibonacci_sum.cpp) + * [Finding Number Of Digits In A Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/finding_number_of_digits_in_a_number.cpp) + * [Gcd Iterative Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/gcd_iterative_euclidean.cpp) + * [Gcd Of N Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/gcd_of_n_numbers.cpp) + * [Gcd Recursive Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/gcd_recursive_euclidean.cpp) + * [Integral Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/integral_approximation.cpp) + * [Integral Approximation2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/integral_approximation2.cpp) + * [Inv Sqrt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/inv_sqrt.cpp) + * [Large Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/large_factorial.cpp) + * [Large Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/large_number.h) + * [Largest Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/largest_power.cpp) + * [Lcm Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/lcm_sum.cpp) + * [Least Common Multiple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/least_common_multiple.cpp) + * [Linear Recurrence Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/linear_recurrence_matrix.cpp) + * [Magic Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/magic_number.cpp) + * [Miller Rabin](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/miller_rabin.cpp) + * [Modular Division](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_division.cpp) + * [Modular Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_exponentiation.cpp) + * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_inverse_fermat_little_theorem.cpp) + * [Modular Inverse Simple](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/modular_inverse_simple.cpp) + * [N Bonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/n_bonacci.cpp) + * [N Choose R](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/n_choose_r.cpp) + * [Ncr Modulo P](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/ncr_modulo_p.cpp) + * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/number_of_positive_divisors.cpp) + * [Perimeter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/perimeter.cpp) + * [Power For Huge Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/power_for_huge_numbers.cpp) + * [Power Of Two](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/power_of_two.cpp) + * [Prime Factorization](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/prime_factorization.cpp) + * [Prime Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/prime_numbers.cpp) + * [Primes Up To Billion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/primes_up_to_billion.cpp) + * [Realtime Stats](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/realtime_stats.cpp) + * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sieve_of_eratosthenes.cpp) + * [Sqrt Double](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sqrt_double.cpp) + * [String Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/string_fibonacci.cpp) + * [Sum Of Binomial Coefficient](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sum_of_binomial_coefficient.cpp) + * [Sum Of Digits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/sum_of_digits.cpp) + * [Vector Cross Product](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/vector_cross_product.cpp) + * [Volume](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/volume.cpp) ## Numerical Methods - * [Babylonian Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/babylonian_method.cpp) - * [Bisection Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/bisection_method.cpp) - * [Brent Method Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/brent_method_extrema.cpp) - * [Composite Simpson Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/composite_simpson_rule.cpp) - * [Durand Kerner Roots](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/durand_kerner_roots.cpp) - * [False Position](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/false_position.cpp) - * [Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/fast_fourier_transform.cpp) - * [Gaussian Elimination](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gaussian_elimination.cpp) - * [Golden Search Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/golden_search_extrema.cpp) - * [Gram Schmidt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gram_schmidt.cpp) - * [Inverse Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/inverse_fast_fourier_transform.cpp) - * [Lu Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decompose.cpp) - * [Lu Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decomposition.h) - * [Midpoint Integral Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/midpoint_integral_method.cpp) - * [Newton Raphson Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/newton_raphson_method.cpp) - * [Ode Forward Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_forward_euler.cpp) - * [Ode Midpoint Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_midpoint_euler.cpp) - * [Ode Semi Implicit Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_semi_implicit_euler.cpp) - * [Qr Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decompose.h) - * [Qr Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_decomposition.cpp) - * [Qr Eigen Values](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/qr_eigen_values.cpp) - * [Rungekutta](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/rungekutta.cpp) - * [Successive Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/successive_approximation.cpp) + * [Babylonian Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/babylonian_method.cpp) + * [Bisection Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/bisection_method.cpp) + * [Brent Method Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/brent_method_extrema.cpp) + * [Composite Simpson Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/composite_simpson_rule.cpp) + * [Durand Kerner Roots](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/durand_kerner_roots.cpp) + * [False Position](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/false_position.cpp) + * [Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/fast_fourier_transform.cpp) + * [Gaussian Elimination](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/gaussian_elimination.cpp) + * [Golden Search Extrema](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/golden_search_extrema.cpp) + * [Gram Schmidt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/gram_schmidt.cpp) + * [Inverse Fast Fourier Transform](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/inverse_fast_fourier_transform.cpp) + * [Lu Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/lu_decompose.cpp) + * [Lu Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/lu_decomposition.h) + * [Midpoint Integral Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/midpoint_integral_method.cpp) + * [Newton Raphson Method](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/newton_raphson_method.cpp) + * [Ode Forward Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/ode_forward_euler.cpp) + * [Ode Midpoint Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/ode_midpoint_euler.cpp) + * [Ode Semi Implicit Euler](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/ode_semi_implicit_euler.cpp) + * [Qr Decompose](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/qr_decompose.h) + * [Qr Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/qr_decomposition.cpp) + * [Qr Eigen Values](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/qr_eigen_values.cpp) + * [Rungekutta](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/rungekutta.cpp) + * [Successive Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/numerical_methods/successive_approximation.cpp) ## Operations On Datastructures - * [Array Left Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/array_left_rotation.cpp) - * [Array Right Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/array_right_rotation.cpp) - * [Circular Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_linked_list.cpp) - * [Circular Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/circular_queue_using_array.cpp) - * [Get