MaxFlow_MinCut.cpp

#include <iostream>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <queue>
#define V 6
using namespace std;

/* Returns true if there is a path from source 's' to sink 't' in
  residual graph. Also fills parent[] to store the path */
int bfs(int rGraph[V][V], int s, int t, int parent[])
{
    bool visited[V];
    memset(visited, 0, sizeof(visited));
    queue <int> q;
    q.push(s);
    visited[s] = true;
    parent[s] = -1;
    while (!q.empty())
    {
        int u = q.front();
        q.pop();
        for (int v = 0; v < V; v++)
        {
            if (visited[v] == false && rGraph[u][v] > 0)
            {
                q.push(v);
                parent[v] = u;
                visited[v] = true;
            }
        }
    }
    return (visited[t] == true);
}

// A DFS based function to find all reachable vertices from s.  The function
// marks visited[i] as true if i is reachable from s.  The initial values in
// visited[] must be false. We can also use BFS to find reachable vertices
void dfs(int rGraph[V][V], int s, bool visited[])
{
    visited[s] = true;
    for (int i = 0; i < V; i++)
    {
        if (rGraph[s][i] && !visited[i])
           dfs(rGraph, i, visited);
    }
}

// Prints the minimum s-t cut
void minCut(int graph[V][V], int s, int t)
{
    int u, v;
    int rGraph[V][V];
    for (u = 0; u < V; u++)
    {
        for (v = 0; v < V; v++)
             rGraph[u][v] = graph[u][v];
    }
    int parent[V];
    while (bfs(rGraph, s, t, parent))
    {
        int path_flow = 65536;
        for (v = t; v != s; v = parent[v])
        {
            u = parent[v];
            path_flow = min(path_flow, rGraph[u][v]);
        }
        for (v = t; v != s; v = parent[v])
        {
            u = parent[v];
            rGraph[u][v] -= path_flow;
            rGraph[v][u] += path_flow;
        }
    }
    bool visited[V];
    memset(visited, 0, sizeof(visited));
    dfs(rGraph, s, visited);
    for (int i = 0; i < V; i++)
    {
        for (int j = 0; j < V; j++)
        {
            if (visited[i] && !visited[j] && graph[i][j])
                cout << i << " - " << j << endl;
        }
    }
    return;
}

int main()
{
    int graph[V][V] = { {0, 16, 13, 0, 0, 0},
                        {0, 0, 10, 12, 0, 0},
                        {0, 4, 0, 0, 14, 0},
                        {0, 0, 9, 0, 0, 20},
                        {0, 0, 0, 7, 0, 4},
                        {0, 0, 0, 0, 0, 0}
                      };

    minCut(graph, 0, 5);
    return 0;
}