Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG.
For example, a topological sorting of the following graph is “5 4 2 3 1 0”. There can be more than one topological sorting for a graph. For example, another topological sorting of the following graph is “4 5 2 3 1 0”. The first vertex in topological sorting is always a vertex with in-degree as 0 (a vertex with no in-coming edges).
// A Java program to print topological sorting of a DAG import java.io.*;
import java.util.*;
// This class represents a directed graph using adjacency // list representation class Graph
{ private int V; // No. of vertices
private LinkedList<Integer> adj[]; // Adjacency List
//Constructor
Graph( int v)
{
V = v;
adj = new LinkedList[v];
for ( int i= 0 ; i<v; ++i)
adj[i] = new LinkedList();
}
// Function to add an edge into the graph
void addEdge( int v, int w) { adj[v].add(w); }
// A recursive function used by topologicalSort
void topologicalSortUtil( int v, boolean visited[],
Stack stack)
{
// Mark the current node as visited.
visited[v] = true ;
Integer i;
// Recur for all the vertices adjacent to this
// vertex
Iterator<Integer> it = adj[v].iterator();
while (it.hasNext())
{
i = it.next();
if (!visited[i])
topologicalSortUtil(i, visited, stack);
}
// Push current vertex to stack which stores result
stack.push( new Integer(v));
}
// The function to do Topological Sort. It uses
// recursive topologicalSortUtil()
void topologicalSort()
{
Stack stack = new Stack();
// Mark all the vertices as not visited
boolean visited[] = new boolean [V];
for ( int i = 0 ; i < V; i++)
visited[i] = false ;
// Call the recursive helper function to store
// Topological Sort starting from all vertices
// one by one
for ( int i = 0 ; i < V; i++)
if (visited[i] == false )
topologicalSortUtil(i, visited, stack);
// Print contents of stack
while (stack.empty()== false )
System.out.print(stack.pop() + " " );
}
// Driver method
public static void main(String args[])
{
// Create a graph given in the above diagram
Graph g = new Graph( 6 );
g.addEdge( 5 , 2 );
g.addEdge( 5 , 0 );
g.addEdge( 4 , 0 );
g.addEdge( 4 , 1 );
g.addEdge( 2 , 3 );
g.addEdge( 3 , 1 );
System.out.println( "Following is a Topological " +
"sort of the given graph" );
g.topologicalSort();
}
} // This code is contributed by Aakash Hasija |
Output:
Following is a Topological Sort of the given graph 5 4 2 3 1 0
Please refer complete article on Topological Sorting for more details!