Add Gale-Shapley Algorithm and Tests (#5494)

src/main/java/com/thealgorithms/greedyalgorithms/GaleShapley.java

@@ -0,0 +1,65 @@
+package com.thealgorithms.greedyalgorithms;
+
+import java.util.HashMap;
+import java.util.LinkedList;
+import java.util.Map;
+
+/**
+ * Implementation of the Gale-Shapley Algorithm for Stable Matching.
+ * Problem link: https://en.wikipedia.org/wiki/Stable_marriage_problem
+ */
+public final class GaleShapley {
+
+    private GaleShapley() {
+    }
+
+    /**
+     * Function to find stable matches between men and women.
+     *
+     * @param womenPrefs A map containing women's preferences where each key is a woman and the value is an array of men in order of preference.
+     * @param menPrefs   A map containing men's preferences where each key is a man and the value is an array of women in order of preference.
+     * @return A map containing stable matches where the key is a woman and the value is her matched man.
+     */
+    public static Map<String, String> stableMatch(Map<String, LinkedList<String>> womenPrefs, Map<String, LinkedList<String>> menPrefs) {
+        // Initialize all men as free
+        Map<String, String> engagements = new HashMap<>();
+        LinkedList<String> freeMen = new LinkedList<>(menPrefs.keySet());
+
+        // While there are free men
+        while (!freeMen.isEmpty()) {
+            String man = freeMen.poll(); // Get the first free man
+            LinkedList<String> manPref = menPrefs.get(man); // Get the preferences of the man
+
+            // Check if manPref is null or empty
+            if (manPref == null || manPref.isEmpty()) {
+                continue; // Skip if no preferences
+            }
+
+            // Propose to the first woman in the man's preference list
+            String woman = manPref.poll();
+            String fiance = engagements.get(woman);
+
+            // If the woman is not engaged, engage her with the current man
+            if (fiance == null) {
+                engagements.put(woman, man);
+            } else {
+                // If the woman prefers the current man over her current fiance
+                LinkedList<String> womanPrefList = womenPrefs.get(woman);
+
+                // Check if womanPrefList is null
+                if (womanPrefList == null) {
+                    continue; // Skip if no preferences for the woman
+                }
+
+                if (womanPrefList.indexOf(man) < womanPrefList.indexOf(fiance)) {
+                    engagements.put(woman, man);
+                    freeMen.add(fiance); // Previous fiance becomes free
+                } else {
+                    // Woman rejects the new proposal, the man remains free
+                    freeMen.add(man);
+                }
+            }
+        }
+        return engagements; // Return the stable matches
+    }
+}