Java Program to Apply DFS to Perform the Topological Sorting of a Directed Acyclic Graph

This is a java program to find topological sort of DAG. In computer science, a topological sort (sometimes abbreviated topsort or toposort) or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time.

Here is the source code of the Java Program to Apply DFS to Perform the Topological Sorting of a Directed Acyclic Graph. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

package com.sanfoundry.graph;
 
import java.util.InputMismatchException;
import java.util.Scanner;
import java.util.Stack;
 
public class DigraphTopologicalSortingDFS
{
    private Stack<Integer> stack;
 
    public DigraphTopologicalSortingDFS()
    {
        stack = new Stack<Integer>();
    }
 
    public int[] topological(int adjacency_matrix[][], int source)
            throws NullPointerException
    {
        int number_of_nodes = adjacency_matrix.length - 1;
        int[] topological_sort = new int[number_of_nodes + 1];
        int pos = 1;
        int j;
        int visited[] = new int[number_of_nodes + 1];
        int element = source;
        int i = source;
        visited = 1;
        stack.push(source);
        while (!stack.isEmpty())
        {
            element = stack.peek();
            while (i <= number_of_nodes)
            {
                if (adjacency_matrix[element][i] == 1 && visited[i] == 1)
                {
                    if (stack.contains(i))
                    {
                        System.out.println("TOPOLOGICAL SORT NOT POSSIBLE");
                        return null;
                    }
                }
                if (adjacency_matrix[element][i] == 1 && visited[i] == 0)
                {
                    stack.push(i);
                    visited[i] = 1;
                    element = i;
                    i = 1;
                    continue;
                }
                i++;
            }
            j = stack.pop();
            topological_sort[pos++] = j;
            i = ++j;
        }
        return topological_sort;
    }
 
    public static void main(String... arg)
    {
        int number_no_nodes, source;
        Scanner scanner = null;
        int topological_sort[] = null;
        try
        {
            System.out.println("Enter the number of nodes in the graph");
            scanner = new Scanner(System.in);
            number_no_nodes = scanner.nextInt();
            int adjacency_matrix[][] = new int[number_no_nodes + 1][number_no_nodes + 1];
            System.out.println("Enter the adjacency matrix");
            for (int i = 1; i <= number_no_nodes; i++)
                for (int j = 1; j <= number_no_nodes; j++)
                    adjacency_matrix[i][j] = scanner.nextInt();
            System.out.println("Enter the source for the graph");
            source = scanner.nextInt();
            System.out
                    .println("The Topological sort for the graph is given by ");
            DigraphTopologicalSortingDFS toposort = new DigraphTopologicalSortingDFS();
            topological_sort = toposort.topological(adjacency_matrix, source);
            for (int i = topological_sort.length - 1; i > 0; i--)
            {
                if (topological_sort[i] != 0)
                    System.out.print(topological_sort[i] + "\t");
            }
        }
        catch (InputMismatchException inputMismatch)
        {
            System.out.println("Wrong Input format");
        }
        catch (NullPointerException nullPointer)
        {
        }
        scanner.close();
    }
}

Output:

Enter the number of nodes in the graph
6
Enter the adjacency matrix
0 1 0 0 0 0
0 0 1 1 0 0 
0 0 0 0 0 0 
0 0 0 0 1 0
0 0 0 0 0 1
0 0 1 1 0 0 
Enter the source for the graph
1
The Topological sort for the graph is given by 
TOPOLOGICAL SORT NOT POSSIBLE
 
Enter the number of nodes in the graph
6
Enter the adjacency matrix
0 1 0 0 0 1
0 0 1 1 0 0
0 0 0 0 0 0 
0 0 0 0 1 0
0 0 0 0 0 1
0 0 1 0 0 0
Enter the source for the graph
1
The Topological sort for the graph is given by 
1	2	4	5	6	3