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Depth First Search or DFS for a Graph

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Depth First Traversal (or DFS) for a graph is similar to Depth First Traversal of a tree. The only catch here is, that, unlike trees, graphs may contain cycles (a node may be visited twice). To avoid processing a node more than once, use a boolean visited array. A graph can have more than one DFS traversal.

Example: 

Input: n = 4, e = 6 
0 -> 1, 0 -> 2, 1 -> 2, 2 -> 0, 2 -> 3, 3 -> 3 
Output: DFS from vertex 1 : 1 2 0 3 
Explanation: 
DFS Diagram: 

Example 1

Example 1

Input: n = 4, e = 6 
2 -> 0, 0 -> 2, 1 -> 2, 0 -> 1, 3 -> 3, 1 -> 3 
Output: DFS from vertex 2 : 2 0 1 3 
Explanation: 
DFS Diagram: 

Example 2

Example 2

Recommended Practice

How does DFS work?

Depth-first search is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.

Let us understand the working of Depth First Search with the help of the following illustration:

Step1: Initially stack and visited arrays are empty.

Queue and visited arrays are empty initially.

Stack and visited arrays are empty initially.

Step 2: Visit 0 and put its adjacent nodes which are not visited yet into the stack.

 Visit node 0 and put its adjacent nodes (1, 2, 3) into the stack

 Visit node 0 and put its adjacent nodes (1, 2, 3) into the stack

Step 3: Now, Node 1 at the top of the stack, so visit node 1 and pop it from the stack and put all of its adjacent nodes which are not visited in the stack.

Visit node 1

 Visit node 1

Step 4: Now, Node 2 at the top of the stack, so visit node 2 and pop it from the stack and put all of its adjacent nodes which are not visited (i.e, 3, 4) in the stack.

 Visit node 2 and put its unvisited adjacent nodes (3, 4) into the stack

 Visit node 2 and put its unvisited adjacent nodes (3, 4) into the stack

Step 5: Now, Node 4 at the top of the stack, so visit node 4 and pop it from the stack and put all of its adjacent nodes which are not visited in the stack.

 Visit node 4

 Visit node 4

Step 6: Now, Node 3 at the top of the stack, so visit node 3 and pop it from the stack and put all of its adjacent nodes which are not visited in the stack.

Visit node 3

Visit node 3

Now, Stack becomes empty, which means we have visited all the nodes and our DFS traversal ends.

Below is the implementation of the above approach:

C++

// C++ program to print DFS traversal from
// a given vertex in a  given graph
#include <bits/stdc++.h>
using namespace std;
 
// Graph class represents a directed graph
// using adjacency list representation
class Graph {
public:
    map<int, bool> visited;
    map<int, list<int> > adj;
 
    // Function to add an edge to graph
    void addEdge(int v, int w);
 
    // DFS traversal of the vertices
    // reachable from v
    void DFS(int v);
};
 
void Graph::addEdge(int v, int w)
{
    // Add w to v’s list.
    adj[v].push_back(w);
}
 
void Graph::DFS(int v)
{
    // Mark the current node as visited and
    // print it
    visited[v] = true;
    cout << v << " ";
 
    // Recur for all the vertices adjacent
    // to this vertex
    list<int>::iterator i;
    for (i = adj[v].begin(); i != adj[v].end(); ++i)
        if (!visited[*i])
            DFS(*i);
}
 
// Driver code
int main()
{
    // Create a graph given in the above diagram
    Graph g;
    g.addEdge(0, 1);
    g.addEdge(0, 2);
    g.addEdge(1, 2);
    g.addEdge(2, 0);
    g.addEdge(2, 3);
    g.addEdge(3, 3);
 
    cout << "Following is Depth First Traversal"
            " (starting from vertex 2) \n";
 
    // Function call
    g.DFS(2);
 
    return 0;
}
 
// improved by Vishnudev C

                    

Java

// Java program to print DFS traversal
// from a given graph
import java.io.*;
import java.util.*;
 
// This class represents a
// directed graph using adjacency
// list representation
class Graph {
    private int V;
 
    // Array  of lists for
    // Adjacency List Representation
    private LinkedList<Integer> adj[];
 
    // Constructor
    @SuppressWarnings("unchecked") 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)
    {
        // Add w to v's list.
        adj[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 = adj[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);
    }
 
    // Driver Code
    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)");
 
        // Function call
        g.DFS(2);
    }
}
// This code is contributed by Aakash Hasija

                    

