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.

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package com.sanfoundry.graph;
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import java.util.InputMismatchException;

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import java.util.Scanner;
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import java.util.Stack;
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public class DigraphTopologicalSortingDFS

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{
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    private Stack<Integer> stack;
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    public DigraphTopologicalSortingDFS()

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    {
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        stack = new Stack<Integer>();
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    }
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    public int[] topological(int adjacency_matrix[][], int source)

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            throws NullPointerException
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    {
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        int number_of_nodes = adjacency_matrix[source].length - 1;

        int[] topological_sort = new int[number_of_nodes + 1];

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        int pos = 1;
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        int j;
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        int visited[] = new int[number_of_nodes + 1];

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        int element = source;
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        int i = source;
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        visited[source] = 1;
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        stack.push(source);
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        while (!stack.isEmpty())
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        {
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            element = stack.peek();
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            while (i <= number_of_nodes)

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            {
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                if (adjacency_matrix[element][i] == 1 && visited[i] == 1)

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                {
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                    if (stack.contains(i))

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                    {
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                        System.out.println("TOPOLOGICAL SORT NOT POSSIBLE");

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                        return null;
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                    }
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                }
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                if (adjacency_matrix[element][i] == 1 && visited[i] == 0)

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                {
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                    stack.push(i);
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                    visited[i] = 1;
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                    element = i;
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                    i = 1;
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                    continue;
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                }
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                i++;
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            }
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            j = stack.pop();
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            topological_sort[pos++] = j;

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            i = ++j;
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        }
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        return topological_sort;
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    }
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    public static void main(String... arg)

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    {
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        int number_no_nodes, source;
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        Scanner scanner = null;
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        int topological_sort[] = null;
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        try
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        {
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            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");

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            source = scanner.nextInt();
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            System.out
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                    .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--)

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            {
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                if (topological_sort[i] != 0)

                    System.out.print(topological_sort[i] + "\t");

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            }
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        }
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        catch (InputMismatchException inputMismatch)

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        {
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            System.out.println("Wrong Input format");

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        }
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        catch (NullPointerException nullPointer)

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        {
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        }
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        scanner.close();
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    }
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}
```

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

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