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 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 described in this post.
Below is the implementation of the above approach:
// C++ implementation of the approach #include<bits/stdc++.h> using namespace std;
vector<vector< int >> adj;
// function to add edge to the graph void addEdge( int x, int y)
{ adj[x][y] = 1;
adj[y][x] = 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
vector< bool > visited(adj.size(), 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 < adj[vis].size(); 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()
{ // number of vertices
int v = 5;
// adjacency matrix
adj= vector<vector< int >>(v,vector< int >(v,0));
addEdge(0,1);
addEdge(0,2);
addEdge(1,3);
// perform bfs on the graph
bfs(0);
} |
// 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 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 |
// C# implementation of the approach using System;
using System.Collections.Generic;
public class GFG{
class Graph
{
// Number of vertex
public int v;
// Number of edges
public int e;
// Adjacency matrix
public int [,] adj;
// Function to fill the empty
// adjacency matrix
public Graph( int v, int e)
{
this .v = v;
this .e = e;
adj = new int [v,v];
for ( int row = 0; row < v; row++)
for ( int col = 0; col < v; col++)
adj[row, col] = 0;
}
// Function to add an edge to the graph
public 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
public 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
bool [] visited = new bool [v];
List< int > q = new List< int >();
q.Add(start);
// Set source as visited
visited[start] = true ;
int vis;
while (q.Count != 0)
{
vis = q[0];
// Print the current node
Console.Write(vis + " " );
q.Remove(q[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 shikhasingrajput |
// JavaScript implementation of the approach const adj = []; // function to add edge to the graph function addEdge(x, y) {
adj[x][y] = 1;
adj[y][x] = 1;
} // Function to perform BFS on the graph function bfs(start) {
// Visited array to keep track of visited nodes
// Initializing the array with all false values as no vertex
// is visited at the beginning
const visited = Array(adj.length).fill( false );
const q = [];
q.push(start);
// Set source as visited
visited[start] = true ;
let vis;
while (q.length >0) {
vis = q.shift();
// Print the current node
console.log(vis + " " );
// For every adjacent vertex to the current vertex
for (let i = 0; i < adj[vis].length; i++) {
if (adj[vis][i] === 1 && !visited[i]) {
// Push the adjacent node to the queue
q.push(i);
// Set the adjacent node as visited
visited[i] = true ;
}
}
}
} // Driver code // number of vertices
const v = 5;
// adjacency matrix
for (let i = 0; i < v; i++) {
adj[i] = Array(v).fill(0);
}
addEdge(0, 1);
addEdge(0, 2);
addEdge(1, 3);
// perform bfs on the graph
bfs(0);
|
0 1 2 3
Time Complexity: O(N*N)
Auxiliary Space: O(N)