For the flow graph above find the maximum flow starting from

For the flow graph above, find the maximum flow starting from an all zero flow using the Ford-Fulkerson algorithm. Draw the resulting flow graph and give the associated minimum cut of the maximum flow. Identify the minimum cut by giving two sets of vertices.

Solution

Answer   

program
#include <iostream>
#include <limits.h>
#include <string.h>
#include <queue>
using namespace std;
#define V 6
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);
}
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);
}
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 = INT_MAX;
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, false, 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;
}