# C++ Program to Implement a Heuristic to Find the Vertex Cover of a Graph

C++Server Side ProgrammingProgramming

Vertex Cover of a Graph is to find a set of vertices V, such that for every edge connecting M to N in graph, either M or N (or both) are present in V. In this program, we Implement a Heuristic to Find the Vertex Cover of a Graph.

## Algorithm

Begin
1) Initialize a set S as empty.
2) Take an edge E of the connecting graph Say M and N.
3) Add both vertex to the set S.
4) Discard all edges in the graph with endpoints at M or N.
5) If some edge is still left in the graph Go to step 2,
6) Print the final set S is a vertex cover of the graph.
End

## Example

#include<bits/stdc++.h>
using namespace std;
vector<vector<int> > g;
bool v;
int i,j;
vector<int> sol_vertex(int n,int e) {
vector<int> S;
for(i=0;i<n;i++) {
if(!v[i]) {
for(j=0;j<(int)g[i].size();j++) {
if(!v[g[i][j]]) {
v[i]=true;
v[g[i][j]]=true;
break;
}
}
}
}
for(i=0;i<n;i++)
if(v[i])
S.push_back(i);
return S;
}
int main() {
int n,e,a,b;
cout<<"Enter number of vertices:";
cin>>n;
cout<<"Enter number of Edges:";
cin>>e;
g.resize(n);
memset(v,0,sizeof(v));
for(i=0;i<e;i++) {
cout<<"Enter the end-points of edge "<<i+1<<" : ";
cin>>a>>b;
a--; b--;
g[a].push_back(b);
g[b].push_back(a);
}
vector<int> S = sol_vertex(n,e);
cout<<"The required vertex cover is as follows:\n";
for(i=0;i<(int)S.size();i++)
cout<<S[i]+1<<" ";
return 0;
}

## Ouput:

Enter number of vertices:4
Enter number of Edges:5
Enter the end-points of edge 1 : 2 1
Enter the end-points of edge 2 : 3 2
Enter the end-points of edge 3 : 4 3
Enter the end-points of edge 4 : 1 4
Enter the end-points of edge 5 : 1 3
The required vertex cover is as follows:
1 2 3 4