# 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][i] = 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 = 0Output:0 1 3 2Input:source = 0Output: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 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; ` ` ` `class` `Graph { ` ` ` ` ` `// Number of vertex ` ` ` `int` `v; ` ` ` ` ` `// Number of edges ` ` ` `int` `e; ` ` ` ` ` `// Adjacency matrix ` ` ` `int` `** adj; ` ` ` `public` `: ` ` ` `// To create the initial adjacency matrix ` ` ` `Graph(` `int` `v, ` `int` `e); ` ` ` ` ` `// Function to insert a new edge ` ` ` `void` `addEdge(` `int` `start, ` `int` `e); ` ` ` ` ` `// Function to display the DFS traversal ` ` ` `void` `DFS(` `int` `start, vector<` `bool` `>& visited); ` `}; ` ` ` `// Function to fill the empty adjacency matrix ` `Graph::Graph(` `int` `v, ` `int` `e) ` `{ ` ` ` `this` `->v = v; ` ` ` `this` `->e = e; ` ` ` `adj = ` `new` `int` `*[v]; ` ` ` `for` `(` `int` `row = 0; row < v; row++) { ` ` ` `adj[row] = ` `new` `int` `[v]; ` ` ` `for` `(` `int` `column = 0; column < v; column++) { ` ` ` `adj[row][column] = 0; ` ` ` `} ` ` ` `} ` `} ` ` ` `// Function to add an edge to the graph ` `void` `Graph::addEdge(` `int` `start, ` `int` `e) ` `{ ` ` ` ` ` `// Considering a bidirectional edge ` ` ` `adj[start][e] = 1; ` ` ` `adj[e][start] = 1; ` `} ` ` ` `// Function to perform DFS on the graph ` `void` `Graph::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 < v; 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); ` ` ` `} ` ` ` `} ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `v = 5, e = 4; ` ` ` ` ` `// Create the graph ` ` ` `Graph G(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 ` ` ` `vector<` `bool` `> visited(v, ` `false` `); ` ` ` ` ` `// Perform DFS ` ` ` `G.DFS(0, visited); ` `} ` |

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**Output:**

0 1 2 3 4

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