graph_ford_fulkerson.cpp

// C++ program for implementation of Ford Fulkerson
// algorithm
#include <iostream>
#include <limits.h>
#include <queue>
#include <string.h>
using namespace std;

// Number of vertices in given graph
#define V 6

/* 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[])
{
	// Create a visited array and mark all vertices as not
	// visited
	bool visited[V];
	memset(visited, 0, sizeof(visited));

	// Create a queue, enqueue source vertex and mark source
	// vertex as visited
	queue<int> q;
	q.push(s);
	visited[s] = true;
	parent[s] = -1;

	// Standard BFS Loop
	while (!q.empty())
	{
		int u = q.front();
		q.pop();

		for (int v = 0; v < V; v++)
		{
			if (visited[v] == false && rGraph[u][v] > 0)
			{
				// If we find a connection to the sink node,
				// then there is no point in BFS anymore We
				// just have to set its parent and can return
				// true
				if (v == t)
				{
					parent[v] = u;
					return true;
				}
				q.push(v);
				parent[v] = u;
				visited[v] = true;
			}
		}
	}

	// We didn't reach sink in BFS starting from source, so
	// return false
	return false;
}

// Returns the maximum flow from s to t in the given graph
int fordFulkerson(int graph[V][V], int s, int t)
{
	int u, v;

	// Create a residual graph and fill the residual graph
	// with given capacities in the original graph as
	// residual capacities in residual graph
	int rGraph[V]
			  [V]; // Residual graph where rGraph[i][j]
				   // indicates residual capacity of edge
				   // from i to j (if there is an edge. If
				   // rGraph[i][j] is 0, then there is not)
	for (u = 0; u < V; u++)
		for (v = 0; v < V; v++)
			rGraph[u][v] = graph[u][v];

	int parent[V]; // This array is filled by BFS and to
				   // store path

	int max_flow = 0; // There is no flow initially

	// Augment the flow while there is path from source to
	// sink
	while (bfs(rGraph, s, t, parent))
	{
		// Find minimum residual capacity of the edges along
		// the path filled by BFS. Or we can say find the
		// maximum flow through the path found.
		int path_flow = INT_MAX;
		for (v = t; v != s; v = parent[v])
		{
			u = parent[v];
			path_flow = min(path_flow, rGraph[u][v]);
		}

		// update residual capacities of the edges and
		// reverse edges along the path
		for (v = t; v != s; v = parent[v])
		{
			u = parent[v];
			rGraph[u][v] -= path_flow;
			rGraph[v][u] += path_flow;
		}

		// Add path flow to overall flow
		max_flow += path_flow;
	}

	// Return the overall flow
	return max_flow;
}

// Driver program to test above functions
int main()
{
	// Let us create a graph shown in the above example
	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);

	return 0;
}