Size Of Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/get_size_of_linked_list.cpp) - * [Inorder Successor Of Bst](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/inorder_successor_of_bst.cpp) - * [Intersection Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/intersection_of_two_arrays.cpp) - * [Reverse A Linked List Using Recusion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_a_linked_list_using_recusion.cpp) - * [Reverse Binary Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/reverse_binary_tree.cpp) - * [Selectionsortlinkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/selectionsortlinkedlist.cpp) - * [Trie Multiple Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/trie_multiple_search.cpp) - * [Union Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/operations_on_datastructures/union_of_two_arrays.cpp) + * [Array Left Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/array_left_rotation.cpp) + * [Array Right Rotation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/array_right_rotation.cpp) + * [Circular Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/circular_linked_list.cpp) + * [Circular Queue Using Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/circular_queue_using_array.cpp) + * [Get Size Of Linked List](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/get_size_of_linked_list.cpp) + * [Inorder Successor Of Bst](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/inorder_successor_of_bst.cpp) + * [Intersection Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/intersection_of_two_arrays.cpp) + * [Reverse A Linked List Using Recusion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/reverse_a_linked_list_using_recusion.cpp) + * [Reverse Binary Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/reverse_binary_tree.cpp) + * [Selectionsortlinkedlist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/selectionsortlinkedlist.cpp) + * [Trie Multiple Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/trie_multiple_search.cpp) + * [Union Of Two Arrays](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/operations_on_datastructures/union_of_two_arrays.cpp) ## Others - * [Buzz Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/buzz_number.cpp) - * [Decimal To Binary](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_binary.cpp) - * [Decimal To Hexadecimal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_hexadecimal.cpp) - * [Decimal To Roman Numeral](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/decimal_to_roman_numeral.cpp) - * [Easter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/easter.cpp) - * [Fast Integer Input](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/fast_integer_input.cpp) - * [Happy Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/happy_number.cpp) - * [Iterative Tree Traversals](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/iterative_tree_traversals.cpp) - * [Kadanes3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/kadanes3.cpp) - * [Lru Cache](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/lru_cache.cpp) - * [Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/matrix_exponentiation.cpp) - * [Palindrome Of Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/palindrome_of_number.cpp) - * [Paranthesis Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/paranthesis_matching.cpp) - * [Pascal Triangle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/pascal_triangle.cpp) - * [Postfix Evaluation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/postfix_evaluation.cpp) - * [Primality Test](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/primality_test.cpp) - * [Recursive Tree Traversal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/recursive_tree_traversal.cpp) - * [Smallest Circle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/smallest_circle.cpp) - * [Sparse Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/sparse_matrix.cpp) - * [Spiral Print](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/spiral_print.cpp) - * [Stairs Pattern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/stairs_pattern.cpp) - * [Tower Of Hanoi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/tower_of_hanoi.cpp) - * [Vector Important Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/others/vector_important_functions.cpp) + * [Buzz Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/buzz_number.cpp) + * [Decimal To Binary](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/decimal_to_binary.cpp) + * [Decimal To Hexadecimal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/decimal_to_hexadecimal.cpp) + * [Decimal To Roman Numeral](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/decimal_to_roman_numeral.cpp) + * [Easter](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/easter.cpp) + * [Fast Integer Input](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/fast_integer_input.cpp) + * [Happy Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/happy_number.cpp) + * [Iterative Tree Traversals](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/iterative_tree_traversals.cpp) + * [Kadanes3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/kadanes3.cpp) + * [Lru Cache](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/lru_cache.cpp) + * [Matrix Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/matrix_exponentiation.cpp) + * [Palindrome Of Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/palindrome_of_number.cpp) + * [Paranthesis Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/paranthesis_matching.cpp) + * [Pascal Triangle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/pascal_triangle.cpp) + * [Postfix Evaluation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/postfix_evaluation.cpp) + * [Primality Test](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/primality_test.cpp) + * [Recursive Tree Traversal](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/recursive_tree_traversal.cpp) + * [Smallest Circle](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/smallest_circle.cpp) + * [Sparse Matrix](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/sparse_matrix.cpp) + * [Spiral Print](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/spiral_print.cpp) + * [Stairs Pattern](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/stairs_pattern.cpp) + * [Tower Of Hanoi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/tower_of_hanoi.cpp) + * [Vector Important Functions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/others/vector_important_functions.cpp) ## Physics - * [Ground To Ground Projectile Motion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/physics/ground_to_ground_projectile_motion.cpp) + * [Ground To Ground Projectile Motion](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/physics/ground_to_ground_projectile_motion.cpp) ## Probability - * [Addition Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/addition_rule.cpp) - * [Bayes Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/bayes_theorem.cpp) - * [Binomial Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/binomial_dist.cpp) - * [Geometric Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/geometric_dist.cpp) - * [Poisson Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/poisson_dist.cpp) - * [Windowed Median](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/probability/windowed_median.cpp) + * [Addition Rule](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/addition_rule.cpp) + * [Bayes Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/bayes_theorem.cpp) + * [Binomial Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/binomial_dist.cpp) + * [Geometric Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/geometric_dist.cpp) + * [Poisson Dist](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/poisson_dist.cpp) + * [Windowed Median](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/probability/windowed_median.cpp) ## Range Queries - * [Fenwick Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/fenwick_tree.cpp) - * [Heavy