diff --git a/dynamic_programming/subset_sum.cpp b/dynamic_programming/subset_sum.cpp new file mode 100644 index 00000000000..897fc9a96a7 --- /dev/null +++ b/dynamic_programming/subset_sum.cpp @@ -0,0 +1,125 @@ +/** + * @file + * @brief Implements [Sub-set sum problem] + * (https://en.wikipedia.org/wiki/Subset_sum_problem) algorithm, which tells + * whether a subset with target sum exists or not. + * + * @details + * In this problem, we use dynamic programming to find if we can pull out a + * subset from an array whose sum is equal to a given target sum. The overall + * time complexity of the problem is O(n * targetSum) where n is the size of + * the array. For example, array = [1, -10, 2, 31, -6], targetSum = -14. + * Output: true => We can pick subset [-10, 2, -6] with sum as + * (-10) + 2 + (-6) = -14. + * @author [KillerAV](https://github.com/KillerAV) + */ + +#include /// for std::assert +#include /// for IO operations +#include /// for std::vector +#include /// for unordered map + +/** + * @namespace dynamic_programming + * @brief Dynamic Programming algorithms + */ +namespace dynamic_programming { + +/** + * @namespace subset_sum + * @brief Functions for [Sub-set sum problem] + * (https://en.wikipedia.org/wiki/Subset_sum_problem) algorithm + */ +namespace subset_sum { + +/** + * Recursive function using dynamic programming to find if the required sum + * subset exists or not. + * @param arr input array + * @param targetSum the target sum of the subset + * @param dp the map storing the results + * @returns true/false based on if the target sum subset exists or not. + */ +bool subset_sum_recursion( + const std::vector &arr, + int targetSum, + std::vector> *dp, + int index = 0) { + + if(targetSum == 0) { // Found a valid subset with required sum. + return true; + } + if(index == arr.size()) { // End of array + return false; + } + + if ((*dp)[index].count(targetSum)) { // Answer already present in map + return (*dp)[index][targetSum]; + } + + bool ans = subset_sum_recursion(arr, targetSum - arr[index], dp, index + 1) + || subset_sum_recursion(arr, targetSum, dp, index + 1); + (*dp)[index][targetSum] = ans; // Save ans in dp map. + return ans; +} + +/** + * Function implementing subset sum algorithm using top-down approach + * @param arr input array + * @param targetSum the target sum of the subset + * @returns true/false based on if the target sum subset exists or not. + */ +bool subset_sum_problem(const std::vector &arr, const int targetSum) { + size_t n = arr.size(); + std::vector> dp(n); + return subset_sum_recursion(arr, targetSum, &dp); +} +} // namespace subset_sum +} // namespace dynamic_programming + +/** + * @brief Test Function + * @return void + */ +static void test() { + // custom input vector + std::vector> custom_input_arr(3); + custom_input_arr[0] = std::vector {1, -10, 2, 31, -6}; + custom_input_arr[1] = std::vector {2, 3, 4}; + custom_input_arr[2] = std::vector {0, 1, 0, 1, 0}; + + std::vector custom_input_target_sum(3); + custom_input_target_sum[0] = -14; + custom_input_target_sum[1] = 10; + custom_input_target_sum[2] = 2; + + // calculated output vector by pal_part Function + std::vector calculated_output(3); + + for (int i = 0; i < 3; i++) { + calculated_output[i] = + dynamic_programming::subset_sum::subset_sum_problem( + custom_input_arr[i], custom_input_target_sum[i]); + } + + // expected output vector + std::vector expected_output{true, false, true}; + + // Testing implementation via assert function + // It will throw error if any of the expected test fails + // Else it will give nothing + for (int i = 0; i < 3; i++) { + assert(expected_output[i] == calculated_output[i]); + } + + std::cout << "All tests passed successfully!\n"; +} + +/** + * @brief Main function + * @returns 0 on exit + */ +int main() { + test(); // execute the test + return 0; +}