Implementation of DFS using adjacency matrix

Depth First Search (DFS) has been discussed in this article which uses adjacency list for the graph representation. In this article, adjacency matrix will be used to represent the graph.
Adjacency matrix representation: In adjacency matrix representation of a graph, the matrix mat[][] of size n*n (where n is the number of vertices) will represent the edges of the graph where mat[i][j] = 1 represents that there is an edge between the vertices i and j while mat[i][j] = 0 represents that there is no edge between the vertices i and j.
 

Below is the adjacency matrix representation of the graph shown in the above image: 
 

   0 1 2 3 4
0  0 1 1 1 1
1  1 0 0 0 0
2  1 0 0 0 0
3  1 0 0 0 0
4  1 0 0 0 0

Examples: 
 

Input: source = 0

Output: 0 1 3 2

Input: source = 0

Output: 0 1 2 3 4

Approach: 
 

• Create a matrix of size n*n where every element is 0 representing there is no edge in the graph.
• Now, for every edge of the graph between the vertices i and j set mat[i][j] = 1.
• After the adjacency matrix has been created and filled, call the recursive function for the source i.e. vertex 0 that will recursively call the same function for all the vertices adjacent to it.
• Also, keep an array to keep track of the visited vertices i.e. visited[i] = true represents that vertex i has been visited before and the DFS function for some already visited node need not be called.

Below is the implementation of the above approach: 
 

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// adjacency matrix
vector<vector<int> > adj;

// function to add edge to the graph
void addEdge(int x, int y)
{
    adj[x][y] = 1;
    adj[y][x] = 1;
}

// function to perform DFS on the graph
void dfs(int start, vector<bool>& visited)
{

    // Print the current node
    cout << start << " ";

    // Set current node as visited
    visited[start] = true;

    // For every node of the graph
    for (int i = 0; i < adj[start].size(); i++) {

        // If some node is adjacent to the current node
        // and it has not already been visited
        if (adj[start][i] == 1 && (!visited[i])) {
            dfs(i, visited);
        }
    }
}

int main()
{
    // number of vertices
    int v = 5;

    // number of edges
    int e = 4;

    // adjacency matrix
    adj = vector<vector<int> >(v, vector<int>(v, 0));

    addEdge(0, 1);
    addEdge(0, 2);
    addEdge(0, 3);
    addEdge(0, 4);

    // Visited vector to so that
    // a vertex is not visited more than once
    // Initializing the vector to false as no
    // vertex is visited at the beginning
    vector<bool> visited(v, false);

    // Perform DFS
    dfs(0, visited);
}

// Java implementation of the approach
import java.io.*;

class GFG {
    // adjacency matrix
    static int[][] adj;

    // function to add edge to the graph
    static void addEdge(int x, int y)
    {
        adj[x][y] = 1;
        adj[y][x] = 1;
    }

    // function to perform DFS on the graph
    static void dfs(int start, boolean[] visited)
    {

        // Print the current node
        System.out.print(start + " ");

        // Set current node as visited
        visited[start] = true;

        // For every node of the graph
        for (int i = 0; i < adj[start].length; i++) {

            // If some node is adjacent to the current node
            // and it has not already been visited
            if (adj[start][i] == 1 && (!visited[i])) {
                dfs(i, visited);
            }
        }
    }

    public static void main(String[] args)
    {
        // number of vertices
        int v = 5;

        // number of edges
        int e = 4;

        // adjacency matrix
        adj = new int[v][v];

        addEdge(0, 1);
        addEdge(0, 2);
        addEdge(0, 3);
        addEdge(0, 4);

        // Visited vector to so that
        // a vertex is not visited more than once
        // Initializing the vector to false as no
        // vertex is visited at the beginning
        boolean[] visited = new boolean[v];

        // Perform DFS
        dfs(0, visited);
    }
}

// This code is contributed by kdeepsingh2002

# Python3 implementation of the approach 
class Graph:
    
    adj = []

    # Function to fill empty adjacency matrix
    def __init__(self, v, e):
        
        self.v = v
        self.e = e
        Graph.adj = [[0 for i in range(v)] 
                        for j in range(v)]

