Prim’s Algorithm

Explanation :

The Prim’s algorithm is a type of greedy algorithm which is used to find the MST of a weighted undirected graph.

Watch this video for full understanding.

Code :

#include<bits/stdc++.h>
using namespace std;
#define V 6		//No of vertices

int selectMinVertex(vector<int>& value,vector<bool>& setMST)
{
	int minimum = INT_MAX;
	int vertex;
	for(int i=0;i<V;++i)
	{
		if(setMST[i]==false && value[i]<minimum)
		{
			vertex = i;
			minimum = value[i];
		}
	}
	return vertex;
}

void findMST(int graph[V][V])
{
	int parent[V];		//Stores MST
	vector<int> value(V,INT_MAX);	//Used for edge relaxation
	vector<bool> setMST(V,false);	//TRUE->Vertex is included in MST

	//Assuming start point as Node-0
	parent[0] = -1;	//Start node has no parent
	value[0] = 0;	//start node has value=0 to get picked 1st

	//Form MST with (V-1) edges
	for(int i=0;i<V-1;++i)
	{
		//Select best Vertex by applying greedy method
		int U = selectMinVertex(value,setMST);
		setMST[U] = true;	//Include new Vertex in MST

		//Relax adjacent vertices (not yet included in MST)
		for(int j=0;j<V;++j)
		{
			/* 3 constraints to relax:-
			      1.Edge is present from U to j.
			      2.Vertex j is not included in MST
			      3.Edge weight is smaller than current edge weight
			*/
			if(graph[U][j]!=0 && setMST[j]==false && graph[U][j]<value[j])
			{
				value[j] = graph[U][j];
				parent[j] = U;
			}
		}
	}
	//Print MST
	for(int i=1;i<V;++i)
		cout<<"U->V: "<<parent[i]<<"->"<<i<<"  wt = "<<graph[parent[i]][i]<<"\n";
}

int main()
{
	int graph[V][V] = { {0, 4, 6, 0, 0, 0},
						{4, 0, 6, 3, 4, 0},
						{6, 6, 0, 1, 8, 0},
						{0, 3, 1, 0, 2, 3},
						{0, 4, 8, 2, 0, 7},
						{0, 0, 0, 3, 7, 0} };

	findMST(graph);	
	return 0;
}

//TIME COMPLEXITY: O(V^2)

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