Light Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/heavy_light_decomposition.cpp) - * [Mo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/mo.cpp) - * [Persistent Seg Tree Lazy Prop](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/persistent_seg_tree_lazy_prop.cpp) - * [Prefix Sum Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/prefix_sum_array.cpp) - * [Segtree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/segtree.cpp) - * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/range_queries/sparse_table.cpp) + * [Fenwick Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/fenwick_tree.cpp) + * [Heavy Light Decomposition](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/heavy_light_decomposition.cpp) + * [Mo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/mo.cpp) + * [Persistent Seg Tree Lazy Prop](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/persistent_seg_tree_lazy_prop.cpp) + * [Prefix Sum Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/prefix_sum_array.cpp) + * [Segtree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/segtree.cpp) + * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/sparse_table.cpp) ## Search - * [Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/binary_search.cpp) - * [Exponential Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/exponential_search.cpp) - * [Fibonacci Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/fibonacci_search.cpp) - * [Floyd Cycle Detection Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/floyd_cycle_detection_algo.cpp) - * [Hash Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/hash_search.cpp) - * [Interpolation Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/interpolation_search.cpp) - * [Interpolation Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/interpolation_search2.cpp) - * [Jump Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/jump_search.cpp) - * [Linear Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/linear_search.cpp) - * [Median Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/median_search.cpp) - * [Median Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/median_search2.cpp) - * [Saddleback Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/saddleback_search.cpp) - * [Sublist Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/sublist_search.cpp) - * [Ternary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/ternary_search.cpp) - * [Text Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/search/text_search.cpp) + * [Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/binary_search.cpp) + * [Exponential Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/exponential_search.cpp) + * [Fibonacci Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/fibonacci_search.cpp) + * [Floyd Cycle Detection Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/floyd_cycle_detection_algo.cpp) + * [Hash Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/hash_search.cpp) + * [Interpolation Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/interpolation_search.cpp) + * [Interpolation Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/interpolation_search2.cpp) + * [Jump Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/jump_search.cpp) + * [Linear Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/linear_search.cpp) + * [Median Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/median_search.cpp) + * [Median Search2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/median_search2.cpp) + * [Saddleback Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/saddleback_search.cpp) + * [Sublist Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/sublist_search.cpp) + * [Ternary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/ternary_search.cpp) + * [Text Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/text_search.cpp) ## Sorting - * [Bead Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bead_sort.cpp) - * [Binary Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/binary_insertion_sort.cpp) - * [Bitonic Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bitonic_sort.cpp) - * [Bogo Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bogo_sort.cpp) - * [Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bubble_sort.cpp) - * [Bucket Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/bucket_sort.cpp) - * [Cocktail Selection Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/cocktail_selection_sort.cpp) - * [Comb Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/comb_sort.cpp) - * [Count Inversions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/count_inversions.cpp) - * [Counting Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort.cpp) - * [Counting Sort String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/counting_sort_string.cpp) - * [Cycle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/cycle_sort.cpp) - * [Dnf Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/dnf_sort.cpp) - * [Gnome Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/gnome_sort.cpp) - * [Heap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/heap_sort.cpp) - * [Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/insertion_sort.cpp) - * [Library Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/library_sort.cpp) - * [Merge Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/merge_insertion_sort.cpp) - * [Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/merge_sort.cpp) - * [Non Recursive Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/non_recursive_merge_sort.cpp) - * [Numeric String Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/numeric_string_sort.cpp) - * [Odd Even Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/odd_even_sort.cpp) - * [Pancake Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/pancake_sort.cpp) - * [Pigeonhole Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/pigeonhole_sort.cpp) - * [Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/quick_sort.cpp) - * [Quick Sort 3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/quick_sort_3.cpp) - * [Radix Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort.cpp) - * [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/radix_sort2.cpp) - * [Random Pivot Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/random_pivot_quick_sort.cpp) - * [Recursive Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/recursive_bubble_sort.cpp) - * [Selection Sort Iterative](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort_iterative.cpp) - * [Selection Sort Recursive](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/selection_sort_recursive.cpp) - * [Shell Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort.cpp) - * [Shell Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/shell_sort2.cpp) - * [Slow Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/slow_sort.cpp) - * [Strand Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/strand_sort.cpp) - * [Swap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/swap_sort.cpp) - * [Tim Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/tim_sort.cpp) - * [Wave Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/wave_sort.cpp) - * [Wiggle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/sorting/wiggle_sort.cpp) + * [Bead Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bead_sort.cpp) + * [Binary Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/binary_insertion_sort.cpp) + * [Bitonic Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bitonic_sort.cpp) + * [Bogo Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bogo_sort.cpp) + * [Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bubble_sort.cpp) + * [Bucket Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/bucket_sort.cpp) + * [Cocktail Selection Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/cocktail_selection_sort.cpp) + * [Comb Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/comb_sort.cpp) + * [Count Inversions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/count_inversions.cpp) + * [Counting Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/counting_sort.cpp) + * [Counting Sort