DFS algorithm in Java

Traversal meaning visiting all the nodes of a given graph. Depth first Search is also know as Depth first traversal. DFS is a recursive algorithm for searching all the vertices of a graph or tree.

DFS algorithm
A standard DFS implementation puts each vertex of the graph into one of two categories:

1.Visited
2. Not Visited

The purpose of the algorithm is to mark each vertex as visited while avoiding cycles.

The DFS algorithm works as follows:

1. Start by putting any one of the graph's vertices on top of a stack.
2. Take the top item of the stack and add it to the visited list.
3. Create a list of that vertex's adjacent nodes. Add the ones which aren't in the visited list to the top of stack.
4. Keep repeating steps 2 and 3 until the stack is empty.

DFS example
Let's see how the Depth First Search algorithm works with an example. We use an undirected graph with 5 vertices.

We start from node 0, the DFS algorithm starts by putting it in the Visited list and putting all its adjacent nodes in the stack.

Next, we visit the element at the top of stack i.e. 1 and go to its adjacent nodes. Since 0 has already been visited, we visit 2 instead.

Node 2 has an unvisited adjacent node in 4, so we add that to the top of the stack and visit it.

After we visit the last element 3, it doesn't have any unvisited adjacent nodes, so we have completed the Depth First Traversal of the graph.

DFS pseudocode (recursive implementation)
The pseudocode for Depth first Search is shown below. In the init() function, notice that we run the DFS function on every node. This is because the graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the DFS algorithm on every node.

DFS(G, u)
    u.visited = true
    for each v ∈ G.Adj[u]
        if v.visited == false
            DFS(G,v)
     
init() {
    For each u ∈ G
        u.visited = false
     For each u ∈ G
       DFS(G, u)
}

DFS Java code

import java.io.*;
import java.util.*;
 
class Graph
{
    private int numVertices;
    private LinkedList adjLists[];
    private boolean visited[];
 
    Graph(int vertices)
    {
        numVertices = vertices;
        adjLists = new LinkedList[vertices];
        visited = new boolean[vertices];
        
        for (int i = 0; i < vertices; i++)
            adjLists[i] = new LinkedList();
    }
 
    void addEdge(int src, int dest)
    {
        adjLists[src].add(dest);
    }
 
    void DFS(int vertex)
    {
        visited[vertex] = true;
        System.out.print(vertex + " ");
 
        Iterator ite = adjLists[vertex].listIterator();
        while (ite.hasNext())
        {
            int adj = ite.next();
            if (!visited[adj])
                DFS(adj);
        }
    }
 
 
    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, 3);
 
        System.out.println("Following is Depth First Traversal");
 
        g.DFS(2);
    }
}