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Create subset_sum.cpp (TheAlgorithms#1517)
* Create subset_sum.cpp * Update subset_sum.cpp * Update subset_sum.cpp * updating DIRECTORY.md * clang-format and clang-tidy fixes for 4827805 * Update subset_sum.cpp * clang-format and clang-tidy fixes for dac3246 * Update backtracking/subset_sum.cpp Co-authored-by: Filip Hlasek <fhlasek@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: Filip Hlasek <fhlasek@gmail.com> * clang-format and clang-tidy fixes for 1328571 * Update backtracking/subset_sum.cpp Co-authored-by: Filip Hlasek <fhlasek@gmail.com> * Update subset_sum.cpp * clang-format and clang-tidy fixes for 2325e16 * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * clang-format and clang-tidy fixes for 1b82d49 * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * clang-format and clang-tidy fixes for 31a1dea * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update backtracking/subset_sum.cpp Co-authored-by: David Leal <halfpacho@gmail.com> * Update subset_sum.cpp * clang-format and clang-tidy fixes for 9cd0763 * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update backtracking/subset_sum.cpp Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> * Update subset_sum.cpp * Update subset_sum.cpp * clang-format and clang-tidy fixes for 2405a14 * Update subset_sum.cpp * clang-format and clang-tidy fixes for 383baeb * Update subset_sum.cpp * Update backtracking/subset_sum.cpp * Update backtracking/subset_sum.cpp * Update backtracking/subset_sum.cpp * Update backtracking/subset_sum.cpp * Update backtracking/subset_sum.cpp * Update backtracking/subset_sum.cpp * Update backtracking/subset_sum.cpp Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Filip Hlasek <fhlasek@gmail.com> Co-authored-by: Abhinn Mishra <49574460+mishraabhinn@users.noreply.github.com> Co-authored-by: David Leal <halfpacho@gmail.com>
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DIRECTORY.md

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* [N Queens All Solution Optimised](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/n_queens_all_solution_optimised.cpp)
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* [Nqueen Print All Solutions](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/nqueen_print_all_solutions.cpp)
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* [Rat Maze](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/rat_maze.cpp)
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* [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subset_sum.cpp)
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* [Sudoku Solve](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solve.cpp)
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## Bit Manipulation

backtracking/subset_sum.cpp

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/**
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* @file
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* @brief Implementation of the [Subset
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* Sum](https://en.wikipedia.org/wiki/Subset_sum_problem) problem.
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* @details
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* We are given an array and a sum value. The algorithm finds all
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* the subsets of that array with sum equal to the given sum and return such
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* subsets count. This approach will have exponential time complexity.
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* @author [Swastika Gupta](https://github.com/Swastyy)
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*/
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#include <cassert> /// for assert
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#include <iostream> /// for IO operations
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#include <vector> /// for std::vector
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/**
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* @namespace backtracking
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* @brief Backtracking algorithms
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*/
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namespace backtracking {
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/**
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* @namespace Subsets
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* @brief Functions for the [Subset
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* Sum](https://en.wikipedia.org/wiki/Subset_sum_problem) problem.
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*/
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namespace subset_sum {
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/**
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* @brief The main function implements count of subsets
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* @param sum is the required sum of any subset
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* @param in_arr is the input array
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* @returns count of the number of subsets with required sum
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*/
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uint64_t number_of_subsets(int32_t sum, const std::vector<int32_t> &in_arr) {
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int32_t nelement = in_arr.size();
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uint64_t count_of_subset = 0;
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for (int32_t i = 0; i < (1 << (nelement)); i++) {
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int32_t check = 0;
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for (int32_t j = 0; j < nelement; j++) {
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if (i & (1 << j)) {
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check += (in_arr[j]);
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}
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}
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if (check == sum) {
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count_of_subset++;
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}
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}
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return count_of_subset;
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}
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} // namespace subset_sum
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} // namespace backtracking
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/**
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* @brief Test implementations
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* @returns void
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*/
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static void test() {
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// 1st test
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std::cout << "1st test ";
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std::vector<int32_t> array1 = {-7, -3, -2, 5, 8}; // input array
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assert(backtracking::subset_sum::number_of_subsets(0, array1) ==
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2); // first argument in subset_sum function is the required sum and
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// second is the input array
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std::cout << "passed" << std::endl;
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// 2nd test
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std::cout << "2nd test ";
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std::vector<int32_t> array2 = {1, 2, 3, 3};
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assert(backtracking::subset_sum::number_of_subsets(6, array2) ==
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3); // here we are expecting 3 subsets which sum up to 6 i.e.
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// {(1,2,3),(1,2,3),(3,3)}
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std::cout << "passed" << std::endl;
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// 3rd test
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std::cout << "3rd test ";
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std::vector<int32_t> array3 = {1, 1, 1, 1};
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assert(backtracking::subset_sum::number_of_subsets(1, array3) ==
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4); // here we are expecting 4 subsets which sum up to 1 i.e.
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// {(1),(1),(1),(1)}
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std::cout << "passed" << std::endl;
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// 4th test
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std::cout << "4th test ";
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std::vector<int32_t> array4 = {3, 3, 3, 3};
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assert(backtracking::subset_sum::number_of_subsets(6, array4) ==
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6); // here we are expecting 6 subsets which sum up to 6 i.e.
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// {(3,3),(3,3),(3,3),(3,3),(3,3),(3,3)}
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std::cout << "passed" << std::endl;
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// Test 5
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std::cout << "5th test ";
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std::vector<int32_t> array5 = {};
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assert(backtracking::subset_sum::number_of_subsets(6, array5) ==
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0); // here we are expecting 0 subsets which sum up to 6 i.e. we
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// cannot select anything from an empty array
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std::cout << "passed" << std::endl;
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main() {
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test(); // run self-test implementations
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return 0;
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}

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