Here is the code:
// Java program for implementation of Ford Fulkerson algorithm
import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.LinkedList;
class MaxFlow
{
static final int V = 8; //Number of vertices in graph
/* Returns true if there is a path from source 's' to sink
't' in residual graph. Also fills parent[] to store the
path */
boolean bfs(int rGraph[][], int s, int t, int parent[])
{
// Create a visited array and mark all vertices as not
// visited
boolean visited[] = new boolean[V];
for(int i=0; i<V; ++i)
visited[i]=false;
// Create a queue, enqueue source vertex and mark
// source vertex as visited
LinkedList<Integer> queue = new LinkedList<Integer>();
queue.add(s);
visited[s] = true;
parent[s]=-1;
// Standard BFS Loop
while (queue.size()!=0)
{
int u = queue.poll();
for (int v=0; v<V; v++)
{
if (visited[v]==false && rGraph[u][v] > 0)
{
queue.add(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 tne maximum flow from s to t in the given graph
int fordFulkerson(int graph[][], 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
// 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)
int rGraph[][] = new int[V][V];
for (u = 0; u < V; u++)
for (v = 0; v < V; v++)
rGraph[u][v] = graph[u][v];
// This array is filled by BFS and to store path
int parent[] = new int[V];
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 edhes
// along the path filled by BFS. Or we can say
// find the maximum flow through the path found.
int path_flow = Integer.MAX_VALUE;
for (v=t; v!=s; v=parent[v])
{
u = parent[v];
path_flow = Math.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
public static void main (String[] args) throws java.lang.Exception
{
int graph[][] =new int[][] { {0, 14, 0, 10, 0, 18, 0, 0},
{0, 0, 18, 0, 14, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0, 10},
{0, 0, 10, 0, 8, 0, 0, 0},
{0, 0, 14, 0, 8, 0, 20},
{0, 0, 0, 6, 0, 0, 16},
{0, 0, 16, 0, 0, 0, 0, 6},
{0,0,0,0,0,0,0,0} };
MaxFlow m = new MaxFlow();
System.out.println("The maximum possible flow is " +
m.fordFulkerson(graph, 0, 7));
}
}
I'd like to modify it to output the path and the weight of each edge but I'm not sure how. I would like to know the path taken so i can see whats going on graphically
edit: The error as someone has pointed out was that I was missing two elements when i created my matrix. Still unsure how to output the path used.
