Breadth First Search (BFS- Traversal)

Breadth-First Traversal (or Search) for a graph is similar to Breadth-First Traversal of a tree . 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 an adjacency list representation of graphs. STL‘s list container is used to store lists of adjacent nodes and the queue of nodes needed for BFS traversal.

Python3 Program to print BFS traversal

from collections import defaultdict
class Graph:
# Constructor
def __init__(self):
    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] * (max(self.graph) + 1)

    # 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

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)

Java program to print BFS traversal

import java.io.*;
import java.util.*;
class Graph
{
private int V;   // No. of vertices
private LinkedList adj[]; //Adjacency Lists
// Constructor
Graph(int v) {
    V = v;
    adj = new LinkedList[v];
    for (int i=0; i < v; ++i)
        adj[i] = new LinkedList();
}

void addEdge(int v,int w)
{
    adj[v].add(w);
}

void BFS(int s)
{
    boolean visited[] = new boolean[V];

    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);
}

}

Time Complexity: O(V+E), where V is the number of nodes and E is the number of edges.
Auxiliary Space: O(V)