prims_algorithm.cpp

#include<bits/stdc++.h>
using namespace std;
# define INF 0x3f3f3f3f


typedef pair<int, int> iPair;


class Graph
{
	int V; // No. of vertices

	
	list< pair<int, int> > *adj;

public:
	Graph(int V); // Constructor

	
	void addEdge(int u, int v, int w);

	// Print MST using Prim's algorithm
	void primMST();
};


Graph::Graph(int V)
{
	this->V = V;
	adj = new list<iPair> [V];
}

void Graph::addEdge(int u, int v, int w)
{
	adj[u].push_back(make_pair(v, w));
	adj[v].push_back(make_pair(u, w));
}


void Graph::primMST()
{
	
	priority_queue< iPair, vector <iPair> , greater<iPair> > pq;

	int src = 0; // Taking vertex 0 as source

	
	vector<int> key(V, INF);

	
	vector<int> parent(V, -1);

	
	vector<bool> inMST(V, false);

	
	pq.push(make_pair(0, src));
	key[src] = 0;

	
	while (!pq.empty())
	{
		
		int u = pq.top().second;
		pq.pop();
		
		
		if(inMST[u] == true){
			continue;
		}
	
		inMST[u] = true; 

		
		list< pair<int, int> >::iterator i;
		for (i = adj[u].begin(); i != adj[u].end(); ++i)
		{
			
			int v = (*i).first;
			int weight = (*i).second;

			
			if (inMST[v] == false && key[v] > weight)
			{
				
				key[v] = weight;
				pq.push(make_pair(key[v], v));
				parent[v] = u;
			}
		}
	}

	
	for (int i = 1; i < V; ++i)
		printf("%d - %d\n", parent[i], i);
}


int main()
{
	
	int V = 9;
	Graph g(V);

	
	g.addEdge(0, 1, 4);
	g.addEdge(0, 7, 8);
	g.addEdge(1, 2, 8);
	g.addEdge(1, 7, 11);
	g.addEdge(2, 3, 7);
	g.addEdge(2, 8, 2);
	g.addEdge(2, 5, 4);
	g.addEdge(3, 4, 9);
	g.addEdge(3, 5, 14);
	g.addEdge(4, 5, 10);
	g.addEdge(5, 6, 2);
	g.addEdge(6, 7, 1);
	g.addEdge(6, 8, 6);
	g.addEdge(7, 8, 7);

	g.primMST();

	return 0;
}