feat: add gale shapley algorithm

Author: Mastermind-sap

data_structures/graphs/gale_shapley.c

@@ -0,0 +1,201 @@
+/**
+ * @file
+ * @brief [Gale-Shapley
+ * Algorithm](https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm):
+ * Stable matching between two sets.
+ * @details
+ * This implementation uses the Gale-Shapley algorithm to find stable matches
+ * between two equally sized sets, given their preferences.
+ *
+ * **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)
+ *   - [Stable matching
+ * problem](https://en.wikipedia.org/wiki/Stable_matching_problem)
+ *   - [Original
+ * Paper](https://sites.math.washington.edu/~billey/classes/562.winter.2018/articles/Gale.Shapley.pdf)
+ *
+ * Math: Stable matching means no pair prefers each other over their current
+ * match.
+ *
+ * @author [Mastermind-sap](https://github.com/Mastermind-sap)
+ */
+
+#include <assert.h>  /// for assert
+#include <stdio.h>   /// for IO operations
+
+#define N 4  // number of proposers and acceptors
+
+/**
+ * @brief Find the index of value in an array
+ * @param arr array to search
+ * @param size length of array
+ * @param val value to find
+ * @return index of value if found, -1 otherwise
+ */
+int index_of(int arr[], int size, int val)
+{
+    for (int i = 0; i < size; i++)
+    {
+        if (arr[i] == val)
+            return i;
+    }
+    return -1;
+}
+
+/**
+ * @brief Initialize matches and free status
+ * @param matches array to store final matches
+ * @param is_free_proposer array to check which proposer free
+ * @param proposal_index array to keep track of next index to propose for each
+ * proposer
+ * @returns void
+ */
+void initialize(int matches[], int is_free_proposer[], int proposal_index[])
+{
+    for (int i = 0; i < N; i++)
+    {
+        matches[i] = -1;          // all acceptors unmatched
+        is_free_proposer[i] = 1;  // all proposers are free
+        proposal_index[i] = 0;    // start from first preference
+    }
+}
+
+/**
+ * @brief Find the next free proposer
+ * @param is_free_proposer array to check which proposer is free
+ * @returns index of free proposer or -1 if none free
+ */
+int get_free_proposer(int is_free_proposer[])
+{
+    for (int i = 0; i < N; i++)
+    {
+        if (is_free_proposer[i])
+            return i;
+    }
+    return -1;
+}
+
+/**
+ * @brief Gale–Shapley stable matching algorithm
+ * @param proposer_pref preferences of proposers
+ * @param acceptor_pref preferences of acceptors
+ * @param matches output: matches[j] = i means acceptor j is matched with
+ * proposer i
+ * @returns void
+ */
+void gale_shapley(int proposer_pref[N][N], int acceptor_pref[N][N],
+                  int matches[])
+{
+    int is_free_proposer[N];
+    int proposal_index[N];
+    initialize(matches, is_free_proposer, proposal_index);
+
+    while (1)
+    {
+        int p = get_free_proposer(is_free_proposer);  // free proposer
+        if (p == -1)
+            break;  // no free proposer left
+
+        int s = proposer_pref[p][proposal_index[p]];  // acceptor to propose
+        proposal_index[p]++;
+
+        int current_match = matches[s];
+
+        if (current_match == -1)
+        {
+            // acceptor is free
+            matches[s] = p;
+            is_free_proposer[p] = 0;
+        }
+        else
+        {
+            // acceptor already matched, check preference
+            int rank_new = index_of(acceptor_pref[s], N, p);
+            int rank_current = index_of(acceptor_pref[s], N, current_match);
+
+            if (rank_new < rank_current)
+            {
+                // acceptor prefers new proposer
+                matches[s] = p;
+                is_free_proposer[p] = 0;
+                is_free_proposer[current_match] = 1;  // old match becomes free
+            }
+        }
+    }
+}
+
+/**
+ * @brief Print final matches
+ * @param matches output: matches[j] = i means acceptor j is matched with
+ * proposer i
+ */
+void print_matches(int matches[])
+{
+    printf("Stable Matching Results:\n");
+    for (int s = 0; s < N; s++)
+    {
+        printf("acceptor %d is matched with proposer %d\n", s, matches[s]);
+    }
+}
+
+/**
+ * @brief Self-test for Gale-Shapley implementation
+ * @returns void
+ */
+static void test()
+{
+    // Test case 1:
+    int proposer_pref1[N][N] = {
+        {1, 0, 2, 3}, {2, 1, 3, 0}, {2, 1, 0, 3}, {3, 0, 1, 2}};
+    int acceptor_pref1[N][N] = {
+        {1, 0, 2, 3}, {3, 0, 1, 2}, {0, 2, 1, 3}, {1, 2, 0, 3}};
+    int matches1[N];
+    gale_shapley(proposer_pref1, acceptor_pref1, matches1);
+    int expected1[N] = {3, 0, 2, 1};
+    for (int i = 0; i < N; i++)
+    {
+        assert(matches1[i] == expected1[i]);
+    }
+
+    // Test case 2:
+    int proposer_pref2[N][N] = {
+        {0, 1, 2, 3}, {0, 1, 2, 3}, {0, 1, 2, 3}, {0, 1, 2, 3}};
+    int acceptor_pref2[N][N] = {
+        {0, 1, 2, 3}, {1, 0, 2, 3}, {2, 1, 0, 3}, {3, 2, 1, 0}};
+    int matches2[N];
+    gale_shapley(proposer_pref2, acceptor_pref2, matches2);
+    int expected2[N] = {0, 1, 2, 3};
+    for (int i = 0; i < N; i++)
+    {
+        assert(matches2[i] == expected2[i]);
+    }
+
+    // Test case 3:
+    int proposer_pref3[N][N] = {
+        {3, 2, 1, 0}, {3, 2, 1, 0}, {3, 2, 1, 0}, {3, 2, 1, 0}};
+    int acceptor_pref3[N][N] = {
+        {3, 2, 1, 0}, {2, 3, 1, 0}, {1, 2, 3, 0}, {0, 1, 2, 3}};
+    int matches3[N];
+    gale_shapley(proposer_pref3, acceptor_pref3, matches3);
+    int expected3[N] = {3, 2, 1, 0};
+    for (int i = 0; i < N; i++)
+    {
+        assert(matches3[i] == expected3[i]);
+    }
+
+    printf("All Gale-Shapley tests have successfully passed!\n");
+}
+
+/**
+ * @brief Main function with test case
+ * @returns 0 on exit
+ */
+int main()
+{
+    test();  // Run Gale-Shapley self-test
+    return 0;
+}