DAA P5 kruskal

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 Kruskal

// 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;
}

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