Depth First Search Algorithm(DFS) Example Java

Depth First Search algorithm(DFS) traverses a graph in a depth ward motion and uses a stack to remember to get the next vertex to start a search when a dead end occurs in any iteration.

The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again. To avoid processing a node more than once, we use a boolean visited array.
For example, in the following graph, we start traversal from vertex 2. When we come to vertex 0, we look for all adjacent vertices of it. 2 is also an adjacent vertex of 0. If we don’t mark visited vertices, then 2 will be processed again and it will become a non-terminating process. A Depth First Traversal of the following graph is 2, 0, 1, 3.

As in example given above, DFS algorithm traverses from A to B to C to D first then to E, then to F and lastly to G.

It employs following rules.

Rule 1 − Visit adjacent unvisited vertex. Mark it visited. Display it. Push it in a stack.

Rule 2 − If no adjacent vertex found, pop up a vertex from stack. (It will pop up all the vertices from the stack which do not have adjacent vertices.)

Rule 3 − Repeat Rule 1 and Rule 2 until stack is empty.

As C does not have any unvisited adjacent node so we keep popping the stack until we find a node which has unvisited adjacent node. In this case, there's none and we keep popping until stack is empty.

DFS Implementation:

import java.util.Iterator;
import java.util.LinkedList;

/**
 *
 */

/**
 * @author Abhinaw.Tripathi
 *
 */
public class Graph
{
private int V;
private LinkedList<Integer> adjacentList[];

Graph(int v)
    {
        V = v;
        adjacentList = new LinkedList[v];
        for (int i=0; i<v; ++i)
        adjacentList[i] = new LinkedList();
    }

// Function to add an edge into the graph
    void addEdge(int v,int w)
    {
    adjacentList[v].add(w);
    }


 // A function used by DFS
    void DFSUtil(int v,boolean visited[])
    {
        // Mark the current node as visited and print it
        visited[v] = true;
        System.out.print(v+" ");

        // Recur for all the vertices adjacent to this vertex
        Iterator<Integer> i = adjacentList[v].listIterator();
        while (i.hasNext())
        {
            int n = i.next();
            if (!visited[n])
                DFSUtil(n, visited);
        }
    }

    // The function to do DFS traversal. It uses recursive DFSUtil()
    void DFS(int v)
    {
        // Mark all the vertices as not visited(set as
        // false by default in java)
        boolean visited[] = new boolean[V];

        // Call the recursive helper function to print DFS traversal
        DFSUtil(v, visited);
    }

public static void main(String[] args)
{

Graph g = new Graph(4);

        g.addEdge(0, 1);
        g.addEdge(0, 2);
        g.addEdge(1, 2);
        g.addEdge(2, 0);
        g.addEdge(2, 3);
        g.addEdge(3, 3);

        System.out.println("Following is Depth First Traversal "+
                           "(starting from vertex 2)");

        g.DFS(2);
}

}

Result: 

Following is Depth First Traversal (starting from vertex 2)
2 0 1 3

Note that the above code traverses only the vertices reachable from a given source vertex. All the vertices may not be reachable from a given vertex (example Disconnected graph). To do complete DFS traversal of such graphs, we must call DFSUtil() for every vertex. Also, before calling DFSUtil(), we should check if it is already printed by some other call of DFSUtil().