From 8bbb8869d9a8ebab0dab095a32d8835afdae28ba Mon Sep 17 00:00:00 2001
From: Gokul45-45 <2400032465@kluniversity.in>
Date: Tue, 25 Nov 2025 22:29:39 +0530
Subject: [PATCH] Add Kruskal's Algorithm implementation

---
 .../graph/KruskalsAlgorithm.java              | 166 ++++++++++++++++++
 1 file changed, 166 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/graph/KruskalsAlgorithm.java

diff --git a/src/main/java/com/thealgorithms/graph/KruskalsAlgorithm.java b/src/main/java/com/thealgorithms/graph/KruskalsAlgorithm.java
new file mode 100644
index 000000000000..2fbee4e4ac78
--- /dev/null
+++ b/src/main/java/com/thealgorithms/graph/KruskalsAlgorithm.java
@@ -0,0 +1,166 @@
+package com.thealgorithms.graph;
+
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.List;
+
+/**
+ * Kruskal's Algorithm for finding Minimum Spanning Tree (MST)
+ * 
+ * Kruskal's algorithm is a greedy algorithm that finds a minimum spanning tree
+ * for a connected weighted graph. It works by sorting all edges by weight and
+ * adding them one by one to the MST if they don't form a cycle.
+ * 
+ * Time Complexity: O(E log E) where E is the number of edges
+ * Space Complexity: O(V + E) where V is the number of vertices
+ * 
+ * @author YourName
+ */
+public final class KruskalsAlgorithm {
+    private KruskalsAlgorithm() {
+    }
+
+    /**
+     * Edge class representing a weighted edge in the graph
+     */
+    static class Edge implements Comparable<Edge> {
+        int src;
+        int dest;
+        int 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);
+        }
+    }
+
+    /**
+     * Disjoint Set (Union-Find) data structure
+     */
+    static class DisjointSet {
+        private final int[] parent;
+        private final int[] rank;
+
+        DisjointSet(int n) {
+            parent = new int[n];
+            rank = new int[n];
+            for (int i = 0; i < n; i++) {
+                parent[i] = i;
+                rank[i] = 0;
+            }
+        }
+
+        /**
+         * Find the representative (root) of the set containing element x
+         * Uses path compression for optimization
+         */
+        int find(int x) {
+            if (parent[x] != x) {
+                parent[x] = find(parent[x]); // Path compression
+            }
+            return parent[x];
+        }
+
+        /**
+         * Unite two sets containing elements x and y
+         * Uses union by rank for optimization
+         */
+        void union(int x, int y) {
+            int rootX = find(x);
+            int rootY = find(y);
+
+            if (rootX == rootY) {
+                return;
+            }
+
+            // Union by rank
+            if (rank[rootX] < rank[rootY]) {
+                parent[rootX] = rootY;
+            } else if (rank[rootX] > rank[rootY]) {
+                parent[rootY] = rootX;
+            } else {
+                parent[rootY] = rootX;
+                rank[rootX]++;
+            }
+        }
+    }
+
+    /**
+     * Find Minimum Spanning Tree using Kruskal's Algorithm
+     * 
+     * @param vertices Number of vertices in the graph
+     * @param edges List of edges in the graph
+     * @return List of edges in the Minimum Spanning Tree
+     */
+    public static List<Edge> kruskalMST(int vertices, List<Edge> edges) {
+        List<Edge> mst = new ArrayList<>();
+        
+        // Sort edges by weight in ascending order
+        Collections.sort(edges);
+        
+        DisjointSet ds = new DisjointSet(vertices);
+        
+        // Iterate through sorted edges
+        for (Edge edge : edges) {
+            int srcRoot = ds.find(edge.src);
+            int destRoot = ds.find(edge.dest);
+            
+            // If including this edge doesn't form a cycle, add it to MST
+            if (srcRoot != destRoot) {
+                mst.add(edge);
+                ds.union(srcRoot, destRoot);
+                
+                // MST is complete when we have V-1 edges
+                if (mst.size() == vertices - 1) {
+                    break;
+                }
+            }
+        }
+        
+        return mst;
+    }
+
+    /**
+     * Calculate total weight of the MST
+     * 
+     * @param mst List of edges in the Minimum Spanning Tree
+     * @return Total weight of the MST
+     */
+    public static int getMSTWeight(List<Edge> mst) {
+        int totalWeight = 0;
+        for (Edge edge : mst) {
+            totalWeight += edge.weight;
+        }
+        return totalWeight;
+    }
+
+    /**
+     * Main method for testing
+     */
+    public static void main(String[] args) {
+        int vertices = 4;
+        List<Edge> edges = new ArrayList<>();
+        
+        // Example graph
+        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(vertices, edges);
+        
+        System.out.println("Edges in the Minimum Spanning Tree:");
+        for (Edge edge : mst) {
+            System.out.println(edge.src + " -- " + edge.dest + " : " + edge.weight);
+        }
+        
+        System.out.println("\nTotal weight of MST: " + getMSTWeight(mst));
+    }
+}