MST.java

//Minimum Spanning Tree
import java.io.*;
import java.lang.*;
import java.util.*;

class Graph {

	class Edge implements Comparable<Edge> {
		int src, dest, weight;



		public int compareTo(Edge compareEdge)
		{
			return this.weight - compareEdge.weight;
		}
	};

	class subset {
		int parent, rank;
	};

	int V, E
	Edge edge[]

	Graph(int v, int e)
	{
		V = v;
		E = e;
		edge = new Edge[E];
		for (int i = 0; i < e; ++i)
			edge[i] = new Edge();
	}

	int find(subset subsets[], int i)
	{


		if (subsets[i].parent != i)
			subsets[i].parent
				= find(subsets, subsets[i].parent);

		return subsets[i].parent;
	}

	void Union(subset subsets[], int x, int y)
	{
		int xroot = find(subsets, x);
		int yroot = find(subsets, y);



		if (subsets[xroot].rank < subsets[yroot].rank)
			subsets[xroot].parent = yroot;
		else if (subsets[xroot].rank > subsets[yroot].rank)
			subsets[yroot].parent = xroot;



		else {
			subsets[yroot].parent = xroot;
			subsets[xroot].rank++;
		}
	}

	void KruskalMST()
	{

		Edge result[] = new Edge[V];


		int e = 0;


		int i = 0;
		for (i = 0; i < V; ++i)
			result[i] = new Edge();





		Arrays.sort(edge);


		subset subsets[] = new subset[V];
		for (i = 0; i < V; ++i)
			subsets[i] = new subset();


		for (int v = 0; v < V; ++v) {
			subsets[v].parent = v;
			subsets[v].rank = 0;
		}

		i = 0


		while (e < V - 1) {
	
	
			Edge next_edge = edge[i++];

			int x = find(subsets, next_edge.src);
			int y = find(subsets, next_edge.dest);

	
	
	
			if (x != y) {
				result[e++] = next_edge;
				Union(subsets, x, y);
			}
	
		}



		System.out.println("Following are the edges in "
						+ "the constructed MST");
		int minimumCost = 0;
		for (i = 0; i < e; ++i) {
			System.out.println(result[i].src + " -- "
							+ result[i].dest
							+ " == " + result[i].weight);
			minimumCost += result[i].weight;
		}
		System.out.println("Minimum Cost Spanning Tree "
						+ minimumCost);
	}

	public static void main(String[] args)
	{

		/* Let us create following weighted graph
				10
			0--------1
			| \	 |
		6| 5\ |15
			|	 \ |
			2--------3
				4	 */
		int V = 4
		int E = 5
		Graph graph = new Graph(V, E);


		graph.edge[0].src = 0;
		graph.edge[0].dest = 1;
		graph.edge[0].weight = 10;


		graph.edge[1].src = 0;
		graph.edge[1].dest = 2;
		graph.edge[1].weight = 6;


		graph.edge[2].src = 0;
		graph.edge[2].dest = 3;
		graph.edge[2].weight = 5;


		graph.edge[3].src = 1;
		graph.edge[3].dest = 3;
		graph.edge[3].weight = 15;


		graph.edge[4].src = 2;
		graph.edge[4].dest = 3;
		graph.edge[4].weight = 4;


		graph.KruskalMST();
	}