Question

I need to write a small program in c++ that executes Kruskal or Prim algorithm whatever you want to do. It must ask for a graph and present at the end The minimum cost spanning tree that results from applying the algorithm. It can be presented as if it were a list of Vertices with ordered pairs that solve the edges. Kruskal or Prim will work with non-directed graphs.

Answer 1

//kruskal algorithm

#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
int main()
{
  
int V = 9, E = 14;
Graph kru(V, E);
  
// EDGES FROM 1ST VERTEX
kru.addEdge(0, 1, 1);
kru.addEdge(0, 2, 5);
kru.addEdge(0, 3, 8);
kru.addEdge(0, 4, 6);
     
kru.addEdge(1, 2, 9);
kru.addEdge(1, 3, 10);
kru.addEdge(1, 4, 2);
  
     
kru.addEdge(2, 3, 4);
kru.addEdge(2, 4, 7);
  
kru.addEdge(3, 4, 3);
  
  
  
cout << "Edges of MST are \n";
int mst_wt = kru.kruskalMST();
  
cout << "\nWeight of MST is " << mst_wt;
  
return 0;
}

output