// A C / C++ program for Prim's Minimum 
// Spanning Tree (MST) algorithm. The program is 
// for adjacency matrix representation of the graph 
#include <stdio.h>
#include <limits.h>
#include<stdbool.h>
// Number of vertices in the graph 
#define 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[], bool mstSet[])
{
// Initialize min value 
	int min = INT_MAX, min_index;
	
	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[V][V])
{
	printf("Edge \tWeight\n");
	for (int i = 1; i < V; i++)
		printf("%d - %d \t%d \n", 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[V][V])
{
	// Array to store constructed MST 
	int parent[V];
	// Key values used to pick minimum weight edge in cut 
	int key[V];
	// To represent set of vertices not yet included in MST 
	bool mstSet[V];
	
	// Initialize all keys as INFINITE 
	for (int i = 0; i < V; i++)
		key[i] = INT_MAX, mstSet[i] = false;
	
	// Always include first 1st vertex in MST. 
	// Make key 0 so that this vertex is picked as first vertex. 
	key[0] = 0;
	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 the 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] && mstSet[v] == false && graph[u][v] < key[v])
				parent[v] = u, key[v] = graph[u][v];
	}
	
	// print the constructed MST 
	printMST(parent, V, graph);
}


// driver program to test above function 
int main()
{
/* Let us create the following graph 
		2     3
	(0)----(1)--(2)
	 |     / \   |
    6|  8/    \5 |7
	 | /	   \ |
	(3)--------(4)
			9		 */
	int graph[V][V] = {{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 
	primMST(graph);
	
	return 0;
}