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Prims.cpp
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Prims.cpp
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#include <iostream>
#include <climits>
#include <vector>
using namespace std;
//Prims is applied to find MST to a graph with property of graph as follows:-
//1) Undirected
//2) Connected
//3) Weighted
/*
1 --- 3
/ | /|
Graph is 0 | / |
\ |/ |
2 --- 4
weights of edges are as follows:-
0----1 : 4
0----2 : 8
1----3 : 6
1----2 : 2
2----3 : 3
2----4 : 9
3----4 : 5
*/
//compile it using g++ Prims.cpp -o prims -std=c++11
//run it as ./prims and paste this below test case
/*run this test case
5 7
0 1 4
0 2 8
1 2 2
1 3 6
2 3 3
2 4 9
3 4 5
*/
void printMatrix(vector<vector<int>> adjMatrix)
{
int n = adjMatrix.size();
for(int i=0; i<n; i++)
{
for(int j=0; j<n; j++)
{
cout << adjMatrix[i][j] << " ";
}
cout << endl;
}
}
int findMinVertex(bool *visited, int *weight, int nodes)
{
int minVertex = -1;
for(int i=0; i<nodes; i++)
{
if(!visited[i] && (minVertex==-1 || weight[i] < weight[minVertex]))
{
minVertex = i;
}
}
return minVertex;
}
void primsAlgo(vector<vector<int>> adjMatrix, int nodes)
{
int *parent = new int[nodes];
bool *visited = new bool[nodes];
int *weight = new int[nodes];
for(int i=0; i<nodes; i++)
{
visited[i] = false;
weight[i] = INT_MAX;
}
parent[0] = -1;
weight[0] = 0;
for(int i=0;i<nodes;i++)
{
//find min vertex
int minVertex = findMinVertex(visited,weight,nodes);
visited[minVertex] = true;
//explore the unvisited neighbours of min vertex
for(int j=0; j<nodes; j++)
{
if(adjMatrix[minVertex][j]!=0 && !visited[j])
{
if(adjMatrix[minVertex][j] < weight[j])
{
weight[j] = adjMatrix[minVertex][j];
parent[j] = minVertex;
}
}
}
}
int total_min_distance = 0;
for(int i=1; i<nodes; i++)
{
if(parent[i] < i)
{
total_min_distance += weight[i];
cout << parent[i] << " " << i << " " << weight[i] << endl;
}
else
{
total_min_distance += weight[i];
cout << i << " " << parent[i] << " " << weight[i] << endl;
}
}
cout << "Total Minimum Distance taken is " << total_min_distance << endl;
}
int main() {
int nodes, edges;
cin >> nodes >> edges;
vector<vector<int>> adjMatrix(nodes, vector<int>(nodes, 0));
for(int i=0; i<edges; i++)
{
int u, v, w;
cin >> u >> v >> w;
adjMatrix[u][v] = w;
adjMatrix[v][u] = w;
}
printMatrix(adjMatrix);
primsAlgo(adjMatrix,nodes);
return 0;
}