Kruskal’s Algorithm c++

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Kruskal’s Algorithm c++

In this tutorial, we’ll look at a program that uses STL in C++ to understand Kruskal’s minimum spanning tree.

We will be given a connected, undirected, and weighted graph to work with. The aim of this exercise is to find the minimum spanning tree for the given graph.

Example

include
using namespace std;
typedef pair iPair;
//structure for graph
struct Graph{
int V, E;
vector< pair > 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 >::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);
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;
}

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

Resources

Kruskal’s Algorithm c++

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