# Implementation of BFS using adjacency matrix

Breadth First Search (BFS) 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 0 0 1 1 0 1 1 0 0 1 2 1 0 0 0 3 0 1 0 0

**Examples:**

Input:source = 0

Output:0 1 2 3Input:source = 1

Output:1 0 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, find the BFS traversal of the graph as described in this post.

Below is the implementation of the above approach:

## C++

`// 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 BFS traversal` ` ` `void` `BFS(` `int` `start);` `};` `// 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 BFS on the graph` `void` `Graph::BFS(` `int` `start)` `{` ` ` `// 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` `);` ` ` `vector<` `int` `> q;` ` ` `q.push_back(start);` ` ` `// Set source as visited` ` ` `visited[start] = ` `true` `;` ` ` `int` `vis;` ` ` `while` `(!q.empty()) {` ` ` `vis = q[0];` ` ` `// Print the current node` ` ` `cout << vis << ` `" "` `;` ` ` `q.erase(q.begin());` ` ` `// For every adjacent vertex to the current vertex` ` ` `for` `(` `int` `i = 0; i < v; i++) {` ` ` `if` `(adj[vis][i] == 1 && (!visited[i])) {` ` ` `// Push the adjacent node to the queue` ` ` `q.push_back(i);` ` ` `// Set` ` ` `visited[i] = ` `true` `;` ` ` `}` ` ` `}` ` ` `}` `}` `// 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(1, 3);` ` ` `G.BFS(0);` `}` |

## Java

`// Java implementation of the approach` `import` `java.util.ArrayList;` `import` `java.util.Arrays;` `import` `java.util.List;` `class` `GFG{` `static` `class` `Graph` `{` ` ` ` ` `// Number of vertex` ` ` `int` `v;` ` ` `// Number of edges` ` ` `int` `e;` ` ` `// Adjacency matrix` ` ` `int` `[][] adj;` ` ` `// Function to fill the empty` ` ` `// adjacency matrix` ` ` `Graph(` `int` `v, ` `int` `e)` ` ` `{` ` ` `this` `.v = v;` ` ` `this` `.e = e;` ` ` ` ` `adj = ` `new` `int` `[v][v];` ` ` `for` `(` `int` `row = ` `0` `; row < v; row++)` ` ` `Arrays.fill(adj[row], ` `0` `);` ` ` `}` ` ` ` ` `// Function to add an edge to the graph` ` ` `void` `addEdge(` `int` `start, ` `int` `e)` ` ` `{` ` ` ` ` `// Considering a bidirectional edge` ` ` `adj[start][e] = ` `1` `;` ` ` `adj[e][start] = ` `1` `;` ` ` `}` ` ` `// Function to perform BFS on the graph` ` ` `void` `BFS(` `int` `start)` ` ` `{` ` ` ` ` `// 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];` ` ` `Arrays.fill(visited, ` `false` `);` ` ` `List<Integer> q = ` `new` `ArrayList<>();` ` ` `q.add(start);` ` ` `// Set source as visited` ` ` `visited[start] = ` `true` `;` ` ` `int` `vis;` ` ` `while` `(!q.isEmpty())` ` ` `{` ` ` `vis = q.get(` `0` `);` ` ` `// Print the current node` ` ` `System.out.print(vis + ` `" "` `);` ` ` `q.remove(q.get(` `0` `));` ` ` `// For every adjacent vertex to` ` ` `// the current vertex` ` ` `for` `(` `int` `i = ` `0` `; i < v; i++)` ` ` `{` ` ` `if` `(adj[vis][i] == ` `1` `&& (!visited[i]))` ` ` `{` ` ` ` ` `// Push the adjacent node to` ` ` `// the queue` ` ` `q.add(i);` ` ` `// Set` ` ` `visited[i] = ` `true` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `}` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `int` `v = ` `5` `, e = ` `4` `;` ` ` `// Create the graph` ` ` `Graph G = ` `new` `Graph(v, e);` ` ` `G.addEdge(` `0` `, ` `1` `);` ` ` `G.addEdge(` `0` `, ` `2` `);` ` ` `G.addEdge(` `1` `, ` `3` `);` ` ` `G.BFS(` `0` `);` `}` `}` `// This code is contributed by sanjeev2552` |

## 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` `BFS(` `self` `, start):` ` ` ` ` `# 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` `] ` `*` `self` `.v` ` ` `q ` `=` `[start]` ` ` `# Set source as visited` ` ` `visited[start] ` `=` `True` ` ` `while` `q:` ` ` `vis ` `=` `q[` `0` `]` ` ` `# Print current node` ` ` `print` `(vis, end ` `=` `' '` `)` ` ` `q.pop(` `0` `)` ` ` ` ` `# For every adjacent vertex to` ` ` `# the current vertex` ` ` `for` `i ` `in` `range` `(` `self` `.v):` ` ` `if` `(Graph.adj[vis][i] ` `=` `=` `1` `and` ` ` `(` `not` `visited[i])):` ` ` ` ` `# Push the adjacent node` ` ` `# in the queue` ` ` `q.append(i)` ` ` ` ` `# set` ` ` `visited[i] ` `=` `True` `# Driver code` `v, e ` `=` `5` `, ` `4` `# Create the graph` `G ` `=` `Graph(v, e)` `G.addEdge(` `0` `, ` `1` `)` `G.addEdge(` `0` `, ` `2` `)` `G.addEdge(` `1` `, ` `3` `)` `# Perform BFS` `G.BFS(` `0` `)` `# This code is contributed by ng24_7` |

**Output:**

0 1 2 3

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