Java Program to Implement Network Flow Problem

This Java program is to Implement Network Flow problem. In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in Operations Research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, except when it is a source, which has more outgoing flow, or sink, which has more incoming flow. A network can be used to model traffic in a road system, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes.

Here is the source code of the Java program to implement network flow problem. 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;
```
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import java.util.Iterator;
```
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import java.util.LinkedList;
```
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import java.util.Queue;
```
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import java.util.Scanner;
```
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import java.util.Set;
```
```
 
```
```
public class NetworkFlowProb
```
```
{                                 
```
```
    private int[] parent;
```
```
    private Queue<Integer> queue;
```
```
    private int numberOfVertices;
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```
    private boolean[] visited;
```
```
    private Set<Pair> cutSet;
```

    private ArrayList<Integer> reachable;

    private ArrayList<Integer> unreachable;

```
 
```

    public NetworkFlowProb (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;
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```
            visited[vertex] = false;
```
```
        }
```
```
        queue.add(source);
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```
        parent[source] = -1;
```
```
        visited[source] = true;
```
```
 
```
```
        while (!queue.isEmpty())
```
```
        {
```
```
            element = queue.remove();
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            destination = 1;
```

            while (destination <= numberOfVertices)

```
            {
```

                if (graph[element][destination] > 0 &&  !visited[destination])

```
                {
```

                    parent[destination] = element;

                    queue.add(destination);

                    visited[destination] = true;

```
                }
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                destination++;
```
```
            }
```
```
        }
```
```
 
```
```
        if (visited[goal])
```
```
        {
```
```
            pathFound = true;
```
```
        }
```
```
        return pathFound;
```
```
    }
```
```
 
```

    public int  networkFlow (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))

```
        {
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            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++)

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            {
```

                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();
```
```
 
```

        NetworkFlowProb networkFlowProb = new NetworkFlowProb(numberOfNodes);

        maxFlow = networkFlowProb.networkFlow(graph, source, sink);

```
 
```

        System.out.println("The Max flow in the graph is " + maxFlow);

        System.out.println("The Minimum Cut Set in the Graph is ");

```
        networkFlowProb.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 NetworkFlowProb.java
$java NetworkFlowProb
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 in the graph is 23
The Minimum Cut Set in the Graph is 
2-4
5-6
5-4

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