kruskal

#include <bits/stdc++.h>

using namespace std;
typedef pair<int, int> pii;

struct Graph
{
    int V, E;
    vector<pair<int, pii>> 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
{
    vector<int> parent, rank;
    int n;
    DisjointSets(int n)
    {
        this->n = n;
        this->parent.resize(n + 1);
        this->rank.resize(n + 1, 0);
        for (int i = 0; i <= n; i++)
        {
            this->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 (rank[x] > rank[y])
            parent[y] = x;
        else
            parent[x] = y;

        if (rank[x] == rank[y])
            rank[y]++;
    }
};
int Graph::kruskalMST()
{
    int totalWeight = 0;
    sort(edges.begin(), edges.end());
    DisjointSets ds(V);
    for (auto edge : edges)
    {
        int u = edge.second.first;
        int v = edge.second.second;

        int set_u = ds.find(u);
        int set_v = ds.find(v);
        if (set_u != set_v)
        {
            cout << u << " - " << v << endl;
            totalWeight += edge.first;
            ds.merge(set_u, set_v);
        }
    }

    return totalWeight;
}
int main()
{
    int V = 9, E = 14;
    Graph g(V, E);

    g.addEdge(0, 1, 4);
    g.addEdge(0, 7, 8);
    g.addEdge(1, 2, 8);
    g.addEdge(1, 7, 11);
    g.addEdge(2, 3, 7);
    g.addEdge(2, 8, 2);
    g.addEdge(2, 5, 4);
    g.addEdge(3, 4, 9);
    g.addEdge(3, 5, 14);
    g.addEdge(4, 5, 10);
    g.addEdge(5, 6, 2);
    g.addEdge(6, 7, 1);
    g.addEdge(6, 8, 6);
    g.addEdge(7, 8, 7);

    cout << "Edges of MST are \n";
    int mst_wt = g.kruskalMST();

    cout << "\nWeight of MST is " << mst_wt;

    return 0;
}