String](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/counting_sort_string.cpp) + * [Cycle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/cycle_sort.cpp) + * [Dnf Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/dnf_sort.cpp) + * [Gnome Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/gnome_sort.cpp) + * [Heap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/heap_sort.cpp) + * [Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/insertion_sort.cpp) + * [Library Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/library_sort.cpp) + * [Merge Insertion Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/merge_insertion_sort.cpp) + * [Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/merge_sort.cpp) + * [Non Recursive Merge Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/non_recursive_merge_sort.cpp) + * [Numeric String Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/numeric_string_sort.cpp) + * [Odd Even Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/odd_even_sort.cpp) + * [Pancake Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/pancake_sort.cpp) + * [Pigeonhole Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/pigeonhole_sort.cpp) + * [Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort.cpp) + * [Quick Sort 3](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/quick_sort_3.cpp) + * [Radix Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/radix_sort.cpp) + * [Radix Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/radix_sort2.cpp) + * [Random Pivot Quick Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/random_pivot_quick_sort.cpp) + * [Recursive Bubble Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/recursive_bubble_sort.cpp) + * [Selection Sort Iterative](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/selection_sort_iterative.cpp) + * [Selection Sort Recursive](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/selection_sort_recursive.cpp) + * [Shell Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/shell_sort.cpp) + * [Shell Sort2](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/shell_sort2.cpp) + * [Slow Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/slow_sort.cpp) + * [Strand Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/strand_sort.cpp) + * [Swap Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/swap_sort.cpp) + * [Tim Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/tim_sort.cpp) + * [Wave Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/wave_sort.cpp) + * [Wiggle Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/sorting/wiggle_sort.cpp) ## Strings - * [Brute Force String Searching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/brute_force_string_searching.cpp) - * [Horspool](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/horspool.cpp) - * [Knuth Morris Pratt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/knuth_morris_pratt.cpp) - * [Manacher Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp) - * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp) - * [Z Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/z_function.cpp) + * [Brute Force String Searching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/brute_force_string_searching.cpp) + * [Horspool](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/horspool.cpp) + * [Knuth Morris Pratt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/knuth_morris_pratt.cpp) + * [Manacher Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/manacher_algorithm.cpp) + * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/rabin_karp.cpp) + * [Z Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/strings/z_function.cpp) From 02439b57d8701089a2b07f97aeeaca4064a2ba83 Mon Sep 17 00:00:00 2001 From: Ashish Daulatabad Date: Tue, 15 Nov 2022 10:47:10 +0530 Subject: [PATCH 03/12] Fix cpp lint error --- divide_and_conquer/strassen_matrix_multiplication.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp index 1171f84513b..054ef482f7f 100644 --- a/divide_and_conquer/strassen_matrix_multiplication.cpp +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -5,7 +5,7 @@ #include /// Complement of 0 is a max integer. -#define MAX_SIZE ~0ULL +constexpr size_t MAX_SIZE = ~0ULL; /** * @brief Matrix class. */ From 4da11dccf8360008b6707f2c756bdd416b607def Mon Sep 17 00:00:00 2001 From: David Date: Tue, 15 Nov 2022 05:17:51 +0000 Subject: [PATCH 04/12] updating DIRECTORY.md --- DIRECTORY.md | 1 + 1 file changed, 1 insertion(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index 5ea0f928ce4..0752f842d22 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -80,6 +80,7 @@ ## Divide And Conquer * [Karatsuba Algorithm For Fast Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp) + * [Strassen Matrix Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/divide_and_conquer/strassen_matrix_multiplication.cpp) ## Dynamic Programming * [0 1 Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/0_1_knapsack.cpp) From 9243c4ff90f7f4f8a4fc02e2b5debdf2177d4c0b Mon Sep 17 00:00:00 2001 From: David Date: Tue, 15 Nov 2022 05:18:13 +0000 Subject: [PATCH 05/12] clang-format and clang-tidy fixes for 02439b57 --- .../strassen_matrix_multiplication.cpp | 2 +- range_queries/sparse_table.cpp | 52 ++++++++++--------- 2 files changed, 29 insertions(+), 25 deletions(-) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp index 054ef482f7f..065644ac54c 100644 --- a/divide_and_conquer/strassen_matrix_multiplication.cpp +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -26,7 +26,7 @@ class Matrix { template ::value, Integer>::type> - Matrix(const Integer size) { + explicit Matrix(const Integer size) { for (size_t i = 0; i < size; ++i) { _mat.emplace_back(std::vector(size, 0)); } diff --git a/range_queries/sparse_table.cpp b/range_queries/sparse_table.cpp index 465532f3b60..4f13945ba1c 100644 --- a/range_queries/sparse_table.cpp +++ b/range_queries/sparse_table.cpp @@ -1,21 +1,23 @@ /** * @file sparse_table.cpp - * @brief Implementation of [Sparse Table](https://en.wikipedia.org/wiki/Range_minimum_query) data structure + * @brief Implementation of [Sparse + * Table](https://en.wikipedia.org/wiki/Range_minimum_query) data structure * * @details * Sparse Table is a data structure, that allows answering range queries. - * It can answer most range queries in O(logn), but its true power is answering range minimum queries - * or equivalent range maximum queries). For those queries it can compute the answer in O(1) time. + * It can answer most range queries in O(logn), but its true power is answering + * range minimum queries or equivalent range maximum queries). For those queries + * it can compute the answer in O(1) time. * * * Running Time Complexity \n * * Build : O(NlogN) \n * * Range Query : O(1) \n -*/ + */ -#include +#include #include #include -#include +#include /** * @namespace range_queries @@ -26,19 +28,19 @@ namespace range_queries { * @namespace sparse_table * @brief Range queries using sparse-tables */ - namespace sparse_table { +namespace sparse_table { /** * This function precomputes intial log table for further use. * @param n value of the size of the input array * @return corresponding vector of the log table */ -template +template std::vector computeLogs(const std::vector& A) { int n = A.size(); std::vector logs(n); logs[1] = 0; - for (int i = 2 ; i < n ; i++) { - logs[i] = logs[i/2] + 1; + for (int i = 2; i < n; i++) { + logs[i] = logs[i / 2] + 1; } return logs; } @@ -50,19 +52,20 @@ std::vector computeLogs(const std::vector& A) { * @param logs array of the log table * @return created sparse table data structure */ -template -std::vector > buildTable(const std::vector& A, const std::vector& logs) { +template +std::vector > buildTable(const std::vector& A, + const std::vector& logs) { int n = A.size(); - std::vector > table(20, std::vector(n+5, 0)); + std::vector > table(20, std::vector(n + 5, 0)); int curLen = 0; - for (int i = 0 ; i <= logs[n] ; i++) { + for (int i = 0; i <= logs[n]; i++) { curLen = 1 << i; - for (int j = 0 ; j + curLen < n ; j++) { + for (int j = 0; j + curLen < n; j++) { if (curLen == 1) { table[i][j] = A[j]; - } - else { - table[i][j] = std::min(table[i-1][j], table[i-1][j + curLen/2]); + } else { + table[i][j] = + std::min(table[i - 1][j], table[i - 1][j + curLen / 2]); } } } @@ -77,14 +80,15 @@ std::vector > buildTable(const