feat: Added gale_shapley.cpp in greedy_algorithms

greedy_algorithms/gale_shapley.cpp

@@ -0,0 +1,101 @@
+/**
+ * @file
+ * @brief [Gale Shapley Algorithm](https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm)
+ * @details
+ * This implementation utilizes the Gale-Shapley algorithm to find stable matches
+ *
+ * **Gale Shapley Algorithm** aims to find a stable matching between two equally sized 
+ * sets of elements given an ordinal preference for each element. The algorithm was
+ * introduced by David Gale and Lloyd Shapley in 1962.
+ * 
+ * Reference: 
+ * [Wikipedia](https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm)
+ * [Wikipedia](https://en.wikipedia.org/wiki/Stable_matching_problem)
+ *
+ * @author [B Karthik](https://github.com/BKarthik7)
+ */
+
+#include <iostream>
+#include <vector>
+#include <cstring>
+#include <algorithm>
+
+/**
+ * @namespace
+ * @brief Greedy Algorithms
+ */
+namespace greedy_algorithms {
+/**
+ * @namespace
+ * @brief Functions for the Gale Shapley Algorithm
+ */
+namespace stable_matching {
+void gale_shapley(const std::vector<std::vector<int>>& set_2_prefs, const std::vector<std::vector<int>>& set_1_prefs) {
+    int n = set_2_prefs.size();
+    std::vector<int> engagements(n, -1);
+    std::vector<bool> free_set_1_s(n, true);
+    std::vector<int> next_proposal(n, 0); // Tracks the next set_2 to propose for each set_1
+
+    while (true) {
+        int free_set_1;
+        for (free_set_1 = 0; free_set_1 < n; free_set_1++) {
+            if (free_set_1_s[free_set_1]) break;
+        }
+        if (free_set_1 == n) break;
+
+        int set_2_to_propose = set_1_prefs[free_set_1][next_proposal[free_set_1]];
+        next_proposal[free_set_1]++;
+        int currentFiance = engagements[set_2_to_propose];
+
+        if (currentFiance == -1) {
+            engagements[set_2_to_propose] = free_set_1;
+            free_set_1_s[free_set_1] = false;
+        } else {
+            if (std::find(set_2_prefs[set_2_to_propose].begin(), set_2_prefs[set_2_to_propose].end(), free_set_1) <
+                std::find(set_2_prefs[set_2_to_propose].begin(), set_2_prefs[set_2_to_propose].end(), currentFiance)) {
+                engagements[set_2_to_propose] = free_set_1;
+                free_set_1_s[free_set_1] = false;
+                free_set_1_s[currentFiance] = true;
+            }
+        }
+    }
+
+    std::cout << "Stable Matches:\n";
+    for (int set_2 = 0; set_2 < n; set_2++) {
+        std::cout << "set_2's " << set_2 << " is matched to set_1's " << engagements[set_2] << std::endl;
+    }
+    std::cout << std::endl;
+}
+}  // namespace stable_matching
+}  // namespace greedy_algorithms
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+
+static void tests() {
+    // Test Case 1
+    std::vector<std::vector<int>> set_1_prefs = {{0, 1, 2, 3}, {2, 1, 3, 0}, {1, 2, 0, 3}, {3, 0, 1, 2}};
+    std::vector<std::vector<int>> set_2_prefs = {{1, 0, 2, 3},{3, 0, 1, 2},{0, 2, 1, 3},{1, 2, 0, 3}};
+    greedy_algorithms::stable_matching::gale_shapley(set_2_prefs, set_1_prefs);
+
+    // Test Case 2
+    set_1_prefs = {{0, 2, 1, 3}, {2, 3, 0, 1}, {3, 1, 2, 0}, {2, 1, 0, 3}};
+    set_2_prefs = {{1, 0, 2, 3},{3, 0, 1, 2},{0, 2, 1, 3},{1, 2, 0, 3}};
+    greedy_algorithms::stable_matching::gale_shapley(set_2_prefs, set_1_prefs);
+
+    // Test Case 3
+    set_1_prefs = {{0, 1, 2}, {2, 1, 0}, {1, 2, 0}};
+    set_2_prefs = {{1, 0, 2},{2, 0, 1},{0, 2, 1}};
+    greedy_algorithms::stable_matching::gale_shapley(set_2_prefs, set_1_prefs);
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    tests(); // run self-test implementations
+    return 0;
+}