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++

// 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)
"; 
    g.BFS(2); 
  
    return 0; 
} 

Java

// 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 

/div>

Python3

# 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 

Output:

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

Illustration :
bfs1 bfs2
bfs3 bfs4
bfs6 bfs7
bfs8 bfs9
bfs10 bfs11

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.

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

Breadth First Search or BFS for a Graph

C++

Java

Python3

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