MST (Kruskal with DSU , rank and path comp)

bool cmp(vector<int>&a,vector<int>&b){
    return a[2]<b[2];
}



    vector<int> parent, rank;

    void make_set(int x){
        parent[x] =x ;
        rank[x] = 0;
    }

    int find_set(int x){
        if(x == parent[x])return x;
        else parent[x] = find_set(parent[x]);

    }

    void union_set(int a, int b){
        a = find_set(a);
        b = find_set(b);

        if(a != b){
            if(rank[a] < rank[b]){
                parent[a] = b;
            }
            else if(rank[a]>rank[b]){
                parent[b]=a;

            }
            else{
                parent[b] =a;
                rank[a]++;
            }
        }
    }



    int spanningTree(int V, vector<vector<int>> adj[])
    {
        int cost=0;
        parent.resize(V+1);
        rank.resize(V);
        for(int i=0;i<V;i++)make_set(i);
        vector<vector<int>> edges;
        for(int i=0;i<V;i++){
            for(auto it:adj[i]){
                edges.push_back({i,it[0],it[1]});

            }
        }

        sort(edges.begin(),edges.end(),cmp);

        for(vector<int> e : edges){
            if(find_set(e[0])!=find_set(e[1])){
                cost+=e[2];
                union_set(e[0],e[1]);
            }
        }
        return cost;
    }
};