Tree Traversal : Breadth First Search (BFS)

Tree Traversal : Breadth First Search (BFS)

Breadth-first search (BFS) is an algorithm for traversing or searching tree data structures. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a search key and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level.

Tree Traversal Breadth First Search

Example - Breadth First Search

Example of Breadth First Search Tree Traversal

Steps for Breadth First Search Tree Treaversal

  • Step 1 : Push the root i.e. 50 to the queue.
  • Step 2 : Pop the element 50 from the queue and print it.
  • Step 3 : Now, Add it’s left and right child i.e. add 30 and 70 to queue.
  • Step 4 : Again pop the front element i.e. 30 from queue and print it .
  • Step 5 :  Add it’s left and right child i.e. 10 and 40 in the queue.
  • Step 6 : Pop the element 70 from the queue and  print it.
  • Step 7 : add it’s left and right child i.e. 60 and 90.
  • Step 8 : Now pop all the elements from the queue and print them as there is no child of these elements.

      Therefore the printing sequence will be 50 30 70 10 40 60 90 .

Algorithm

  1. If the root is NULL, return.
  2. Otherwise push the root in queue.
  3. Pop the node from the queue.
  4. Print the node’s data and add its left and right child.
  5. Repeat until the queue is empty.

CODE FOR BREADTH FIRST SEARCH

import java.util.*;
//Representing a Node of a Binary tree
class Node{
   int value;
   Node left,right;
   //constructor
   Node(int value)
   {
       this.value=value;
       left=right=null;
   } 
}
class BreadthFirstSearch
{
   Node root;  //Root of the Binary tree
   BreadthFirstSearch()
  {
      root=null;
  }
   /*level order traversal of a binary tree */  
   public void levelOrder(Node ptr)    
   {
       if(ptr==null)
       return ;
       //Creating a Queue Object
       Queue queue=new LinkedList();
       queue.add(ptr);  //adding an element to queue
       while(!queue.isEmpty())
       {
           Node node=queue.poll();  //removing an element from queue
           System.out.print(node.value+" ");
           if(node.left!=null)
           queue.add(node.left);  //adding an element to queue
           if(node.right!=null)
           queue.add(node.right); //adding an element to queue
       }
   }
  public static void main(String[] args)
   {
       BreadthFirstSearch bst=new BreadthFirstSearch();
       //creating the nodes of binarytree
       bst.root=new Node(50);
       bst.root.left=new Node(30);
       bst.root.right=new Node(70);
       bst.root.left.left=new Node(10);
       bst.root.left.right=new Node(40);
       bst.root.right.left=new Node(60);
       bst.root.right.right=new Node(90);
       bst.levelOrder(bst.root);
}
}

 

Output:

50 30 70 10 40 60 90

Time And Space Complexity of level order Traversal

Time Complexity :

O(n)

Space complexity :

O(n)