std::vector& A, const std::vect * @param table sparse table data structure for the input array * @return minimum value for the [beg, end] range for the input array */ -template -int getMinimum(int beg, int end, const std::vector& logs, const std::vector >& table) { +template +int getMinimum(int beg, int end, const std::vector& logs, + const std::vector >& table) { int p = logs[end - beg + 1]; int pLen = 1 << p; return std::min(table[p][beg], table[p][end - pLen + 1]); } -} -} // namespace range_queries +} // namespace sparse_table +} // namespace range_queries /** * Main function @@ -92,10 +96,10 @@ int getMinimum(int beg, int end, const std::vector& logs, const std::vector A{1, 2, 0, 3, 9}; std::vector logs = range_queries::sparse_table::computeLogs(A); - std::vector > table = range_queries::sparse_table::buildTable(A, logs); + std::vector > table = + range_queries::sparse_table::buildTable(A, logs); assert(range_queries::sparse_table::getMinimum(0, 0, logs, table) == 1); assert(range_queries::sparse_table::getMinimum(0, 4, logs, table) == 0); assert(range_queries::sparse_table::getMinimum(2, 4, logs, table) == 0); return 0; } - From 66eca89522667040aa0c3c53d4c7859b5634f402 Mon Sep 17 00:00:00 2001 From: Ashish Daulatabad Date: Tue, 15 Nov 2022 10:58:34 +0530 Subject: [PATCH 06/12] Fix windows error --- .../strassen_matrix_multiplication.cpp | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp index 054ef482f7f..5717bb2b4a9 100644 --- a/divide_and_conquer/strassen_matrix_multiplication.cpp +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -230,7 +230,8 @@ class Matrix { bool>::type> inline Matrix operator*(const Matrix &other) const { assert(_mat[0].size() == other._mat.size()); - auto [row, col] = this->size(); + auto size = this->size(); + const size_t row = size.first, col = size.second; // Main condition for applying strassen's method: // 1: matrix should be a square matrix // 2: matrix should be of even size (mat.size() % 2 == 0) @@ -397,17 +398,16 @@ class Matrix { void test() { const size_t s = 1024; auto matrix_demo = Matrix(s, s); - auto [row, col] = matrix_demo.size(); - for (size_t i = 0; i < row; ++i) { - for (size_t j = 0; j < col; ++j) { + + for (size_t i = 0; i < s; ++i) { + for (size_t j = 0; j < s; ++j) { matrix_demo[i][j] = i + j; } } auto matrix_demo2 = Matrix(s, s); - std::tie(row, col) = matrix_demo2.size(); - for (size_t i = 0; i < row; ++i) { - for (size_t j = 0; j < col; ++j) { + for (size_t i = 0; i < s; ++i) { + for (size_t j = 0; j < s; ++j) { matrix_demo2[i][j] = 2 + i + j; } } From 194e1b920decb83a5de294f25119935c75bbc0d7 Mon Sep 17 00:00:00 2001 From: Ashish Daulatabad Date: Fri, 18 Nov 2022 22:29:17 +0530 Subject: [PATCH 07/12] Add namespaces --- .../strassen_matrix_multiplication.cpp | 22 +++++++++++++++++-- 1 file changed, 20 insertions(+), 2 deletions(-) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp index a79b5528f86..7e34e4bb6b0 100644 --- a/divide_and_conquer/strassen_matrix_multiplication.cpp +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -4,6 +4,18 @@ #include #include +/** + * @namespace divide_and_conquer + * @brief Divide and Conquer algorithms + */ +namespace divide_and_conquer { + +/** + * @namespace strassens_multiplication + * @brief Namespace for performing strassen's multiplication + */ +namespace strassens_multiplication { + /// Complement of 0 is a max integer. constexpr size_t MAX_SIZE = ~0ULL; /** @@ -392,12 +404,17 @@ class Matrix { } }; +} // namespace strassens_multiplication + +} // namespace divide_and_conquer + /** * @brief Method for testing current implementation */ void test() { const size_t s = 1024; - auto matrix_demo = Matrix(s, s); + auto matrix_demo = + divide_and_conquer::strassens_multiplication::Matrix(s, s); for (size_t i = 0; i < s; ++i) { for (size_t j = 0; j < s; ++j) { @@ -405,7 +422,8 @@ void test() { } } - auto matrix_demo2 = Matrix(s, s); + auto matrix_demo2 = + divide_and_conquer::strassens_multiplication::Matrix(s, s); for (size_t i = 0; i < s; ++i) { for (size_t j = 0; j < s; ++j) { matrix_demo2[i][j] = 2 + i + j; From d57f796b2d887f0e5f53a7158bc3fc6ab11c1b11 Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" Date: Thu, 29 Dec 2022 04:47:51 +0000 Subject: [PATCH 08/12] updating DIRECTORY.md --- DIRECTORY.md | 3 --- 1 file changed, 3 deletions(-) diff --git a/DIRECTORY.md b/DIRECTORY.md index 4fb4b88e1bd..14877695224 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -17,10 +17,7 @@ * [Count Bits Flip](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_bits_flip.cpp) * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_set_bits.cpp) * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp) -<<<<<<< HEAD -======= * [Find Non Repeating Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/find_non_repeating_number.cpp) ->>>>>>> 582cdc7cc43c2e6bab2662127485c1965443c8bf * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/hamming_distance.cpp) * [Set Kth Bit](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/bit_manipulation/set_kth_bit.cpp) From 5cd34dc6421726188ba2f34eb60231f810d15f7e Mon Sep 17 00:00:00 2001 From: AshishYUO Date: Thu, 29 Dec 2022 12:22:25 +0530 Subject: [PATCH 09/12] Proper documentation --- .../strassen_matrix_multiplication.cpp | 30 ++++++++++++++----- 1 file changed, 22 insertions(+), 8 deletions(-) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp index 45dd1764355..1d06bf5a8e3 100644 --- a/divide_and_conquer/strassen_matrix_multiplication.cpp +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -1,8 +1,20 @@ -#include -#include -#include -#include -#include +/** + * @brief [Strassen's + * algorithm](https://en.wikipedia.org/wiki/Strassen_algorithm) is one of the + * methods for multiplying two matrices. It is one of the faster algorithms for + * larger matrices than naive multiplication method. + * + * It involves dividing each matrices into 4 blocks, given they are evenly + * divisible, and are combined with new defined matrices involving 7 matrix + * multiplications instead of eight, yielding O(n^2.8073) complexity. + * + * @author [AshishYUO](https://github.com/AshishYUO) + */ +#include /// For assert operation +#include /// For std::chrono; time measurement +#include /// For I/O operations +#include /// For std::tuple +#include /// For creating dynamic arrays /** * @namespace divide_and_conquer @@ -409,9 +421,10 @@ class Matrix { } // namespace divide_and_conquer /** - * @brief Method for testing current implementation + * @brief Self-test implementations + * @returns void */ -void test() { +static void test() { const size_t s = 2048; auto matrix_demo = divide_and_conquer::strassens_multiplication::Matrix(s, s); @@ -450,8 +463,9 @@ void test() { /** * @brief main function + * @returns 0 on exit */ int main() { - test(); + test(); // run self-test implementation return 0; } From 729e874a34412edd85fba715afde914104b40027 Mon Sep 17 00:00:00 2001 From: Ashish Bhanu Daulatabad Date: Fri, 13 Jan 2023 18:11:50 +0000 Subject: [PATCH 10/12] Reduce the matrix size. --- divide_and_conquer/strassen_matrix_multiplication.cpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/divide_and_conquer/strassen_matrix_multiplication.cpp b/divide_and_conquer/strassen_matrix_multiplication.cpp index 1d06bf5a8e3..47498c966b1 100644 --- a/divide_and_conquer/strassen_matrix_multiplication.cpp +++ b/divide_and_conquer/strassen_matrix_multiplication.cpp @@ -343,7 +343,7 @@ class Matrix { // multiplication, or the matrix is of odd size, then go with the naive // multiplication route; // else; go with the strassen's method. - if (size <= 128ULL || (size & 1ULL)) { + if (size <= 64ULL || (size & 1ULL)) { return this->naive_multiplication(other); } else { const Matrix @@ -425,7 +425,7 @@ class Matrix { * @returns void */ static void test() { - const size_t s = 2048; + const size_t s = 512; auto matrix_demo = divide_and_conquer::strassens_multiplication::Matrix(s, s); From a426be8b50e346fc687b327a34acc424dfc928e0 Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" Date: Tue, 24 Jan 2023 20:00:02 +0000 Subject: [PATCH 11/12] updating DIRECTORY.md --- DIRECTORY.