Python3

# Python3 program to print DFS traversal
# from a given  graph
from collections import defaultdict
 
 
# This class represents a directed graph using
# adjacency list representation
class Graph:
 
    # Constructor
    def __init__(self):
 
        # Default dictionary to store graph
        self.graph = defaultdict(list)
 
     
    # Function to add an edge to graph
    def addEdge(self, u, v):
        self.graph[u].append(v)
 
     
    # A function used by DFS
    def DFSUtil(self, v, visited):
 
        # Mark the current node as visited
        # and print it
        visited.add(v)
        print(v, end=' ')
 
        # Recur for all the vertices
        # adjacent to this vertex
        for neighbour in self.graph[v]:
            if neighbour not in visited:
                self.DFSUtil(neighbour, visited)
 
     
    # The function to do DFS traversal. It uses
    # recursive DFSUtil()
    def DFS(self, v):
 
        # Create a set to store visited vertices
        visited = set()
 
        # Call the recursive helper function
        # to print DFS traversal
        self.DFSUtil(v, visited)
 
 
# Driver's code
if __name__ == "__main__":
    g = Graph()
    g.addEdge(0, 1)
    g.addEdge(0, 2)
    g.addEdge(1, 2)
    g.addEdge(2, 0)
    g.addEdge(2, 3)
    g.addEdge(3, 3)
 
    print("Following is Depth First Traversal (starting from vertex 2)")
     
    # Function call
    g.DFS(2)
 
# This code is contributed by Neelam Yadav

                    

C#

// C# program to print DFS traversal
// from a given graph
using System;
using System.Collections.Generic;
 
// This class represents a directed graph
// using adjacency list representation
class Graph {
    private int V;
 
    // Array of lists for
    // Adjacency List Representation
    private List<int>[] adj;
 
    // Constructor
    Graph(int v)
    {
        V = v;
        adj = new List<int>[ v ];
        for (int i = 0; i < v; ++i)
            adj[i] = new List<int>();
    }
 
    // Function to Add an edge into the graph
    void AddEdge(int v, int w)
    {
        // Add w to v's list.
        adj[v].Add(w);
    }
 
    // A function used by DFS
    void DFSUtil(int v, bool[] visited)
    {
        // Mark the current node as visited
        // and print it
        visited[v] = true;
        Console.Write(v + " ");
 
        // Recur for all the vertices
        // adjacent to this vertex
        List<int> vList = adj[v];
        foreach(var n in vList)
        {
            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 c#)
        bool[] visited = new bool[V];
 
        // Call the recursive helper function
        // to print DFS traversal
        DFSUtil(v, visited);
    }
 
    // Driver Code
    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);
 
        Console.WriteLine(
            "Following is Depth First Traversal "
            + "(starting from vertex 2)");
 
        // Function call
        g.DFS(2);
        Console.ReadKey();
    }
}
 
// This code is contributed by techno2mahi

                    

Javascript

// Javascript program to print DFS
// traversal from a given
// graph
 
// This class represents a
// directed graph using adjacency
// list representation
class Graph
{
     
    // Constructor
    constructor(v)
    {
        this.V = v;
        this.adj = new Array(v);
        for(let i = 0; i < v; i++)
            this.adj[i] = [];
    }
     
    // Function to add an edge into the graph
    addEdge(v, w)
    {
         
        // Add w to v's list.
        this.adj[v].push(w);
    }
     
    // A function used by DFS
    DFSUtil(v, visited)
    {
         
        // Mark the current node as visited and print it
        visited[v] = true;
        console.log(v + " ");
  
        // Recur for all the vertices adjacent to this
        // vertex
        for(let i of this.adj[v].values())
        {
            let n = i
            if (!visited[n])
                this.DFSUtil(n, visited);
        }
    }
     
    // The function to do DFS traversal.
    // It uses recursive
    // DFSUtil()
    DFS(v)
    {
         
        // Mark all the vertices as
        // not visited(set as
        // false by default in java)
        let visited = new Array(this.V);
        for(let i = 0; i < this.V; i++)
            visited[i] = false;
  
        // Call the recursive helper
        // function to print DFS
        // traversal
        this.DFSUtil(v, visited);
    }
}
 
// Driver Code
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);
 
console.log("Following is Depth First Traversal " +
               "(starting from vertex 2)");
 
g.DFS(2);
 
// This code is contributed by avanitrachhadiya2155

                    

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

Complexity Analysis of Depth First Search:

  • Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
  • Auxiliary Space: O(V + E), since an extra visited array of size V is required, And stack size for iterative call to DFS function.


Last Updated : 16 Feb, 2024
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