programming-examples/java/Graph_Problems_Algorithms/Java Program to Implement Find all Back Edges in a Graph.java

/*This Java program,performs the DFS traversal on the given graph represented by a adjacency matrix to find all the back edges in a graph.the DFS traversal makes use of an stack.*/

import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;

public class BackEdges
{
    private Stack<Integer> stack;
    private HashMap<Integer, Integer> backEdges;
    private int adjacencyMatrix[][];

    public BackEdges()
    {
        stack = new Stack<Integer>();
        backEdges = new HashMap<Integer, Integer>();
    }

    public void dfs(int adjacency_matrix[][], int source)
    {
        int number_of_nodes = adjacency_matrix[source].length - 1;
        adjacencyMatrix = new int[number_of_nodes + 1][number_of_nodes + 1];
        for (int sourcevertex = 1; sourcevertex <= number_of_nodes; sourcevertex++)
            {
                for (int destinationvertex = 1; destinationvertex <= number_of_nodes; destinationvertex++)
                    {
                        adjacencyMatrix[sourcevertex][destinationvertex] =
                            adjacency_matrix[sourcevertex][destinationvertex];
                    }
            }
        int visited[] = new int[number_of_nodes + 1];
        int element = source;
        int destination = source;
        visited[source] = 1;
        stack.push(source);
        while (!stack.isEmpty())
            {
                element = stack.peek();
                destination = element;
                while (destination <= number_of_nodes)
                    {
                        if (adjacencyMatrix[element][destination] == 1 && visited[destination] == 1)
                            {
                                if (stack.contains(destination))
                                    {
                                        backEdges.put(element, destination);
                                        adjacencyMatrix[element][destination]= 0;
                                    }
                            }
                        if (adjacencyMatrix[element][destination] == 1 && visited[destination] == 0)
                            {
                                stack.push(destination);
                                visited[destination] = 1;
                                adjacencyMatrix[element][destination] = 0;
                                element = destination;
                                destination = 1;
                                continue;
                            }
                        destination++;
                    }
                stack.pop();
            }
    }

    public void printBackEdges()
    {
        System.out.println("\nSOURCE  : DESTINATION");
        Set<Integer> source = backEdges.keySet();
        for (Integer sourcevertex : source)
            {
                System.out.println(sourcevertex + "\t:\t"+ backEdges.get(sourcevertex));
            }
    }

    public static void main(String...arg)
    {
        int number_of_nodes, source;
        Scanner scanner = null;
        try
            {
                System.out.println("Enter the number of nodes in the graph");
                scanner = new Scanner(System.in);
                number_of_nodes = scanner.nextInt();
                int adjacency_matrix[][] = new int[number_of_nodes + 1][number_of_nodes + 1];
                System.out.println("Enter the adjacency matrix");
                for (int i = 1; i <= number_of_nodes; i++)
                    for (int j = 1; j <= number_of_nodes; j++)
                        adjacency_matrix[i][j] = scanner.nextInt();
                System.out.println("Enter the source for the graph");
                source = scanner.nextInt();
                BackEdges backEdges = new BackEdges();
                backEdges.dfs(adjacency_matrix, source);
                backEdges.printBackEdges();
            }
        catch(InputMismatchException inputMismatch)
            {
                System.out.println("Wrong Input format");
            }
        scanner.close();
    }
}

/*
Enter the number of nodes in the graph
4
Enter the adjacency matrix
0 1 0 0
0 0 1 0
0 0 0 1
0 1 0 0
Enter the source for the graph
1
The Back Edges are given by

SOURCE  : DESTINATION
4	:	2