1774.cpp

#include <iostream>
#include <vector>
#include <utility>
#include <algorithm>

using namespace std;

typedef  pair<int, int> iPair;

struct Graph
{
    int V, E;
    vector< pair<int, iPair> > edges;

    Graph(int V, int E)
    {
        this->V = V;
        this->E = E;
    }

    void addEdge(int u, int v, int w)
    {
        edges.push_back({w, {u, v}});
    }
    int kruskalMST();
};

struct DisjointSets
{
    int *parent, *rnk;
    int n;

    DisjointSets(int n)
    {
        this->n = n;
        parent = new int[n+1];
        rnk = new int[n+1];

        for (int i = 0; i <= n; i++)
        {
            rnk[i] = 0;
            parent[i] = i;
        }
    }

    int find(int u)
    {
        if (u != parent[u])
            parent[u] = find(parent[u]);
        return parent[u];
    }

    void merge(int x, int y)
    {
        x = find(x), y = find(y);
        if (rnk[x] > rnk[y])
            parent[y] = x;
        else
            parent[x] = y;

        if (rnk[x] == rnk[y])
            rnk[y]++;
    }
};

int Graph::kruskalMST()
{
    int mst_wt = 0;
    sort(edges.begin(), edges.end());
    DisjointSets ds(V);

    vector< pair<int, iPair> >::iterator it;
    for (it=edges.begin(); it!=edges.end(); it++)
    {
        int u = it->second.first;
        int v = it->second.second;

        int set_u = ds.find(u);
        int set_v = ds.find(v);
        if (set_u != set_v)
        {
            mst_wt += it->first;
            ds.merge(set_u, set_v);
        }
    }

    return mst_wt;
}

int main()
{
    int r, c;
    int v, w, p;
    cin >> r >> c;
    Graph g(r, c);

    for (int i = 0; i < c; i++) {
        cin >> v >> w >> p;
        g.addEdge(v, w, p);
    }

    cout << g.kruskalMST() << endl;
    return 0;
}