Kruskal's Minimum Spanning Tree using STL in C++ (original) (raw)

`// C++ program for Kruskal's algorithm to find Minimum // Spanning Tree of a given connected, undirected and // weighted graph #include<bits/stdc++.h> using namespace std;

// Creating shortcut for an integer pair typedef pair<int, int> iPair;

// Structure to represent a graph struct Graph { int V, E; vector< pair<int, iPair> > edges;

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

// Utility function to add an edge
void addEdge(int u, int v, int w)
{
    edges.push_back({w, {u, v}});
}

// Function to find MST using Kruskal's
// MST algorithm
int kruskalMST();

};

// To represent Disjoint Sets struct DisjointSets { int *parent, *rnk; int n;

// Constructor.
DisjointSets(int n)
{
    // Allocate memory
    this->n = n;
    parent = new int[n+1];
    rnk = new int[n+1];

    // Initially, all vertices are in
    // different sets and have rank 0.
    for (int i = 0; i <= n; i++)
    {
        rnk[i] = 0;

        //every element is parent of itself
        parent[i] = i;
    }
}

// Find the parent of a node 'u'
// Path Compression
int find(int u)
{
    /* Make the parent of the nodes in the path
    from u--> parent[u] point to parent[u] */
    if (u != parent[u])
        parent[u] = find(parent[u]);
    return parent[u];
}

// Union by rank
void merge(int x, int y)
{
    x = find(x), y = find(y);

    /* Make tree with smaller height
    a subtree of the other tree */
    if (rnk[x] > rnk[y])
        parent[y] = x;
    else // If rnk[x] <= rnk[y]
        parent[x] = y;

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

};

/* Functions returns weight of the MST*/

int Graph::kruskalMST() { int mst_wt = 0; // Initialize result

// Sort edges in increasing order on basis of cost
sort(edges.begin(), edges.end());

// Create disjoint sets
DisjointSets ds(V);

// Iterate through all sorted edges
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);

    // Check if the selected edge is creating
    // a cycle or not (Cycle is created if u
    // and v belong to same set)
    if (set_u != set_v)
    {
        // Current edge will be in the MST
        // so print it
        cout << u << " - " << v << endl;

        // Update MST weight
        mst_wt += it->first;

        // Merge two sets
        ds.merge(set_u, set_v);
    }
}

return mst_wt;

}

// Driver program to test above functions int main() { /* Let us create above shown weighted and undirected graph */ int V = 9, E = 14; Graph g(V, E);

// making above shown graph
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;

}

`