//SEPEHR FARID SOLOLEARN Sepehrfd@yahoo.com import java.util.*; public class Kruskal { // int[][] spanningtree(int graph[][]) { // // int[][] spanningtree = new int[graph.length][graph.length]; // // for (int i=0; i { int src, dest, weight; @Override public int compareTo(Edge compareEdge) { return this.weight - compareEdge.weight; } }; // A class to represent a subset for union-find class subset { int parent, rank; }; int V, E; // V-> no. of vertices & E->no.of edges Edge edge[]; // collection of all edges // Creates a graph with V vertices and E edges Graph(int v, int e) { V = v; E = e; edge = new Edge[E]; for (int i = 0; i < e; ++i) { edge[i] = new Edge(); } } // A utility function to find set of an element i // (uses path compression technique) int find(subset subsets[], int i) { // find root and make root as parent of i (path compression) if (subsets[i].parent != i) { subsets[i].parent = find(subsets, subsets[i].parent); } return subsets[i].parent; } // A function that does union of two sets of x and y // (uses union by rank) void Union(subset subsets[], int x, int y) { int xroot = find(subsets, x); int yroot = find(subsets, y); // Attach smaller rank tree under root of high rank tree // (Union by Rank) if (subsets[xroot].rank < subsets[yroot].rank) { subsets[xroot].parent = yroot; } else if (subsets[xroot].rank > subsets[yroot].rank) { subsets[yroot].parent = xroot; } // If ranks are same, then make one as root and increment // its rank by one else { subsets[yroot].parent = xroot; subsets[xroot].rank++; } } // The main function to construct MST using Kruskal's algorithm void KruskalMST() { Edge result[] = new Edge[V]; // Tnis will store the resultant MST int e = 0; // An index variable, used for result[] int i; // An index variable, used for sorted edges for (i = 0; i < V; ++i) { result[i] = new Edge(); } // Step 1: Sort all the edges in non-decreasing order of their // weight. If we are not allowed to change the given graph, we // can create a copy of array of edges Arrays.sort(edge); // Allocate memory for creating V ssubsets subset subsets[] = new subset[V]; for (i = 0; i < V; ++i) { subsets[i] = new subset(); } // Create V subsets with single elements for (int v = 0; v < V; ++v) { subsets[v].parent = v; subsets[v].rank = 0; } i = 0; // Index used to pick next edge // Number of edges to be taken is equal to V-1 while (e < V - 1) { // Step 2: Pick the smallest edge. And increment // the index for next iteration Edge next_edge = new Edge(); next_edge = edge[i++]; int x = find(subsets, next_edge.src); int y = find(subsets, next_edge.dest); // If including this edge does't cause cycle, // include it in result and increment the index // of result for next edge if (x != y) { result[e++] = next_edge; Union(subsets, x, y); } // Else discard the next_edge } // print the contents of result[] to display // the built MST System.out.println("Following are the edges in " + "the constructed MST"); for (i = 0; i < e; ++i) { System.out.println(result[i].src + " -- " + result[i].dest + " == " + result[i].weight); } } // Driver Program } public static void main(String[] args) { /* Let us create following weighted graph 10 0--------1 | \ | 6| 5\ |15 | \ | 2--------3 4 */ int V = 4; // Number of vertices in graph int E = 5; // Number of edges in graph Graph graph = new Graph(V, E); // add edge 0-1 graph.edge[0].src = 0; graph.edge[0].dest = 1; graph.edge[0].weight = 10; // add edge 0-2 graph.edge[1].src = 0; graph.edge[1].dest = 2; graph.edge[1].weight = 6; // add edge 0-3 graph.edge[2].src = 0; graph.edge[2].dest = 3; graph.edge[2].weight = 5; // add edge 1-3 graph.edge[3].src = 1; graph.edge[3].dest = 3; graph.edge[3].weight = 15; // add edge 2-3 graph.edge[4].src = 2; graph.edge[4].dest = 3; graph.edge[4].weight = 4; graph.KruskalMST(); } }

Kruskal Algorithm