Add Krushkal's Minimum Spanning Tree algorithm

TheAlgorithms · PayalB24 · Jul 18, 2025 · Jul 18, 2025 · a0461b691e2f3c3a4c6e2e407e118a41e1ddd579
commit a0461b691e2f3c3a4c6e2e407e118a41e1ddd579
@@ -0,0 +1,77 @@
+package com.thealgorithms.graph;
+import java.util.*;
+
+/**
+ * Implements Kruskal's Algorithm to find the Minimum Spanning Tree (MST)
+ * of a connected, undirected, weighted graph using Union-Find.
+ */
+public class KruskalMinimumSpanningTree {
+
+    static class Edge implements Comparable<Edge> {
+        int src, dest, weight;
+
+        Edge(int src, int dest, int weight) {
+            this.src = src;
+            this.dest = dest;
+            this.weight = weight;
+        }
+
+        @Override
+        public int compareTo(Edge other) {
+            return Integer.compare(this.weight, other.weight);
+        }
+    }
+
+    static class UnionFind {
+        int[] parent;
+
+        UnionFind(int size) {
+            parent = new int[size];
+            Arrays.fill(parent, -1);
+        }
+
+        int find(int node) {
+            if (parent[node] < 0) return node;
+            return parent[node] = find(parent[node]);
+        }
+
+        boolean union(int u, int v) {
+            int rootU = find(u);
+            int rootV = find(v);
+            if (rootU == rootV) return false;
+            parent[rootV] = rootU;
+            return true;
+        }
+    }
+
+    public static List<Edge> kruskalMST(List<Edge> edges, int vertices) {
+        Collections.sort(edges);
+        UnionFind uf = new UnionFind(vertices);
+        List<Edge> mst = new ArrayList<>();
+
+        for (Edge edge : edges) {
+            if (uf.union(edge.src, edge.dest)) {
+                mst.add(edge);
+            }
+            if (mst.size() == vertices - 1) break;
+        }
+
+        return mst;
+    }
+
+    public static void main(String[] args) {
+        int V = 4;
+        List<Edge> edges = new ArrayList<>();
+        edges.add(new Edge(0, 1, 10));
+        edges.add(new Edge(0, 2, 6));
+        edges.add(new Edge(0, 3, 5));
+        edges.add(new Edge(1, 3, 15));
+        edges.add(new Edge(2, 3, 4));
+
+        List<Edge> mst = kruskalMST(edges, V);
+        System.out.println("Edges in the Minimum Spanning Tree:");
+        for (Edge edge : mst) {
+            System.out.println(edge.src + " - " + edge.dest + " : " + edge.weight);
+        }
+    }
+}