    # Function to add an edge to the graph
    def addEdge(self, start, e):
        
        # Considering a bidirectional edge
        Graph.adj[start][e] = 1
        Graph.adj[e][start] = 1

    # Function to perform DFS on the graph
    def DFS(self, start, visited):
        
        # Print current node
        print(start, end = ' ')

        # Set current node as visited
        visited[start] = True

        # For every node of the graph
        for i in range(self.v):
            
            # If some node is adjacent to the 
            # current node and it has not 
            # already been visited
            if (Graph.adj[start][i] == 1 and
                    (not visited[i])):
                self.DFS(i, visited)

# Driver code
v, e = 5, 4

# Create the graph
G = Graph(v, e)
G.addEdge(0, 1)
G.addEdge(0, 2)
G.addEdge(0, 3)
G.addEdge(0, 4)

# Visited vector to so that a vertex
# is not visited more than once
# Initializing the vector to false as no
# vertex is visited at the beginning
visited = [False] * v

# Perform DFS
G.DFS(0, visited);

# This code is contributed by ng24_7

using System;
using System.Collections.Generic;

class GFG {
    // adjacency matrix
    static List<List<int>> adj;

    // function to add edge to the graph
    static void addEdge(int x, int y)
    {
        adj[x][y] = 1;
        adj[y][x] = 1;
    }

    // function to perform DFS on the graph
    static void dfs(int start, List<bool> visited)
    {
        // Print the current node
        Console.Write(start + " ");

        // Set current node as visited
        visited[start] = true;

        // For every node of the graph
        for (int i = 0; i < adj[start].Count; i++)
        {
            // If some node is adjacent to the current node
            // and it has not already been visited
            if (adj[start][i] == 1 && (!visited[i]))
            {
                dfs(i, visited);
            }
        }
    }

    static void Main(string[] args) {
        // number of vertices
        int v = 5;

        // number of edges
        int e = 4;

        // adjacency matrix
        adj = new List<List<int>>(v);
        for (int i = 0; i < v; i++)
        {
            adj.Add(new List<int>(v));
            for (int j = 0; j < v; j++)
            {
                adj[i].Add(0);
            }
        }

        addEdge(0, 1);
        addEdge(0, 2);
        addEdge(0, 3);
        addEdge(0, 4);

        // Visited vector to so that
        // a vertex is not visited more than once
        // Initializing the vector to false as no
        // vertex is visited at the beginning
        List<bool> visited = new List<bool>(v);
        for (int i = 0; i < v; i++)
        {
            visited.Add(false);
        }

        // Perform DFS
        dfs(0, visited);
    }
}

// This code is contributed by Prince Kumar

let ans=""; // JavaScript implementation of the Graph class
class Graph {
  constructor(v, e) {
    this.v = v;  // number of vertices
    this.e = e;  // number of edges

    // initialize the adjacency matrix with 0s
    this.adj = Array.from(Array(v), () => new Array(v).fill(0));
  }

  // function to add an edge to the graph
  addEdge(start, end) {
    // considering a bidirectional edge
    this.adj[start][end] = 1;
    this.adj[end][start] = 1;
  }

  // function to perform DFS on the graph
  DFS(start, visited) {
    // print the current node
    ans = ans +start + " ";

    // set current node as visited
    visited[start] = true;

    // for every node of the graph
    for (let i = 0; i < this.v; i++) {
      // if some node is adjacent to the current node
      // and it has not already been visited
      if (this.adj[start][i] === 1 && !visited[i]) {
        this.DFS(i, visited);
      }
    }
  }
}

// driver code
const v = 5;  // number of vertices
const e = 4;  // number of edges

// create the graph
const G = new Graph(v, e);
G.addEdge(0, 1);
G.addEdge(0, 2);
G.addEdge(0, 3);
G.addEdge(0, 4);

// visited array to ensure that a vertex is not visited more than once
// initializing the array to false as no vertex is visited at the beginning
const visited = new Array(v).fill(false);

// perform DFS
G.DFS(0, visited); console.log(ans);

0 1 2 3 4

The time complexity of the above implementation of DFS on an adjacency matrix is O(V^2), where V is the number of vertices in the graph. This is because for each vertex, we need to iterate through all the other vertices to check if they are adjacent or not.

The space complexity of this implementation is also O(V^2) because we are using an adjacency matrix to represent the graph, which requires V^2 space.