Welcome to today's lesson! In this practice-based session, we'll unravel the mysteries of Binary Search Trees (BSTs). We will focus on two well-known interview problems related to BSTs. Solving these problems will solidify your understanding of trees and provide you with hands-on experience that will be invaluable during future job interviews. Think of this as mock interviews before the real one! So, let's put on our problem-solving hats and dive right in!

Here is the first problem: we need to write a function that checks if a BST is balanced. The tree is balanced if for each vertex, the size of the left subtree differs from the size of the right subtree by at most 1.

You might wonder, "Why do we need to do this?". Well, this problem frequently appears in job interviews because checking the balance of a tree optimizes search operations.

Interestingly, consider trying to balance on one foot. If the weight on your left and right sides is not equal, you'll topple over, right? Similarly, a binary tree is considered balanced when the left and right sides are equal, or at least the difference is no more than one. Isn't that fascinating?

So, let's discuss the naive approach to solving this problem. One could start by calculating the heights of all subtrees and then checking whether the heights of each node's left and right subtrees differ by no more than one. While this approach is functional, it is inefficient since it involves traversing the entire tree multiple times and making duplicate calculations.

But don't worry, there's a more efficient way! Instead of traversing the tree multiple times, we can use recursion to do it all in one sweep. We calculate the heights of the subtrees while simultaneously checking the balance condition. So, essentially, we're hitting two birds with one stone!