Breadth First Search or BFS for a Graph

Breadth First Traversal (or Search) for a graph is similar to Breadth First Traversal of a tree (See method 2 of this post). The only catch here is, unlike trees, graphs may contain cycles, so we may come to the same node again. To avoid processing a node more than once, we use a boolean visited array. For simplicity, it is assumed that all vertices are reachable from the starting vertex.
For example, in the following graph, we start traversal from vertex 2. When we come to vertex 0, we look for all adjacent vertices of it. 2 is also an adjacent vertex of 0. If we don’t mark visited vertices, then 2 will be processed again and it will become a non-terminating process. A Breadth First Traversal of the following graph is 2, 0, 3, 1.



Following are the implementations of simple Breadth First Traversal from a given source.

The implementation uses adjacency list representation of graphs. STL‘s list container is used to store lists of adjacent nodes and queue of nodes needed for BFS traversal.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// Program to print BFS traversal from a given
// source vertex. BFS(int s) traverses vertices 
// reachable from s.
#include<iostream>
#include <list>
  
using namespace std;
  
// This class represents a directed graph using
// adjacency list representation
class Graph
{
    int V;    // No. of vertices
  
    // Pointer to an array containing adjacency
    // lists
    list<int> *adj;   
public:
    Graph(int V);  // Constructor
  
    // function to add an edge to graph
    void addEdge(int v, int w); 
  
    // prints BFS traversal from a given source s
    void BFS(int s);  
};
  
Graph::Graph(int V)
{
    this->V = V;
    adj = new list<int>[V];
}
  
void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w); // Add w to v’s list.
}
  
void Graph::BFS(int s)
{
    // Mark all the vertices as not visited
    bool *visited = new bool[V];
    for(int i = 0; i < V; i++)
        visited[i] = false;
  
    // Create a queue for BFS
    list<int> queue;
  
    // Mark the current node as visited and enqueue it
    visited[s] = true;
    queue.push_back(s);
  
    // 'i' will be used to get all adjacent
    // vertices of a vertex
    list<int>::iterator i;
  
    while(!queue.empty())
    {
        // Dequeue a vertex from queue and print it
        s = queue.front();
        cout << s << " ";
        queue.pop_front();
  
        // Get all adjacent vertices of the dequeued
        // vertex s. If a adjacent has not been visited, 
        // then mark it visited and enqueue it
        for (i = adj[s].begin(); i != adj[s].end(); ++i)
        {
            if (!visited[*i])
            {
                visited[*i] = true;
                queue.push_back(*i);
            }
        }
    }
}
  
// Driver program to test methods of graph class
int main()
{
    // Create a graph given in the above diagram
    Graph g(4);
    g.addEdge(0, 1);
    g.addEdge(0, 2);
    g.addEdge(1, 2);
    g.addEdge(2, 0);
    g.addEdge(2, 3);
    g.addEdge(3, 3);
  
    cout << "Following is Breadth First Traversal "
         << "(starting from vertex 2) \n";
    g.BFS(2);
  
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java program to print BFS traversal from a given source vertex. 


// BFS(int s) traverses vertices reachable from s. 


import java.io.*; 


import java.util.*; 


  


// This class represents a directed graph using adjacency list 


// representation 


class Graph 


{ 


    private int V;   // No. of vertices 


    private LinkedList<Integer> adj[]; //Adjacency Lists 


  


    // Constructor 


    Graph(int v) 


    { 


        V = v; 


        adj = new LinkedList[v]; 


        for (int i=0; i<v; ++i) 


            adj[i] = new LinkedList(); 


    } 


  


    // Function to add an edge into the graph 


    void addEdge(int v,int w) 


    { 


        adj[v].add(w); 


    } 


  


    // prints BFS traversal from a given source s 


    void BFS(int s) 


    { 


        // Mark all the vertices as not visited(By default 


        // set as false) 


        boolean visited[] = new boolean[V]; 


  


        // Create a queue for BFS 


        LinkedList<Integer> queue = new LinkedList<Integer>(); 


