# 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.