prim's(TUF).cpp

#include <bits/stdc++.h>
using namespace std;

class Solution
{
public:
    //Function to find sum of weights of edges of the Minimum Spanning Tree.
    int spanningTree(int V, vector<vector<int>> adj[])
    {
        priority_queue<pair<int, int>,
                       vector<pair<int, int> >, greater<pair<int, int>>> pq;

        vector<int> vis(V, 0);
        // {wt, node}
        pq.push({0, 0});
        int sum = 0;
        while (!pq.empty())
        {
            auto it = pq.top();
            pq.pop();
            int node = it.second;
            int wt = it.first;

            if (vis[node] == 1) continue;
            // add it to the mst
            vis[node] = 1;
            sum += wt;
            for (auto it : adj[node])
            {
                int adjNode = it[0];
                int edW = it[1];
                if (!vis[adjNode])
                {
                    pq.push({edW, adjNode});
                }
            }
        }
        return sum;
    }
};


int main()
{

    int V = 5;
    vector<vector<int>> edges = {{0, 1, 2}, {0, 2, 1}, {1, 2, 1}, {2, 3, 2}, {3, 4, 1}, {4, 2, 2}};
    vector<vector<int>> adj[V];
    for (auto it : edges)
    {
        vector<int> tmp(2);
        tmp[0] = it[1];
        tmp[1] = it[2];
        adj[it[0]].push_back(tmp);

        tmp[0] = it[0];
        tmp[1] = it[2];
        adj[it[1]].push_back(tmp);
    }

    Solution obj;
    int sum = obj.spanningTree(V, adj);
    cout << "The sum of all the edge weights: " << sum << endl;

    return 0;
}