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Add Gale-Shapley Algorithm and Tests (#5494)
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‎DIRECTORY.md

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* [ActivitySelection](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/ActivitySelection.java)
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* [CoinChange](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/CoinChange.java)
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* [FractionalKnapsack](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/FractionalKnapsack.java)
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* [GaleShapley](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/GaleShapley.java)
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* [JobSequencing](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/JobSequencing.java)
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* [MinimizingLateness](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/greedyalgorithms/MinimizingLateness.java)
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* io
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* [ActivitySelectionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/ActivitySelectionTest.java)
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* [CoinChangeTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/CoinChangeTest.java)
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* [FractionalKnapsackTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/FractionalKnapsackTest.java)
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* [GaleShapleyTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/GaleShapleyTest.java)
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* [JobSequencingTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/JobSequencingTest.java)
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* [MinimizingLatenessTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/greedyalgorithms/MinimizingLatenessTest.java)
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* io

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

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

‎src/test/java/com/thealgorithms/greedyalgorithms/GaleShapleyTest.java

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package com.thealgorithms.greedyalgorithms;
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import static org.junit.jupiter.api.Assertions.assertEquals;
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import java.util.HashMap;
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import java.util.LinkedList;
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import java.util.List;
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import java.util.Map;
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import org.junit.jupiter.api.Test;
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public class GaleShapleyTest {
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@Test
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public void testStableMatch() {
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Map<String, LinkedList<String>> womenPrefs = new HashMap<>();
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womenPrefs.put("A", new LinkedList<>(List.of("X", "Y", "Z")));
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womenPrefs.put("B", new LinkedList<>(List.of("Y", "X", "Z")));
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womenPrefs.put("C", new LinkedList<>(List.of("X", "Y", "Z")));
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Map<String, LinkedList<String>> menPrefs = new HashMap<>();
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menPrefs.put("X", new LinkedList<>(List.of("A", "B", "C")));
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menPrefs.put("Y", new LinkedList<>(List.of("B", "A", "C")));
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menPrefs.put("Z", new LinkedList<>(List.of("A", "B", "C")));
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Map<String, String> result = GaleShapley.stableMatch(womenPrefs, menPrefs);
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Map<String, String> expected = new HashMap<>();
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expected.put("A", "X");
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expected.put("B", "Y");
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expected.put("C", "Z");
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assertEquals(expected, result);
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}
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@Test
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public void testSinglePair() {
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Map<String, LinkedList<String>> womenPrefs = new HashMap<>();
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womenPrefs.put("A", new LinkedList<>(List.of("X")));
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Map<String, LinkedList<String>> menPrefs = new HashMap<>();
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menPrefs.put("X", new LinkedList<>(List.of("A")));
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Map<String, String> result = GaleShapley.stableMatch(womenPrefs, menPrefs);
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Map<String, String> expected = new HashMap<>();
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expected.put("A", "X");
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assertEquals(expected, result);
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}
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@Test
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public void testEqualPreferences() {
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Map<String, LinkedList<String>> womenPrefs = new HashMap<>();
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womenPrefs.put("A", new LinkedList<>(List.of("X", "Y", "Z")));
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womenPrefs.put("B", new LinkedList<>(List.of("X", "Y", "Z")));
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womenPrefs.put("C", new LinkedList<>(List.of("X", "Y", "Z")));
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Map<String, LinkedList<String>> menPrefs = new HashMap<>();
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menPrefs.put("X", new LinkedList<>(List.of("A", "B", "C")));
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menPrefs.put("Y", new LinkedList<>(List.of("A", "B", "C")));
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menPrefs.put("Z", new LinkedList<>(List.of("A", "B", "C")));
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Map<String, String> result = GaleShapley.stableMatch(womenPrefs, menPrefs);
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Map<String, String> expected = new HashMap<>();
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expected.put("A", "X");
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expected.put("B", "Y");
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expected.put("C", "Z");
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assertEquals(expected, result);
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}
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}

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