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maxflow.cpp
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maxflow.cpp
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// C++ program for implementation of Ford Fulkerson algorithm
#include <iostream>
#include <limits.h>//INT_MAX
#include <string.h>
#include <queue>//coz, using BFS
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));//initialise the array with zeros //needs string.h
// 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)
{
q.push(v);
parent[v] = u;
visited[v] = true;
}
}
}
// If we reached sink in BFS starting from source, then return true, else false
return (visited[t] == true);
}
// 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 to retrace the patth
int max_flow = 0; // There is no flow initially
// Augment the flow while tere 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]);
}//now the path_flow is the min capacity of the path
// 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;
}