C++ Program to Implement Network Flow Problem

This C++ Program demonstrates implementation of Network_Flow Problem.

Here is source code of the C++ Program to demonstrate Network_Flow Problem.
The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
/*
```

 * C++ Program to Implement Network Flow Problem

```
 */
```
```
#include <iostream>
```
```
#include <climits>
```
```
#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 *

```
 */
```

bool 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;
```
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    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);
```
```
}
```
```
 
```
```
/*
```

 *  Returns tne maximum flow from s to t in the given graph

```
 */
```

int fordFulkerson(int graph[V][V], int s, int t)

```
{
```
```
    int u, v;
```
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    int rGraph[V][V];
```
```
    for (u = 0; u < V; u++)
```
```
    {
```
```
        for (v = 0; v < V; v++)
```

             rGraph[u][v] = graph[u][v];

```
    }
```
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    int parent[V];
```
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    int max_flow = 0;
```
```
 
```
```
    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;
```
```
        }
```
```
        max_flow += path_flow;
```
```
    }
```
```
    return max_flow;
```
```
}
```
```
/*
```
```
 * Main Contains Menu
```
```
 */ 
```
```
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}

```
                      };
```
```
 
```

    cout << "The maximum possible flow is " << fordFulkerson(graph, 0, 5);

```
 
```
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    return 0;
```
```
}
```

$ g++ nwtwork_flow.cpp
$ a.out
The maximum possible flow is 23
 
------------------
(program exited with code: 0)
Press return to continue

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