C++ Program to Find the Maximum Cut in a Graph

In this program to find the maximum Cut in a graph, we need to find the Edge Connectivity of a Graph. An Edge Connectivity of a Graph of a graph means it is a bridge, removing it graph will be disconnected. Number of connected components increases with the removing of bridge in a disconnected undirected graph.

Functions and pseudocode

Begin
   Function connections() is a recursive function to find out the connections:
   A) Mark the current node un visited.
   B) Initialize time and low value
   C) Go through all vertices adjacent to this
   D) Check if the subtree rooted with x has a connection to one
   of the ancestors of w. If the lowest vertex reachable from
   subtree under x is below u in DFS tree, then w-x has a
   connection.
   E) Update low value of w for parent function calls.
End
Begin
   Function Con() that uses connections():
   A) Mark all the vertices as unvisited.
   B) Initialize par and visited, and connections.
   C) Print the connections between the edges in the graph.
End

Example

#include
#include 
#define N -1
using namespace std;
class G {
   //declaration of functions
   int n;
   list *adj;
   void connections(int n, bool visited[], int disc[], int low[], int par[]);
   public:
      G(int n); //constructor
      void addEd(int w, int x);
      void Con();
};
G::G(int n) {
   this->n= n;
   adj = new list [n];
}
//add edges to the graph
void G::addEd(int w, int x) {
   adj[x].push_back(w); //add u to v's list
   adj[w].push_back(x); //add v to u's list
}
void G::connections(int w, bool visited[], int dis[], int low[],
int par[]) {
   static int t = 0;
   //mark current node as visited
   visited[w] = true;
   dis[w] = low[w] = ++t;
   //Go through all adjacent vertices
   list::iterator i;
   for (i = adj[w].begin(); i != adj[w].end(); ++i) {
      int x = *i; //x is current adjacent
      if (!visited[x]) {
         par[x] = w;
         connections(x, visited, dis, low, par);
         low[w] = min(low[w], low[x]);
         // If the lowest vertex reachable from subtree under x is below w in DFS tree, then w-x is a connection
         if (low[x] > dis[w])
            cout 
Output
Connections in first graph
2 3
1 2
1 4
0 1