Construct BST from its given level order traversal

In this article, we will explore the process of constructing a Binary Search Tree from its given level order traversal, breaking down each step to ensure a thorough understanding.

Understanding Binary Search Trees (BSTs)

Before diving into constructing a BST from its level order traversal, let's briefly review what a Binary Search Tree is. A BST is a binary tree where each node has at most two child nodes, referred to as the left and right child. The key property of a BST is that for any given node:

• All nodes in its left subtree have values less than the node's value.
• All nodes in its right subtree have values greater than the node's value.

This property makes BSTs an excellent choice for efficient searching, insertion, and deletion operations.

Level Order Traversal

Level order traversal is a method of visiting all nodes in a binary tree level by level, starting from the root and moving from left to right. It's also known as Breadth-First Search (BFS). When we are given the level order traversal of a BST, we can reconstruct the tree while adhering to the BST property.

Steps to Construct a BST from Level Order Traversal

Let's break down the process of constructing a BST from its level order traversal into distinct steps:

Step 1: Create an Empty BST

We begin by creating an empty BST that will be gradually populated using the given level order traversal.

Step 2: Insert the Root Node

The first element in the level order traversal corresponds to the root of the BST. Insert it into the BST.

Step 3: Identify Subtrees

As we move through the level order traversal, we identify the elements that belong to the left and right subtrees of each node. We maintain a queue data structure.

Step 4: Insert Subtrees

For each node in the level order traversal, we dequeue the elements representing its left and right children, if present. Insert these elements into their respective subtrees.

Step 5: Repeat Until All Elements Are Inserted

Continue this process until you have inserted all the elements from the level order traversal into the BST.

Step 6: BST Construction Complete

Once all elements are inserted, you have successfully constructed the BST from its level order traversal.

The Role of the Queue

In our Python program to construct a BST from the level order traversal, we use a queue data structure. The queue helps us keep track of the nodes we need to process.

This queue-based approach ensures that we maintain the structure of the BST while constructing it from the level order traversal. It's a prime example of how data structures like queues can be used effectively in algorithms.

Benefits of Constructing BST from Level Order Traversal

Constructing a BST from its level order traversal has several advantages:

• It allows you to create a BST efficiently without the need for complex algorithms.
• The resulting tree preserves the BST property, ensuring efficient search operations.
• It is a useful exercise for understanding tree traversal and insertion in binary trees.

Code:

Output:

Inorder Traversal of Constructed BST:
> 3
1 2 3 4 5 6 7 3

This program defines a TreeNode class for representing nodes in the BST and two functions:

• constructBST that takes a list level_order and returns the root of the BST constructed from it.
• inorderTraversal to perform an inorder traversal of the constructed BST and print the values.

Replace the level_order list with your own level order traversal values, and the program will construct the BST accordingly.

Conclusion

In this article, we've explored the fascinating process of constructing a Binary Search Tree from its given level order traversal. By following the steps outlined above, you can create a BST that maintains the essential BST properties. This skill is invaluable for algorithm development and problem-solving in computer science and data structures.