feat: Added gale_shapley.cpp in greedy_algorithms

greedy_algorithms/gale_shapley.cpp

@@ -0,0 +1,120 @@
+/**
+ * @file
+ * @brief Stable Marriage Problem implementation
+ * @details
+ * This implementation utilizes the Gale-Shapley algorithm to find stable matches
+ * between men and women based on their preferences.
+ *
+ * **Stable Marriage Problem** 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.
+ *
+ * @author [B Karthik](https://github.com/BKarthik7)
+ */
+
+#include <iostream>
+#include <vector>
+#include <cstring>
+#include <algorithm>
+using namespace std;
+
+void stableMatch(const vector<vector<int>>& women_prefs, const vector<vector<int>>& men_prefs, int n) {
+    vector<int> engagements(n, -1);
+    vector<bool> free_men(n, true);
+    vector<int> next_proposal(n, 0); // Tracks the next woman to propose for each man
+
+    while (true) {
+        int freeMan;
+        for (freeMan = 0; freeMan < n; freeMan++) {
+            if (free_men[freeMan]) break;
+        }
+        if (freeMan == n) break;
+
+        int womanToPropose = men_prefs[freeMan][next_proposal[freeMan]];
+        next_proposal[freeMan]++;
+        int currentFiance = engagements[womanToPropose];
+
+        if (currentFiance == -1) {
+            engagements[womanToPropose] = freeMan;
+            free_men[freeMan] = false;
+        } else {
+            if (find(women_prefs[womanToPropose].begin(), women_prefs[womanToPropose].end(), freeMan) <
+                find(women_prefs[womanToPropose].begin(), women_prefs[womanToPropose].end(), currentFiance)) {
+                engagements[womanToPropose] = freeMan;
+                free_men[freeMan] = false;
+                free_men[currentFiance] = true;
+            }
+        }
+    }
+
+    cout << "Stable Matches:\n";
+    for (int woman = 0; woman < n; woman++) {
+        cout << "Woman " << woman << " is engaged to Man " << engagements[woman] << endl;
+    }
+}
+
+void runTestCase(int caseNum) {
+    const int n = 4; // Number of men and women
+
+    // Test Case 1
+    if (caseNum == 1) {
+        cout << "Test Case 1:\n";
+        vector<vector<int>> women_prefs = {
+            {1, 0, 3, 2}, // Alice
+            {0, 1, 2, 3}, // Becky
+            {1, 2, 0, 3}, // Cathy
+            {3, 2, 1, 0}  // Diana
+        };
+        vector<vector<int>> men_prefs = {
+            {0, 1, 2, 3}, // Bob
+            {1, 0, 3, 2}, // Charlie
+            {0, 2, 3, 1}, // David
+            {2, 1, 0, 3}  // Edward
+        };
+        stableMatch(women_prefs, men_prefs, n);
+    }
+
+    // Test Case 2
+    else if (caseNum == 2) {
+        cout << "Test Case 2:\n";
+        vector<vector<int>> women_prefs = {
+            {0, 1, 2, 3}, // Eve
+            {1, 0, 3, 2}, // Grace
+            {2, 1, 0, 3}, // Hannah
+            {3, 2, 1, 0}  // Ivy
+        };
+        vector<vector<int>> men_prefs = {
+            {1, 0, 3, 2}, // Frank
+            {0, 1, 2, 3}, // George
+            {1, 2, 0, 3}, // Henry
+            {2, 0, 1, 3}  // Ian
+        };
+        stableMatch(women_prefs, men_prefs, n);
+    }
+
+    // Test Case 3
+    else if (caseNum == 3) {
+        cout << "Test Case 3:\n";
+        vector<vector<int>> women_prefs = {
+            {2, 1, 0, 3}, // Jade
+            {0, 2, 3, 1}, // Lucy
+            {3, 2, 1, 0}, // Mia
+            {1, 3, 0, 2}  // Nina
+        };
+        vector<vector<int>> men_prefs = {
+            {1, 0, 2, 3}, // Kyle
+            {0, 2, 3, 1}, // Liam
+            {2, 1, 3, 0}, // Mason
+            {3, 2, 1, 0}  // Nathan
+        };
+        stableMatch(women_prefs, men_prefs, n);
+    }
+}
+
+int main() {
+    for (int i = 1; i <= 3; i++) {
+        runTestCase(i);
+        cout << endl;
+    }
+    return 0;
+}