Binary tree traversal – level order/breadth first search (java/example)

  • Given a binary tree in java, traverse the binary tree using non recursive algorithm.
  • Binary Tree traversal is categorized into two parts.
    • Depth First Search (DFS) Traversal
      • Pre Order Traversal
      • Post Order Traversal
      • In Order Traversal
    • Breadth First search (BFS) or Level Order Traversal.
      • In breadth first search algorithm, we are traversing the binary tree breadth wise (instead of depth wise).

Examples of breadth first search algorithm.

Example 1:

Traverse the binary tree using level order traversal or BFS algorithm

level order traversal tree
Fig 1: Level order traversal – binary tree

In level order traversal, we will traverse the binary tree level by level (or breadth wise) and algorithm is as follows:

  • Go to level 0 & visit all nodes
    • Visit Node A(100)
  • Go to next level i.e. level 1 & visits all nodes
    • Visit nodes Node B and Node C
  • Go to level 2 & visits all nodes
    • Visit nodes Node D, Node E, Node F & Node G
  • Go to level 3 & visits all nodes
    • Visit nodes Node H, Node I, Node J & Node K
breadth first search - binary tree traversal
Fig 2: Breadth first search algorithm

Algorithm: Breadth first search tree traversal

  • Create a queue and push root node in queue.
  • Iterate through the Queue (till queue is empty)
    • Pop node from queue & prints its value.
    • Insert left & right child to queue
  • Loop finished
    • We have visited & printed all nodes of a binary tree
      • Output will be: 60 20 80 10 30 70 90 65 75 85 95
  • We have visited binary tree (level by level)
    • Level 0 -> Level 1 -> Level 2 -> Level 3.

Time complexity of algorithm is O(n).

Program- Level order binary tree traversal in java

1.) TreeTraversalBFS Class:

  • TreeTraversalBFS class is responsible for traversing the binary tree using breadth first search or level order traversal.
package org.learn.Question;

import java.util.LinkedList;
import java.util.Queue;

public class TreeTraversalBFS {

 public static void traverseBinaryTree(Node root) {
  if (root == null) {
   System.out.println("Tree is empty");
   return;
  }

  Queue<Node> queue = new LinkedList<Node>();
  queue.offer(root);

  while (!queue.isEmpty()) {
   Node node = queue.poll();
   System.out.printf("%d ", node.data);
   if (node.left != null) {
    queue.offer(node.left);
   }
   if (node.right != null) {
    queue.offer(node.right);
   }
  }
 }
}

2.) Node Class:

  • Node class is representing the nodes of a binary tree.
package org.learn.Question;

public class Node {
 public int data;
 public Node left;
 public Node right;

 public Node(int num) {
  this.data = num;
  this.left = null;
  this.right = null;
 }

 public Node() {
  this.left = null;
  this.right = null;
 }
 
 public static Node createNode(int number) {
  return new Node(number);
 }
}

3.) App Class:

  • We are constructing the binary tree in main method
  • We will invoke method of TreeTraversalBFS class, to print the binary tree using BFS algorithm.
package org.learn.Client;

import org.learn.Question.Node;
import org.learn.Question.TreeTraversalBFS;

public class App {
 public static void main(String[] args) {
  // root level 0
  Node A = Node.createNode(60);
  // Level 1
  Node B = Node.createNode(20);
  Node C = Node.createNode(80);
  // Level 2
  Node D = Node.createNode(10);
  Node E = Node.createNode(30);
  Node F = Node.createNode(70);
  Node G = Node.createNode(90);
  // Level 3
  Node H = Node.createNode(65);
  Node I = Node.createNode(75);
  Node J = Node.createNode(85);
  Node K = Node.createNode(95);

  // connect Level 0 and 1
  A.left = B;
  A.right = C;
  // connect level 1 and level 2
  B.left = D;
  B.right = E;
  C.left = F;
  C.right = G;
  // connect level 2 and level 3
  F.left  = H;
  F.right = I;
  G.left  = J;
  G.right = K;
  
  System.out.println("Level order traversal or BFS of binary tree:");
  TreeTraversalBFS.traverseBinaryTree(A);
 }
}

Output: binary tree traversal – breadth first search

Level order traversal or BFS of binary tree:
60 20 80 10 30 70 90 65 75 85 95 

Code – binary tree traversal level order traversal (BFS)

 

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