connecting_the_graphs.cpp

//{ Driver Code Starts
#include <bits/stdc++.h>
using namespace std;


// } Driver Code Ends
// User function Template for C++
class DisjointSet {
    vector<int> rank, parent, size;
public:
    DisjointSet(int n) {
        rank.resize(n + 1, 0);
        parent.resize(n + 1);
        size.resize(n + 1);
        for (int i = 0; i <= n; i++) {
            parent[i] = i;
            size[i] = 1;
        }
    }

    int findUPar(int node) {
        if (node == parent[node])
            return node;
        return parent[node] = findUPar(parent[node]);
    }

    void unionByRank(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v) return;
        if (rank[ulp_u] < rank[ulp_v]) {
            parent[ulp_u] = ulp_v;
        }
        else if (rank[ulp_v] < rank[ulp_u]) {
            parent[ulp_v] = ulp_u;
        }
        else {
            parent[ulp_v] = ulp_u;
            rank[ulp_u]++;
        }
    }

    void unionBySize(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v) return;
        if (size[ulp_u] < size[ulp_v]) {
            parent[ulp_u] = ulp_v;
            size[ulp_v] += size[ulp_u];
        }
        else {
            parent[ulp_v] = ulp_u;
            size[ulp_u] += size[ulp_v];
        }
    }
};
class Solution {
  public:
    int Solve(int n, vector<vector<int>>& edge) {
       DisjointSet ds(n);
       int cntExtra=0;
       for(auto it:edge){
           int u=it[0];
           int v=it[1];
           if(ds.findUPar(u)==ds.findUPar(v))cntExtra++;
           else ds.unionBySize(u,v);
       }
       int connected=0;
       for(int i=0;i<n;i++){
           if(ds.findUPar(i)==i)connected++;
       }
       if(cntExtra>=connected-1)return connected-1;
       else return -1;
    }
};

//{ Driver Code Starts.

int main() {
    int t;
    cin >> t;
    while (t--) {
        int n, m;
        cin >> n >> m;
        vector<vector<int>> adj;

        for (int i = 0; i < m; ++i) {
            vector<int> temp;
            for (int j = 0; j < 2; ++j) {
                int x;
                cin >> x;
                temp.push_back(x);
            }
            adj.push_back(temp);
        }

        Solution Obj;
        cout << Obj.Solve(n, adj) << "\n";
    }
    return 0;
}
// } Driver Code Ends