Topological Sort


// A Java program to print topological sorting of a DAG
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

    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 =;
            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");


Following is a Topological sort of the given graph
5 4 2 3 1 0

Time Complexity: O(V+E)
Space Complexity: O(V)
V for vertex E for edge

code courtesy:

I understood the theory but need to understand the code well later

It would be a great help, if you support by sharing :)
Author: zakilive

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