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
Related posts:
How to Add a Single Element to a Stream
Spring Boot - Unit Test Cases
Giới thiệu Swagger – Công cụ document cho RESTfull APIs
Automatic Property Expansion with Spring Boot
Java Program to Implement Randomized Binary Search Tree
New Features in Java 12
Java Program to Implement Fisher-Yates Algorithm for Array Shuffling
Java Program to Implement Bresenham Line Algorithm
Java Program to Compute Discrete Fourier Transform Using the Fast Fourier Transform Approach
Spring 5 WebClient
Java 8 – Powerful Comparison with Lambdas
A Quick Guide to Spring MVC Matrix Variables
Mảng (Array) trong Java
Encode/Decode to/from Base64
Java Program to Implement Ternary Heap
Java Program to Find a Good Feedback Edge Set in a Graph
Multipart Upload with HttpClient 4
Database Migrations with Flyway
Java Program to Generate Randomized Sequence of Given Range of Numbers
Introduction to Spring Cloud CLI
Tìm hiểu về Web Service
Convert char to String in Java
Java Program to Implement the One Time Pad Algorithm
Java Program to Describe the Representation of Graph using Incidence List
Java Program to Create a Random Linear Extension for a DAG
Java Program to Check Whether Graph is DAG
Spring Boot - Batch Service
Java Program to Implement Brent Cycle Algorithm
Object Type Casting in Java
Semaphore trong Java
Java Program to Implement Singly Linked List
Guide to PriorityBlockingQueue in Java