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Implementation of DFS using adjacency matrix
• Difficulty Level : Medium
• Last Updated : 19 Aug, 2020

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 = 0 Output: 0 1 3 2

Input: source = 0 Output: 0 1 2 3 4
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// C++ implementation of the approach``#include ``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);``}`

## Python3

 `# 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`
Output:
```0 1 2 3 4
```

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