This Java code implements the Ford-Fulkerson algorithm to find the maximum flow and minimum cut set in a network flow problem. It takes a graph as input with a specified source and sink node, runs BFS to find augmenting paths, and calculates the residual graph after sending flow along each path to find the maximum flow. It then uses BFS again to separate the graph into reachable and unreachable nodes from the source to determine the minimum cut set.

1. EXP.2 A-
IMPLEMENTATION AND APPLICATION OF NETWORK FLOW
CODE:
import
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import
import
java.util.ArrayList;
java.util.HashSet;
java.util.Iterator;
java.util.LinkedList;
java.util.Queue;
java.util.Scanner;
java.util.Set;
public class NetworkFlowProb
{
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 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;
visited[vertex] = false;
}
queue.add(source);
parent[source] = -1;
visited[source] = true;
while (!queue.isEmpty())
{
element = queue.remove();

2. 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 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))
{
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])
{

3. 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);

4. 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()
{
}
}

5. OUTPUT: