prims algorithm

// 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 graph[][]) 
	{ 
		System.out.println("Edge \tWeight"); 
		for (int i = 1; i < V; i++) 
			System.out.println(parent[i] + " - " + i + "\t" + 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, 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); 
	} 
} 
// This code is contributed by Aakash Hasija