# Implementation of BFS using adjacency matrix

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 3

Input: source = 1 Output:1 0 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, find the BFS traversal of the graph as desribed in this post.

Below is the implementation of the above approach:

 `// 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 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; ` ` `  `        ``// 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); ` `} `

Output:

```0 1 2 3
```

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Improved By : prat31