# Kruskal’s Minimum Spanning Tree using STL in C++

In this tutorial, we will be discussing a program to understand Kruskal’s minimum spanning tree using STL in C++.

For this, we will be provided with a connected, undirected and weighted graph. Our task is to calculate the Minimum spanning tree for the given graph.

## Example

Live Demo

#include<bits/stdc++.h>
using namespace std;
typedef pair<int, int> iPair;
//structure for graph
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){
cout << u << " - " << v << endl;
mst_wt += it->first;
ds.merge(set_u, set_v);
}
}
return mst_wt;
}
int main(){
int V = 9, E = 14;
Graph g(V, E);
cout << "Edges of MST are \n";
int mst_wt = g.kruskalMST();
cout << "\nWeight of MST is " << mst_wt;
return 0;
}

## Output

Edges of MST are
6 - 7
2 - 8
5 - 6
0 - 1
2 - 5
2 - 3
0 - 7
3 - 4
Weight of MST is 37

Updated on: 01-Apr-2020

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