Ford Fulkerson Algorithm in C++

This C++ program displays the Ford-Fulkersson Algorithm which computes the maximum flow present inside a network.

Here is the source code of the C++ program to display the maximum flow present inside a directed graph given as an input. This C++ program is successfully compiled and run on DevCpp, a C++ compiler. The program output is given below.

```
/*
```

 * C++ Program to Implement Ford–Fulkerson Algorithm

```
 */
```
```
#include <iostream>
```
```
#include <string.h>
```
```
#include <queue>
```
```
using namespace std;
```

bool bfs(int rGraph[][6], int s, int t, int parent[])

```
{
```
```
    bool visited[6];
```

    memset(visited, 0, sizeof(visited));

```
    queue <int> q;
```
```
    q.push(s);
```
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    visited[s] = true;
```
```
    parent[s] = -1;
```
```
 
```
```
    while (!q.empty())
```
```
    {
```
```
        int u = q.front();
```
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        q.pop();
```
```
        for (int v = 0; v < 6; v++)
```
```
        {
```

            if (visited[v] == false && rGraph[u][v] > 0)

```
            {
```
```
                q.push(v);
```
```
                parent[v] = u;
```
```
                visited[v] = true;
```
```
            }
```
```
        }
```
```
    }
```
```
    return (visited[t] == true);
```
```
}
```
```
 
```

int fordFulkerson(int graph[6][6], int s, int t)

```
{
```
```
    int u, v;
```
```
    int rGraph[6][6];  
```
```
    for (u = 0; u < 6; u++)
```
```
    {
```
```
        for (v = 0; v < 6; v++)
```
```
        {
```
```
            rGraph[u][v] = graph[u][v];
```
```
        }
```
```
    }
```
```
    int parent[6];
```
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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])

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        {
```
```
            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;
```
```
}
```
```
int main()
```
```
{
```

    int graph[6][6] = { {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);

```
    getch();
```
```
}
```

Output
The maximum possible flow is 23

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