Kruskals.java

// Java program for Kruskal's algorithm to find Minimum
// Spanning Tree of a given connected, undirected and
// weighted graph
import java.util.*;
import java.lang.*;
import java.io.*;

class Graph
{
	// A class to represent a graph edge
	class Edge implements Comparable<Edge>
	{
		int src, dest, weight;

		// Comparator function used for sorting edges
		// based on their weight
		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 = 0; // 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();
	}
}