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/DIRECTORY.md b/DIRECTORY.md index ada2e977bc4..0ed6b7c5bbc 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -111,6 +111,7 @@ * [Partition Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/partition_problem.cpp) * [Searching Of Element In Dynamic Array](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/searching_of_element_in_dynamic_array.cpp) * [Shortest Common Supersequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/shortest_common_supersequence.cpp) + * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/subset_sum.cpp) * [Tree Height](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/tree_height.cpp) * [Word Break](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/word_break.cpp) @@ -147,6 +148,7 @@ * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/graphics/spirograph.cpp) ## Greedy Algorithms + * [Boruvkas Minimum Spanning Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/boruvkas_minimum_spanning_tree.cpp) * [Dijkstra](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/dijkstra.cpp) * [Huffman](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/huffman.cpp) * [Jumpgame](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/greedy_algorithms/jumpgame.cpp) @@ -172,6 +174,7 @@ * [Vector Ops](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/machine_learning/vector_ops.hpp) ## Math + * [Aliquot Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/aliquot_sum.cpp) * [Approximate Pi](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/approximate_pi.cpp) * [Area](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/area.cpp) * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/math/armstrong_number.cpp) From 567ab95bafdd5fe49adb1b74b1facb00904e1847 Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" Date: Tue, 24 Jan 2023 20:00:40 +0000 Subject: [PATCH 12/12] clang-format and clang-tidy fixes for 0545555a --- ...elling_salesman_using_bit_manipulation.cpp | 112 +++--- dynamic_programming/subset_sum.cpp | 48 ++- .../boruvkas_minimum_spanning_tree.cpp | 337 +++++++++--------- 3 files changed, 261 insertions(+), 236 deletions(-) diff --git a/bit_manipulation/travelling_salesman_using_bit_manipulation.cpp b/bit_manipulation/travelling_salesman_using_bit_manipulation.cpp index fb708be2a13..31243ed2921 100644 --- a/bit_manipulation/travelling_salesman_using_bit_manipulation.cpp +++ b/bit_manipulation/travelling_salesman_using_bit_manipulation.cpp @@ -5,12 +5,14 @@ * (https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/) * * @details - * Given the distance/cost(as and adjacency matrix) between each city/node to the other city/node , - * the problem is to find the shortest possible route that visits every city exactly once - * and returns to the starting point or we can say the minimum cost of whole tour. + * Given the distance/cost(as and adjacency matrix) between each city/node to + * the other city/node , the problem is to find the shortest possible route that + * visits every city exactly once and returns to the starting point or we can + * say the minimum cost of whole tour. * * Explanation: - * INPUT -> You are given with a adjacency matrix A = {} which contains the distance between two cities/node. + * INPUT -> You are given with a adjacency matrix A = {} which contains the + * distance between two cities/node. * * OUTPUT -> Minimum cost of whole tour from starting point * @@ -18,11 +20,11 @@ * Space complexity: O(n) * @author [Utkarsh Yadav](https://github.com/Rytnix) */ -#include /// for std::min +#include /// for std::min #include /// for assert -#include /// for IO operations -#include /// for std::vector -#include /// for limits of integral types +#include /// for IO operations +#include /// for limits of integral types +#include /// for std::vector /** * @namespace bit_manipulation @@ -42,40 +44,53 @@ namespace travelling_salesman_using_bit_manipulation { * @param setOfCitites represents the city in bit form.\ * @param city is taken to track the current city movement. * @param n is the no of citys . - * @param dp vector is used to keep a record of state to avoid the recomputation. - * @returns minimum cost of traversing whole nodes/cities from starting point back to starting point + * @param dp vector is used to keep a record of state to avoid the + * recomputation. + * @returns minimum cost of traversing whole nodes/cities from starting point + * back to starting point */ -std::uint64_t travelling_salesman_using_bit_manipulation(std::vector> dist, // dist is the adjacency matrix containing the distance. - // setOfCities as a bit represent the cities/nodes. Ex: if setOfCities = 2 => 0010(in binary) - // means representing the city/node B if city/nodes are represented as D->C->B->A. - std::uint64_t setOfCities, - std::uint64_t city, // city is taken to track our current city/node movement,where we are currently. - std::uint64_t n, // n is the no of cities we have. - std::vector> &dp) //dp is taken to memorize the state to avoid recomputition +std::uint64_t travelling_salesman_using_bit_manipulation( + std::vector> + dist, // dist is the adjacency matrix containing the distance. + // setOfCities as a bit represent the cities/nodes. Ex: if + // setOfCities = 2 => 0010(in binary) means representing the + // city/node B if city/nodes are represented as D->C->B->A. + std::uint64_t setOfCities, + std::uint64_t city, // city is taken to track our current city/node + // movement,where we are currently. + std::uint64_t n, // n is the no of cities we have. + std::vector> + &dp) // dp is taken to memorize the state to avoid recomputition { - //base case; - if (setOfCities == (1 << n) - 1) // we have covered all the cities - return dist[city][0]; //return the cost from the current city to the original city. + // base case; + if (setOfCities == (1 << n) - 1) { // we have covered all the cities + return dist[city][0]; // return the cost from the current city to the + // original city. + } - if (dp[setOfCities][city] != -1) + if (dp[setOfCities][city] != -1) { return dp[setOfCities][city]; - //otherwise try all possible options - uint64_t ans = 2147483647 ; + } + // otherwise try all possible options + uint64_t ans = 2147483647; for (int choice = 0; choice < n; choice++) { - //check if the city is visited or not. - if ((setOfCities & (1 << choice)) == 0 ) { // this means that this perticular city is not visited. - std::uint64_t subProb = dist[city][choice] + travelling_salesman_using_bit_manipulation(dist, setOfCities | (1 << choice), choice, n, dp); - // Here we are doing a recursive call to tsp with the updated set of city/node - // and choice which tells that where we are currently. + // check if the city is visited or not. + if ((setOfCities & (1 << choice)) == + 0) { // this means that this perticular city is not visited. + std::uint64_t subProb = + dist[city][choice] + + travelling_salesman_using_bit_manipulation( + dist, setOfCities | (1 << choice), choice, n, dp); + // Here we are doing a recursive call to tsp with the updated set of + // city/node and choice which tells that where we are currently. ans = std::min(ans, subProb); } - } dp[setOfCities][city] = ans; return ans; } -} // namespace travelling_salesman_using_bit_manipulation -} // namespace bit_manipulation +} // namespace travelling_salesman_using_bit_manipulation +} // namespace bit_manipulation /** * @brief Self-test implementations @@ -84,29 +99,36 @@ std::uint64_t travelling_salesman_using_bit_manipulation(std::vector> dist = { - {0, 20, 42, 35}, {20, 0, 30, 34}, {42, 30, 0, 12}, {35, 34, 12, 0} - }; + {0, 20, 42, 35}, {20, 0, 30, 34}, {42, 30, 0, 12}, {35, 34, 12, 0}}; uint32_t V = dist.size(); std::vector> dp(1 << V, std::vector(V, -1)); - assert(bit_manipulation::travelling_salesman_using_bit_manipulation::travelling_salesman_using_bit_manipulation(dist, 1, 0, V, dp) == 97); - std::cout << "1st test-case: passed!" << "\n"; + assert(bit_manipulation::travelling_salesman_using_bit_manipulation:: + travelling_salesman_using_bit_manipulation(dist, 1, 0, V, dp) == + 97); + std::cout << "1st test-case: passed!" + << "\n"; // 2nd test-case dist = {{0, 5, 10, 15}, {5, 0, 20, 30}, {10, 20, 0, 35}, {15, 30, 35, 0}}; V = dist.size(); - std::vector> dp1(1 << V, std::vector(V, -1)); - assert(bit_manipulation::travelling_salesman_using_bit_manipulation::travelling_salesman_using_bit_manipulation(dist, 1, 0, V, dp1) == 75); - std::cout << "2nd test-case: passed!" << "\n"; + std::vector> dp1(1 << V, + std::vector(V, -1)); + assert(bit_manipulation::travelling_salesman_using_bit_manipulation:: + travelling_salesman_using_bit_manipulation(dist, 1, 0, V, dp1) == + 75); + std::cout << "2nd test-case: passed!" + << "\n"; // 3rd test-case - dist = { - {0, 10, 15, 20}, {10, 0, 35, 25}, {15, 35, 0, 30}, {20, 25, 30, 0} - }; + dist = {{0, 10, 15, 20}, {10, 0, 35, 25}, {15, 35, 0, 30}, {20, 25, 30, 0}}; V = dist.size(); - std::vector> dp2(1 << V, std::vector(V, -1)); - assert(bit_manipulation::travelling_salesman_using_bit_manipulation::travelling_salesman_using_bit_manipulation(dist, 1, 0, V, dp2) == 80); - - std::cout << "3rd test-case: passed!" << "\n"; + std::vector> dp2(1 << V, + std::vector(V, -1)); + assert(bit_manipulation::travelling_salesman_using_bit_manipulation:: + travelling_salesman_using_bit_manipulation(dist, 1, 0, V, dp2) == + 80); + std::cout << "3rd test-case: passed!" + << "\n"; } /** diff --git a/dynamic_programming/subset_sum.cpp b/dynamic_programming/subset_sum.cpp index 897fc9a96a7..ef3953a8286 100644 --- a/dynamic_programming/subset_sum.cpp +++ b/dynamic_programming/subset_sum.cpp @@ -5,19 +5,19 @@ * whether a subset with target sum exists or not. * * @details - * In this problem, we use dynamic programming to find if we can pull out a - * subset from an array whose sum is equal to a given target sum. The overall - * time complexity of the problem is O(n * targetSum) where n is the size of - * the array. For example, array = [1, -10, 2, 31, -6], targetSum = -14. - * Output: true => We can pick subset [-10, 2, -6] with sum as + * In this problem, we use dynamic programming to find if we can pull out a + * subset from an array whose sum is equal to a given target sum. The overall + * time complexity of the problem is O(n * targetSum) where n is the size of + * the array. For example, array = [1, -10, 2, 31, -6], targetSum = -14. + * Output: true => We can pick subset [-10, 2, -6] with sum as * (-10) + 2 + (-6) = -14. * @author [KillerAV](https://github.com/KillerAV) */ #include /// for std::assert #include /// for IO operations -#include /// for std::vector -#include /// for unordered map +#include /// for unordered map +#include /// for std::vector /** * @namespace dynamic_programming @@ -33,33 +33,31 @@ namespace dynamic_programming { namespace subset_sum { /** - * Recursive function using dynamic programming to find if the required sum + * Recursive function using dynamic programming to find if the required sum * subset exists or not. * @param arr input array * @param targetSum the target sum of the subset * @param dp the map storing the results * @returns true/false based on if the target sum subset exists or not. */ -bool subset_sum_recursion( - const std::vector &arr, - int targetSum, - std::vector> *dp, - int index = 0) { - - if(targetSum == 0) { // Found a valid subset with required sum. +bool subset_sum_recursion(const std::vector &arr, int targetSum, + std::vector> *dp, + int index = 0) { + if (targetSum == 0) { // Found a valid subset with required sum. return true; } - if(index == arr.size()) { // End of array + if (index == arr.size()) { // End of array return false; } - if ((*dp)[index].count(targetSum)) { // Answer already present in map + if ((*dp)[index].count(targetSum)) { // Answer already present in map return (*dp)[index][targetSum]; } - - bool ans = subset_sum_recursion(arr, targetSum - arr[index], dp, index + 1) - || subset_sum_recursion(arr, targetSum, dp, index + 1); - (*dp)[index][targetSum] = ans; // Save ans in dp map. + + bool ans = + subset_sum_recursion(arr, targetSum - arr[index], dp, index + 1) || + subset_sum_recursion(arr, targetSum, dp, index + 1); + (*dp)[index][targetSum] = ans; // Save ans in dp map. return ans; } @@ -84,10 +82,10 @@ bool subset_sum_problem(const std::vector &arr, const int targetSum) { static void test() { // custom input vector std::vector> custom_input_arr(3); - custom_input_arr[0] = std::vector {1, -10, 2, 31, -6}; - custom_input_arr[1] = std::vector {2, 3, 4}; - custom_input_arr[2] = std::vector {0, 1, 0, 1, 0}; - + custom_input_arr[0] = std::vector{1, -10, 2, 31, -6}; + custom_input_arr[1] = std::vector{2, 3, 4}; + custom_input_arr[2] = std::vector{0, 1, 0, 1, 0}; + std::vector custom_input_target_sum(3); custom_input_target_sum[0] = -14; custom_input_target_sum[1] = 10; diff --git a/greedy_algorithms/boruvkas_minimum_spanning_tree.cpp b/greedy_algorithms/boruvkas_minimum_spanning_tree.cpp index c5a0360492d..ff8bcb124d8 100644 --- a/greedy_algorithms/boruvkas_minimum_spanning_tree.cpp +++ b/greedy_algorithms/boruvkas_minimum_spanning_tree.cpp @@ -3,36 +3,39 @@ * @file * * @brief - * [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) to find the Minimum Spanning Tree - * - * + * [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) to + *find the Minimum Spanning Tree + * + * * @details - * Boruvka's algorithm is a greepy algorithm to find the MST by starting with small trees, and combining - * them to build bigger ones. + * Boruvka's algorithm is a greepy algorithm to find the MST by starting with + *small trees, and combining them to build bigger ones. * 1. Creates a group for every vertex. - * 2. looks through each edge of every vertex for the smallest weight. Keeps track - * of the smallest edge for each of the current groups. - * 3. Combine each group with the group it shares its smallest edge, adding the smallest - * edge to the MST. + * 2. looks through each edge of every vertex for the smallest weight. Keeps + *track of the smallest edge for each of the current groups. + * 3. Combine each group with the group it shares its smallest edge, adding the + *smallest edge to the MST. * 4. Repeat step 2-3 until all vertices are combined into a single group. - * - * It assumes that the graph is connected. Non-connected edges can be represented using 0 or INT_MAX - * -*/ + * + * It assumes that the graph is connected. Non-connected edges can be + *represented using 0 or INT_MAX + * + */ -#include /// for IO operations -#include /// for std::vector -#include /// for assert -#include /// for INT_MAX +#include /// for assert +#include /// for INT_MAX +#include /// for IO operations +#include /// for std::vector /** * @namespace greedy_algorithms * @brief Greedy Algorithms */ -namespace greedy_algorithms { +namespace greedy_algorithms { /** * @namespace boruvkas_minimum_spanning_tree - * @brief Functions for the [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementation + * @brief Functions for the [Borůvkas + * Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementation */ namespace boruvkas_minimum_spanning_tree { /** @@ -41,123 +44,127 @@ namespace boruvkas_minimum_spanning_tree { * @param v vertex to find parent of * @returns the parent of the vertex */ -int findParent(std::vector> parent, const int v) { - if (parent[v].first != v) { - parent[v].first = findParent(parent, parent[v].first); - } +int findParent(std::vector> parent, const int v) { + if (parent[v].first != v) { + parent[v].first = findParent(parent, parent[v].first); + } - return parent[v].first; + return parent[v].first; } /** * @brief the implementation of boruvka's algorithm - * @param adj a graph adjancency matrix stored as 2d vectors. + * @param adj a graph adjancency matrix stored as 2d vectors. * @returns the MST as 2d vectors */ std::vector> boruvkas(std::vector> adj) { - - size_t size = adj.size(); - size_t total_groups = size; - - if (size <= 1) { - return adj; - } - - // Stores the current Minimum Spanning Tree. As groups are combined, they are added to the MST - std::vector> MST(size, std::vector(size, INT_MAX)); - for (int i = 0; i < size; i++) { - MST[i][i] = 0; - } - - // Step 1: Create a group for each vertex - - // Stores the parent of the vertex and its current depth, both initialized to 0 - std::vector> parent(size, std::make_pair(0, 0)); - - for (int i = 0; i < size; i++) { - parent[i].first = i; // Sets parent of each vertex to itself, depth remains 0 - } - - // Repeat until all are in a single group - while (total_groups > 