EdmondsAlgorithm

src/main/java/com/thealgorithms/datastructures/graphs/EdmondsAlgorithm.java

@@ -0,0 +1,82 @@
+package com.thealgorithms.datastructures.graphs;
+
+import java.util.*;
+
+/*
+Graph Representation: 
+
+The graph is represented as an adjacency matrix, where graph[i][j] indicates the weight of the edge between vertices i and j. A weight of 0 means no edge exists.
+
+Main Method:
+
+A sample graph is defined as an adjacency matrix.
+The maximumWeightMatching method is called to find the maximum weight matching.
+The results are printed, showing which vertices are matched.
+
+Algorithm Functionality:
+
+The algorithm iterates through each vertex, applying a depth-first search (DFS) to find matches.
+It keeps track of matched vertices and updates the matching as it finds new pairs.
+ */
+
+public class EdmondsAlgorithm {
+    private static final int INF = Integer.MAX_VALUE;
+
+    // Method to find maximum weight matching
+    public static List<int[]> maximumWeightMatching(int[][] graph) {
+        int n = graph.length;
+        boolean[] matched = new boolean[n];
+        int[] match = new int[n];
+        Arrays.fill(match, -1);
+        List<int[]> result = new ArrayList<>();
+
+        for (int u = 0; u < n; u++) {
+            if (!matched[u]) {
+                boolean[] visited = new boolean[n];
+                findMatch(u, graph, matched, match, visited);
+            }
+        }
+
+        for (int v = 0; v < n; v++) {
+            if (match[v] != -1) {
+                result.add(new int[]{match[v], v});
+            }
+        }
+        return result;
+    }
+
+    // Helper method to find match using DFS
+    private static boolean findMatch(int u, int[][] graph, boolean[] matched, int[] match, boolean[] visited) {
+        visited[u] = true;
+
+        for (int v = 0; v < graph.length; v++) {
+            if (graph[u][v] > 0 && !visited[v]) {
+                visited[v] = true;
+
+                if (match[v] == -1 || findMatch(match[v], graph, matched, match, visited)) {
+                    matched[v] = true;
+                    match[v] = u;
+                    return true;
+                }
+            }
+        }
+        return false;
+    }
+
+    public static void main(String[] args) {
+        // Example graph represented as an adjacency matrix
+        int[][] graph = {
+            {0, 2, 0, 3},
+            {2, 0, 1, 0},
+            {0, 1, 0, 4},
+            {3, 0, 4, 0}
+        };
+
+        List<int[]> matching = maximumWeightMatching(graph);
+
+        System.out.println("Maximum Weight Matching:");
+        for (int[] pair : matching) {
+            System.out.println("Vertex " + pair[0] + " is matched with Vertex " + pair[1]);
+        }
+    }
+}