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DIRECTORY.md

@@ -7,6 +7,7 @@
   * [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)
+  * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subset_sum.cpp)
   * [Sudoku Solve](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solve.cpp)
 
 ## Bit Manipulation

backtracking/subset_sum.cpp

@@ -0,0 +1,106 @@
+/**
+ * @file
+ * @brief Implementation of the [Subset
+ * Sum](https://en.wikipedia.org/wiki/Subset_sum_problem) problem.
+ * @details
+ * We are given an array and a sum value. The algorithm finds all
+ * the subsets of that array with sum equal to the given sum and return such
+ * subsets count. This approach will have exponential time complexity.
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+#include <vector>    /// for std::vector
+
+/**
+ * @namespace backtracking
+ * @brief Backtracking algorithms
+ */
+namespace backtracking {
+/**
+ * @namespace Subsets
+ * @brief Functions for the [Subset
+ * Sum](https://en.wikipedia.org/wiki/Subset_sum_problem) problem.
+ */
+namespace subset_sum {
+/**
+ * @brief The main function implements count of subsets
+ * @param sum is the required sum of any subset
+ * @param in_arr is the input array
+ * @returns count of the number of subsets with required sum
+ */
+uint64_t number_of_subsets(int32_t sum, const std::vector<int32_t> &in_arr) {
+    int32_t nelement = in_arr.size();
+    uint64_t count_of_subset = 0;
+
+    for (int32_t i = 0; i < (1 << (nelement)); i++) {
+        int32_t check = 0;
+        for (int32_t j = 0; j < nelement; j++) {
+            if (i & (1 << j)) {
+                check += (in_arr[j]);
+            }
+        }
+        if (check == sum) {
+            count_of_subset++;
+        }
+    }
+    return count_of_subset;
+}
+}  // namespace subset_sum
+}  // namespace backtracking
+
+/**
+ * @brief Test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st test
+    std::cout << "1st test ";
+    std::vector<int32_t> array1 = {-7, -3, -2, 5, 8};  // input array
+    assert(backtracking::subset_sum::number_of_subsets(0, array1) ==
+           2);  // first argument in subset_sum function is the required sum and
+                // second is the input array
+    std::cout << "passed" << std::endl;
+
+    // 2nd test
+    std::cout << "2nd test ";
+    std::vector<int32_t> array2 = {1, 2, 3, 3};
+    assert(backtracking::subset_sum::number_of_subsets(6, array2) ==
+           3);  // here we are expecting 3 subsets which sum up to 6 i.e.
+                // {(1,2,3),(1,2,3),(3,3)}
+    std::cout << "passed" << std::endl;
+
+    // 3rd test
+    std::cout << "3rd test ";
+    std::vector<int32_t> array3 = {1, 1, 1, 1};
+    assert(backtracking::subset_sum::number_of_subsets(1, array3) ==
+           4);  // here we are expecting 4 subsets which sum up to 1 i.e.
+                // {(1),(1),(1),(1)}
+    std::cout << "passed" << std::endl;
+
+    // 4th test
+    std::cout << "4th test ";
+    std::vector<int32_t> array4 = {3, 3, 3, 3};
+    assert(backtracking::subset_sum::number_of_subsets(6, array4) ==
+           6);  // here we are expecting 6 subsets which sum up to 6 i.e.
+                // {(3,3),(3,3),(3,3),(3,3),(3,3),(3,3)}
+    std::cout << "passed" << std::endl;
+
+    // Test 5
+    std::cout << "5th test ";
+    std::vector<int32_t> array5 = {};
+    assert(backtracking::subset_sum::number_of_subsets(6, array5) ==
+           0);  // here we are expecting 0 subsets which sum up to 6 i.e. we
+                // cannot select anything from an empty array
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}