1) { - - std::vector> smallest_edge(size, std::make_pair(-1, -1)); //Pairing: start node, end node - - // Step 2: Look throught each vertex for its smallest edge, only using the right half of the adj matrix - for (int i = 0; i < size; i++) { - for (int j = i+1; j < size; j++) { - - if (adj[i][j] == INT_MAX || adj[i][j] == 0) { // No connection - continue; - } - - // Finds the parents of the start and end points to make sure they arent in the same group - int parentA = findParent(parent, i); - int parentB = findParent(parent, j); - - if (parentA != parentB) { - - // Grabs the start and end points for the first groups current smallest edge - int start = smallest_edge[parentA].first; - int end = smallest_edge[parentA].second; - - // If there is no current smallest edge, or the new edge is smaller, records the new smallest - if (start == -1 || adj [i][j] < adj[start][end]) { - smallest_edge[parentA].first = i; - smallest_edge[parentA].second = j; - } - - // Does the same for the second group - start = smallest_edge[parentB].first; - end = smallest_edge[parentB].second; - - if (start == -1 || adj[j][i] < adj[start][end]) { - smallest_edge[parentB].first = j; - smallest_edge[parentB].second = i; - } - } - } - } - - // Step 3: Combine the groups based off their smallest edge - - for (int i = 0; i < size; i++) { - - // Makes sure the smallest edge exists - if (smallest_edge[i].first != -1) { - - // Start and end points for the groups smallest edge - int start = smallest_edge[i].first; - int end = smallest_edge[i].second; - - // Parents of the two groups - A is always itself - int parentA = i; - int parentB = findParent(parent, end); - - // Makes sure the two nodes dont share the same parent. Would happen if the two groups have been - //merged previously through a common shortest edge - if (parentA == parentB) { - continue; - } - - // Tries to balance the trees as much as possible as they are merged. The parent of the shallower - //tree will be pointed to the parent of the deeper tree. - if (parent[parentA].second < parent[parentB].second) { - parent[parentB].first = parentA; //New parent - parent[parentB].second++; //Increase depth - } - else { - parent[parentA].first = parentB; - parent[parentA].second++; - } - // Add the connection to the MST, using both halves of the adj matrix - MST[start][end] = adj[start][end]; - MST[end][start] = adj[end][start]; - total_groups--; // one fewer group - } - } - } - return MST; + size_t size = adj.size(); + size_t total_groups = size; + + if (size <= 1) { + return adj; + } + + // Stores the current Minimum Spanning Tree. As groups are combined, they + // are added to the MST + std::vector> MST(size, std::vector(size, INT_MAX)); + for (int i = 0; i < size; i++) { + MST[i][i] = 0; + } + + // Step 1: Create a group for each vertex + + // Stores the parent of the vertex and its current depth, both initialized + // to 0 + std::vector> parent(size, std::make_pair(0, 0)); + + for (int i = 0; i < size; i++) { + parent[i].first = + i; // Sets parent of each vertex to itself, depth remains 0 + } + + // Repeat until all are in a single group + while (total_groups > 1) { + std::vector> smallest_edge( + size, std::make_pair(-1, -1)); // Pairing: start node, end node + + // Step 2: Look throught each vertex for its smallest edge, only using + // the right half of the adj matrix + for (int i = 0; i < size; i++) { + for (int j = i + 1; j < size; j++) { + if (adj[i][j] == INT_MAX || adj[i][j] == 0) { // No connection + continue; + } + + // Finds the parents of the start and end points to make sure + // they arent in the same group + int parentA = findParent(parent, i); + int parentB = findParent(parent, j); + + if (parentA != parentB) { + // Grabs the start and end points for the first groups + // current smallest edge + int start = smallest_edge[parentA].first; + int end = smallest_edge[parentA].second; + + // If there is no current smallest edge, or the new edge is + // smaller, records the new smallest + if (start == -1 || adj[i][j] < adj[start][end]) { + smallest_edge[parentA].first = i; + smallest_edge[parentA].second = j; + } + + // Does the same for the second group + start = smallest_edge[parentB].first; + end = smallest_edge[parentB].second; + + if (start == -1 || adj[j][i] < adj[start][end]) { + smallest_edge[parentB].first = j; + smallest_edge[parentB].second = i; + } + } + } + } + + // Step 3: Combine the groups based off their smallest edge + + for (int i = 0; i < size; i++) { + // Makes sure the smallest edge exists + if (smallest_edge[i].first != -1) { + // Start and end points for the groups smallest edge + int start = smallest_edge[i].first; + int end = smallest_edge[i].second; + + // Parents of the two groups - A is always itself + int parentA = i; + int parentB = findParent(parent, end); + + // Makes sure the two nodes dont share the same parent. Would + // happen if the two groups have been + // merged previously through a common shortest edge + if (parentA == parentB) { + continue; + } + + // Tries to balance the trees as much as possible as they are + // merged. The parent of the shallower + // tree will be pointed to the parent of the deeper tree. + if (parent[parentA].second < parent[parentB].second) { + parent[parentB].first = parentA; // New parent + parent[parentB].second++; // Increase depth + } else { + parent[parentA].first = parentB; + parent[parentA].second++; + } + // Add the connection to the MST, using both halves of the adj + // matrix + MST[start][end] = adj[start][end]; + MST[end][start] = adj[end][start]; + total_groups--; // one fewer group + } + } + } + return MST; } /** @@ -166,19 +173,18 @@ std::vector> boruvkas(std::vector> adj) { * @returns the int size of the tree */ int test_findGraphSum(std::vector> adj) { - - size_t size = adj.size(); - int sum = 0; - - //Moves through one side of the adj matrix, counting the sums of each edge - for (int i = 0; i < size; i++) { - for (int j = i + 1; j < size; j++) { - if (adj[i][j] < INT_MAX) { - sum += adj[i][j]; - } - } - } - return sum; + size_t size = adj.size(); + int sum = 0; + + // Moves through one side of the adj matrix, counting the sums of each edge + for (int i = 0; i < size; i++) { + for (int j = i + 1; j < size; j++) { + if (adj[i][j] < INT_MAX) { + sum += adj[i][j]; + } + } + } + return sum; } } // namespace boruvkas_minimum_spanning_tree } // namespace greedy_algorithms @@ -186,30 +192,29 @@ int test_findGraphSum(std::vector> adj) { /** * @brief Self-test implementations * @returns void -*/ + */ static void tests() { - std::cout << "Starting tests...\n\n"; - std::vector> graph = { - {0, 5, INT_MAX, 3, INT_MAX} , - {5, 0, 2, INT_MAX, 5} , - {INT_MAX, 2, 0, INT_MAX, 3} , - {3, INT_MAX, INT_MAX, 0, INT_MAX} , - {INT_MAX, 5, 3, INT_MAX, 0} , - }; - std::vector> MST = greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas(graph); - assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum(MST) == 13); - std::cout << "1st test passed!" << std::endl; - - graph = { - { 0, 2, 0, 6, 0 }, - { 2, 0, 3, 8, 5 }, - { 0, 3, 0, 0, 7 }, - { 6, 8, 0, 0, 9 }, - { 0, 5, 7, 9, 0 } - }; - MST = greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas(graph); - assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum(MST) == 16); - std::cout << "2nd test passed!" << std::endl; + std::cout << "Starting tests...\n\n"; + std::vector> graph = { + {0, 5, INT_MAX, 3, INT_MAX}, {5, 0, 2, INT_MAX, 5}, + {INT_MAX, 2, 0, INT_MAX, 3}, {3, INT_MAX, INT_MAX, 0, INT_MAX}, + {INT_MAX, 5, 3, INT_MAX, 0}, + }; + std::vector> MST = + greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas(graph); + assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum( + MST) == 13); + std::cout << "1st test passed!" << std::endl; + + graph = {{0, 2, 0, 6, 0}, + {2, 0, 3, 8, 5}, + {0, 3, 0, 0, 7}, + {6, 8, 0, 0, 9}, + {0, 5, 7, 9, 0}}; + MST = greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas(graph); + assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum( + MST) == 16); + std::cout << "2nd test passed!" << std::endl; } /** @@ -217,6 +222,6 @@ static void tests() { * @returns 0 on exit */ int main() { - tests(); // run self-test implementations - return 0; + tests(); // run self-test implementations + return 0; }