PRIMS-MST

//Efficient approach of PRIMS Algorithm for finding MST
//Time Complexity: O(nlogn) (used heap ds for keeping track of minimum value, brings down the
//search complexity to logn)

/*
input:
altered input   || original input
6 9
0 1 5           ||   1 2 5
0 2 4           ||   1 3 4
0 3 6           ||   1 4 6
1 2 2           ||   2 3 2
2 3 1           ||   3 4 1
1 4 9           ||   2 5 9
2 4 3           ||   3 5 3
3 5 7           ||   4 6 7
4 5 10          ||   5 6 10
*/

/*
output:
2 --- 1
0 --- 2
2 --- 3
2 --- 4
3 --- 5

the MST created will be:

        1
        |
        |4
     2  |  1
  2-----3-----4
        |     |
       3|     |7
        |     |
        5     6

total sum: 17
*/

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

#define int long long
#define inf 2e18
int MOD=1000000007;//998244353;
const int nn=1000050;
bool prime[nn]; //array to store precalculated primes till 10^6
void cal_primes(){memset(prime,true,sizeof(prime)); for(int i=2;i<=sqrt(nn);++i){ if(prime[i]==true){ for(int j=i*i;j<=nn;j+=i){prime[j]=false;}}}}

void solve(int t)
{
    int testcases=t;
    while(t--)
    {
        int n,m;cin>>n>>m;
        vector<pair<int,int>> g[n];

        int x,y,wt;
        for(int i=0;i<m;i++){
            cin>>x>>y>>wt;
            g[x].push_back({y,wt});
            g[y].push_back({x,wt});
        }

        int parent[n],key[n];
        bool mstSet[n];

        memset(parent,-1,sizeof(parent));
        memset(mstSet,false,sizeof(mstSet));

        priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>> pq;

        key[0]=0,parent[0]=(-1);
        pq.push({0,0});

        for(int i=0;i<n-1;i++){
            int u=pq.top().second;
            pq.pop();

            mstSet[u]=true;

            for(auto it:g[u]){
                int v=it.first;
                int weight=it.second;
                if(!mstSet[v] && weight<key[v]){
                    parent[v]=u;
                    pq.push({key[v],v});
                    key[v]=weight;
                }
            }
        }

        for(int i=1;i<n;i++)
            cout<<parent[i]<<" -- "<<i<<endl;
    }
}

main()
{
    auto start=chrono::system_clock::now();
    {
        #ifndef ONLINE_JUDGE
            freopen("input.txt","r",stdin);
            freopen("output.txt","w",stdout);
            freopen("error.txt","w",stderr);
        #endif
        ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
        int t=1;
    //  cin>>t;
        solve(t);
    }
    auto end=chrono::system_clock::now();
    chrono::duration<double> elapsed=end-start;
//  cout<<endl<<"Time taken: "<<elapsed.count()<<" sec";
    return 0;
}