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);

visited[s] = true;

parent[s] = -1;

while (!q.empty())

`{`

int u = q.front();

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];

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;

`}`

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

**Sanfoundry Global Education & Learning Series – 1000 C++ Programs.**

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