From 5990417ede8e3765bd0d9f07d46d82df01d69fa7 Mon Sep 17 00:00:00 2001 From: Ashish Daulatabad Date: Tue, 15 Nov 2022 10:22:58 +0530 Subject: [PATCH] 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 2faa8e47d..5ea0f928c 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 000000000..1171f8451 --- /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