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][i] = 0 represents that there is no edge between the vertices i and j.


Below is the adjcaency 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

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:

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// 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);
}

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Output:

0 1 2 3


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