Java Program to Implement Max-Flow Min-Cut Theorem

This Java program is to Implement Max Flow Min Cut theorem. In optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source to the sink is equal to the minimum capacity that when removed in a specific way from the network causes the situation that no flow can pass from the source to the sink.

Here is the source code of the Java program to implement Max Flow Min Cut theorem. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

import java.util.ArrayList;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
 
public class MaxFlowMinCut
{
    private int[] parent;
    private Queue<Integer> queue;
    private int numberOfVertices;
    private boolean[] visited;
    private Set<Pair> cutSet;
    private ArrayList<Integer> reachable;
    private ArrayList<Integer> unreachable;
 
    public MaxFlowMinCut (int numberOfVertices)
    {
        this.numberOfVertices = numberOfVertices;
        this.queue = new LinkedList<Integer>();
        parent = new int[numberOfVertices + 1];
        visited = new boolean[numberOfVertices + 1];
        cutSet = new HashSet<Pair>();
        reachable = new ArrayList<Integer>();
        unreachable = new ArrayList<Integer>();
    }
 
    public boolean bfs (int source, int goal, int graph[][])
    {
        boolean pathFound = false;
        int destination, element;
        for (int vertex = 1; vertex <= numberOfVertices; vertex++)
        {
            parent[vertex] = -1;
            visited[vertex] = false;
        }
        queue.add(source);
        parent = -1;
        visited = true;
 
        while (!queue.isEmpty())
        {
            element = queue.remove();
            destination = 1;
            while (destination <= numberOfVertices)
            {
                if (graph[element][destination] > 0 &&  !visited[destination])
                {
                    parent[destination] = element;
                    queue.add(destination);
                    visited[destination] = true;
                }
                destination++;
            }
        }
 
        if (visited[goal])
        {
            pathFound = true;
        }
        return pathFound;
    }
 
    public int  maxFlowMinCut (int graph[][], int source, int destination)
    {
        int u, v;
        int maxFlow = 0;
        int pathFlow;
        int[][] residualGraph = new int[numberOfVertices + 1][numberOfVertices + 1];
 
        for (int sourceVertex = 1; sourceVertex <= numberOfVertices; sourceVertex++)
        {
            for (int destinationVertex = 1; destinationVertex <= numberOfVertices; destinationVertex++)
            {
                residualGraph[sourceVertex][destinationVertex] = graph[sourceVertex][destinationVertex];
            }
        }
 
        /*max flow*/
        while (bfs(source, destination, residualGraph))
        {
            pathFlow = Integer.MAX_VALUE;
            for (v = destination; v != source; v = parent[v])
            {
                u = parent[v];
                pathFlow = Math.min(pathFlow,residualGraph[u][v]);
            }
            for (v = destination; v != source; v = parent[v])
            {
                u = parent[v];
                residualGraph[u][v] -= pathFlow;
                residualGraph[v][u] += pathFlow;
            }
            maxFlow += pathFlow;	
        }
 
        /*calculate the cut set*/		
        for (int vertex = 1; vertex <= numberOfVertices; vertex++)
        {
            if (bfs(source, vertex, residualGraph))
            {
                reachable.add(vertex);
            }
            else
            {
                unreachable.add(vertex);
            }
        }
        for (int i = 0; i < reachable.size(); i++)
        {
            for (int j = 0; j < unreachable.size(); j++)
            {
                if (graph[reachable.get(i)][unreachable.get(j)] > 0)
                {
                    cutSet.add(new Pair(reachable.get(i), unreachable.get(j)));
                }
            }
        }
        return maxFlow;
    }
 
    public void printCutSet ()
    {
        Iterator<Pair> iterator = cutSet.iterator();
        while (iterator.hasNext())
        {
            Pair pair = iterator.next();
            System.out.println(pair.source + "-" + pair.destination);
        }
    }
 
    public static void main (String...arg)
    {
        int[][] graph;
        int numberOfNodes;
        int source;
        int sink;
        int maxFlow;
 
        Scanner scanner = new Scanner(System.in);
        System.out.println("Enter the number of nodes");
        numberOfNodes = scanner.nextInt();
        graph = new int[numberOfNodes + 1][numberOfNodes + 1];
 
        System.out.println("Enter the graph matrix");
        for (int sourceVertex = 1; sourceVertex <= numberOfNodes; sourceVertex++)
        {
            for (int destinationVertex = 1; destinationVertex <= numberOfNodes ; destinationVertex++)
            {
                graph[sourceVertex][destinationVertex] = scanner.nextInt();
            }
        }
        System.out.println("Enter the source of the graph");
        source= scanner.nextInt();
 
        System.out.println("Enter the sink of the graph");
        sink = scanner.nextInt();
 
        MaxFlowMinCut maxFlowMinCut = new MaxFlowMinCut(numberOfNodes);
        maxFlow = maxFlowMinCut.maxFlowMinCut(graph, source, sink);
 
        System.out.println("The Max Flow is " + maxFlow);
        System.out.println("The Cut Set is ");
        maxFlowMinCut.printCutSet();
        scanner.close();
    }
}
 
class Pair
{
    public int source;
    public int destination;
 
    public Pair (int source, int destination)
    {
        this.source = source;
        this.destination = destination;
    }
 
    public Pair()
    {
    }
}

$javac MaxFlowMinCut.java
$java MaxFlowMinCut
Enter the number of nodes
6
Enter the graph matrix
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
Enter the source of the graph
1
Enter the sink of the graph
6
The Max Flow is 23
The Cut Set is 
5-4
5-6
2-4