Prim Algo FOR MST

PrimMst.java

// A Java program for Prim's Minimum Spanning Tree (MST) algorithm.
// The program is for adjacency matrix representation of the graph

import java.util.*;
import java.lang.*;
import java.io.*;

class MST
{
	// Number of vertices in the graph
	private static final int V=5;

	// A utility function to find the vertex with minimum key
	// value, from the set of vertices not yet included in MST
	int minKey(int key[], Boolean mstSet[])
	{
		// Initialize min value
		int min = Integer.MAX_VALUE, min_index=-1;

		for (int v = 0; v < V; v++)
			if (mstSet[v] == false && key[v] < min)
			{
				min = key[v];
				min_index = v;
			}

		return min_index;
	}

	// A utility function to print the constructed MST stored in
	// parent[]
	void printMST(int parent[], int n, int graph[][])
	{
		System.out.println("Edge Weight");
		for (int i = 1; i < V; i++)
			System.out.println(parent[i]+" - "+ i+" "+
							graph[i][parent[i]]);
	}

	// Function to construct and print MST for a graph represented
	// using adjacency matrix representation
	void primMST(int graph[][])
	{
		// Array to store constructed MST
		int parent[] = new int[V];

		// Key values used to pick minimum weight edge in cut
		int key[] = new int [V];

		// To represent set of vertices not yet included in MST
		Boolean mstSet[] = new Boolean[V];

		// Initialize all keys as INFINITE
		for (int i = 0; i < V; i++)
		{
			key[i] = Integer.MAX_VALUE;
			mstSet[i] = false;
		}

		// Always include first 1st vertex in MST.
		key[0] = 0;	 // Make key 0 so that this vertex is
						// picked as first vertex
		parent[0] = -1; // First node is always root of MST

		// The MST will have V vertices
		for (int count = 0; count < V-1; count++)
		{
			// Pick thd minimum key vertex from the set of vertices
			// not yet included in MST
			int u = minKey(key, mstSet);

			// Add the picked vertex to the MST Set
			mstSet[u] = true;

			// Update key value and parent index of the adjacent
			// vertices of the picked vertex. Consider only those
			// vertices which are not yet included in MST
			for (int v = 0; v < V; v++)

				// graph[u][v] is non zero only for adjacent vertices of m
				// mstSet[v] is false for vertices not yet included in MST
				// Update the key only if graph[u][v] is smaller than key[v]
				if (graph[u][v]!=0 && mstSet[v] == false &&
					graph[u][v] < key[v])
				{
					parent[v] = u;
					key[v] = graph[u][v];
				}
		}

		// print the constructed MST
		printMST(parent, V, graph);
	}

	public static void main (String[] args)
	{
		/* Let us create the following graph
		2 3
		(0)--(1)--(2)
		| / \ |
		6| 8/ \5 |7
		| /	 \ |
		(3)-------(4)
			9		 */
		MST t = new MST();
		int graph[][] = new int[][] {{0, 2, 0, 6, 0},
									{2, 0, 3, 8, 5},
									{0, 3, 0, 0, 7},
									{6, 8, 0, 0, 9},
									{0, 5, 7, 9, 0},
								};

		// Print the solution
		t.primMST(graph);
	}
}