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

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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.

  1.  
  2. package com.sanfoundry.graph;
  3.  
  4. import java.util.InputMismatchException;
  5. import java.util.Scanner;
  6. import java.util.Stack;
  7.  
  8. public class DigraphTopologicalSortingDFS
  9. {
  10.     private Stack<Integer> stack;
  11.  
  12.     public DigraphTopologicalSortingDFS()
  13.     {
  14.         stack = new Stack<Integer>();
  15.     }
  16.  
  17.     public int[] topological(int adjacency_matrix[][], int source)
  18.             throws NullPointerException
  19.     {
  20.         int number_of_nodes = adjacency_matrix[source].length - 1;
  21.         int[] topological_sort = new int[number_of_nodes + 1];
  22.         int pos = 1;
  23.         int j;
  24.         int visited[] = new int[number_of_nodes + 1];
  25.         int element = source;
  26.         int i = source;
  27.         visited[source] = 1;
  28.         stack.push(source);
  29.         while (!stack.isEmpty())
  30.         {
  31.             element = stack.peek();
  32.             while (i <= number_of_nodes)
  33.             {
  34.                 if (adjacency_matrix[element][i] == 1 && visited[i] == 1)
  35.                 {
  36.                     if (stack.contains(i))
  37.                     {
  38.                         System.out.println("TOPOLOGICAL SORT NOT POSSIBLE");
  39.                         return null;
  40.                     }
  41.                 }
  42.                 if (adjacency_matrix[element][i] == 1 && visited[i] == 0)
  43.                 {
  44.                     stack.push(i);
  45.                     visited[i] = 1;
  46.                     element = i;
  47.                     i = 1;
  48.                     continue;
  49.                 }
  50.                 i++;
  51.             }
  52.             j = stack.pop();
  53.             topological_sort[pos++] = j;
  54.             i = ++j;
  55.         }
  56.         return topological_sort;
  57.     }
  58.  
  59.     public static void main(String... arg)
  60.     {
  61.         int number_no_nodes, source;
  62.         Scanner scanner = null;
  63.         int topological_sort[] = null;
  64.         try
  65.         {
  66.             System.out.println("Enter the number of nodes in the graph");
  67.             scanner = new Scanner(System.in);
  68.             number_no_nodes = scanner.nextInt();
  69.             int adjacency_matrix[][] = new int[number_no_nodes + 1][number_no_nodes + 1];
  70.             System.out.println("Enter the adjacency matrix");
  71.             for (int i = 1; i <= number_no_nodes; i++)
  72.                 for (int j = 1; j <= number_no_nodes; j++)
  73.                     adjacency_matrix[i][j] = scanner.nextInt();
  74.             System.out.println("Enter the source for the graph");
  75.             source = scanner.nextInt();
  76.             System.out
  77.                     .println("The Topological sort for the graph is given by ");
  78.             DigraphTopologicalSortingDFS toposort = new DigraphTopologicalSortingDFS();
  79.             topological_sort = toposort.topological(adjacency_matrix, source);
  80.             for (int i = topological_sort.length - 1; i > 0; i--)
  81.             {
  82.                 if (topological_sort[i] != 0)
  83.                     System.out.print(topological_sort[i] + "\t");
  84.             }
  85.         }
  86.         catch (InputMismatchException inputMismatch)
  87.         {
  88.             System.out.println("Wrong Input format");
  89.         }
  90.         catch (NullPointerException nullPointer)
  91.         {
  92.         }
  93.         scanner.close();
  94.     }
  95. }

Output:

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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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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter