How to find MST using Kruskal's algorithm?

Software Development
#1

Below are the steps for finding MST using Kruskal’s algorithm:

  • Sort all the edges in non-decreasing order of their weight.
  • Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it.
  • Repeat step#2 until there are (V-1) edges in the spanning tree.
#include <bits/stdc++.h>
using namespace std;
 
// DSU data structure
// path compression + rank by union
 
class DSU {
    int* parent;
    int* rank;
 
public:
    DSU(int n)
    {
        parent = new int[n];
        rank = new int[n];
 
        for (int i = 0; i < n; i++) {
            parent[i] = -1;
            rank[i] = 1;
        }
    }
 
    // Find function
    int find(int i)
    {
        if (parent[i] == -1)
            return i;
 
        return parent[i] = find(parent[i]);
    }
   
    // Union function
    void unite(int x, int y)
    {
        int s1 = find(x);
        int s2 = find(y);
 
        if (s1 != s2) {
            if (rank[s1] < rank[s2]) {
                parent[s1] = s2;
                rank[s2] += rank[s1];
            }
            else {
                parent[s2] = s1;
                rank[s1] += rank[s2];
            }
        }
    }
};
 
class Graph {
    vector<vector<int> > edgelist;
    int V;
 
public:
    Graph(int V) { this->V = V; }
 
    void addEdge(int x, int y, int w)
    {
        edgelist.push_back({ w, x, y });
    }
 
    void kruskals_mst()
    {
        // 1. Sort all edges
        sort(edgelist.begin(), edgelist.end());
 
        // Initialize the DSU
        DSU s(V);
        int ans = 0;
        cout << "Following are the edges in the "
                "constructed MST"
             << endl;
        for (auto edge : edgelist) {
            int w = edge[0];
            int x = edge[1];
            int y = edge[2];
 
            // Take this edge in MST if it does
              // not forms a cycle
            if (s.find(x) != s.find(y)) {
                s.unite(x, y);
                ans += w;
                cout << x << " -- " << y << " == " << w
                     << endl;
            }
        }
       
        cout << "Minimum Cost Spanning Tree: " << ans;
    }
};
 
// Driver's code
int main()
{
    /* Let us create following weighted graph
                   10
              0--------1
              |  \     |
             6|   5\   |15
              |      \ |
              2--------3
                  4       */
    Graph g(4);
    g.addEdge(0, 1, 10);
    g.addEdge(1, 3, 15);
    g.addEdge(2, 3, 4);
    g.addEdge(2, 0, 6);
    g.addEdge(0, 3, 5);
 
      // Function call
    g.kruskals_mst();
    return

Output

Following are the edges in the constructed MST
2 -- 3 == 4
0 -- 3 == 5
0 -- 1 == 10
Minimum Cost Spanning Tree: 19