  


        // Mark the current node as visited and enqueue it 


        visited[s]=true; 


        queue.add(s); 


  


        while (queue.size() != 0) 


        { 


            // Dequeue a vertex from queue and print it 


            s = queue.poll(); 


            System.out.print(s+" "); 


  


            // Get all adjacent vertices of the dequeued vertex s 


            // If a adjacent has not been visited, then mark it 


            // visited and enqueue it 


            Iterator<Integer> i = adj[s].listIterator(); 


            while (i.hasNext()) 


            { 


                int n = i.next(); 


                if (!visited[n]) 


                { 


                    visited[n] = true; 


                    queue.add(n); 


                } 


            } 


        } 


    } 


  


    // Driver method to 


    public static void main(String args[]) 


    { 


        Graph g = new Graph(4); 


  


        g.addEdge(0, 1); 


        g.addEdge(0, 2); 


        g.addEdge(1, 2); 


        g.addEdge(2, 0); 


        g.addEdge(2, 3); 


        g.addEdge(3, 3); 


  


        System.out.println("Following is Breadth First Traversal "+ 


                           "(starting from vertex 2)"); 


  


        g.BFS(2); 


    } 


} 


// This code is contributed by Aakash Hasija 



















                        chevron_right







                        filter_none









Python3














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Python3 Program to print BFS traversal 


# from a given source vertex. BFS(int s) 


# traverses vertices reachable from s. 


from collections import defaultdict 


  


# This class represents a directed graph 


# using adjacency list representation 


class Graph: 


  


    # Constructor 


    def __init__(self): 


  


        # default dictionary to store graph 


        self.graph = defaultdict(list) 


  


    # function to add an edge to graph 


    def addEdge(self,u,v): 


        self.graph[u].append(v) 


  


    # Function to print a BFS of graph 


    def BFS(self, s): 


  


        # Mark all the vertices as not visited 


        visited = [False] * (len(self.graph)) 


  


        # Create a queue for BFS 


        queue = [] 


  


        # Mark the source node as  


        # visited and enqueue it 


        queue.append(s) 


        visited[s] = True


  


        while queue: 


  


            # Dequeue a vertex from  


            # queue and print it 


            s = queue.pop(0) 


            print (s, end = " ") 


  


            # Get all adjacent vertices of the 


            # dequeued vertex s. If a adjacent 


            # has not been visited, then mark it 


            # visited and enqueue it 


            for i in self.graph[s]: 


                if visited[i] == False: 


                    queue.append(i) 


                    visited[i] = True


  


# Driver code 


  


# Create a graph given in 


# the above diagram 


g = Graph() 


g.addEdge(0, 1) 


g.addEdge(0, 2) 


g.addEdge(1, 2) 


g.addEdge(2, 0) 


g.addEdge(2, 3) 


g.addEdge(3, 3) 


  


print ("Following is Breadth First Traversal"


                  " (starting from vertex 2)") 


g.BFS(2) 


  


# This code is contributed by Neelam Yadav 



















                        chevron_right







                        filter_none










Output:


Following is Breadth First Traversal (starting from vertex 2)
2 0 3 1



Illustration : 

bfs1bfs2

bfs3bfs4

bfs6bfs7

bfs8bfs9

bfs10bfs11


Note that the above code traverses only the vertices reachable from a given source vertex. All the vertices may not be reachable from a given vertex (example Disconnected graph). To print all the vertices, we can modify the BFS function to do traversal starting from all nodes one by one (Like the DFS modified version) . 


Time Complexity: O(V+E) where V is number of vertices in the graph and E is number of edges in the graph.




You may like to see below also :



Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.


GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details 





    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:

					
		

    Article Tags : 
Graph
Queue

           	
Practice Tags : 
Graph
Queue
BFS

        

         

         
 
                108

                

        



        
        
        
        
        

    

            

            2.4
            

            

             
                 Based on 452 vote(s)
                    

            
            
            
            
            
        

        
        

        

        

        

        

        

        


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.