Convert Sorted Array to Binary Search Tree

Convert Sorted Array to Binary Search Tree

What is this problem about?

The Convert Sorted Array to Binary Search Tree interview question asks you to take an array of integers sorted in ascending order and transform it into a height-balanced Binary Search Tree (BST). A height-balanced tree is one where the depth of the two subtrees of every node never differs by more than one. Because the array is already sorted, the goal is to pick the right root at each step to keep the tree as "flat" as possible.

Why is this asked in interviews?

This is a staple Tree interview pattern used by companies like Apple, Meta, and Amazon. It tests your understanding of the relationship between sorted arrays and BSTs. It also evaluates your ability to implement a "Divide and Conquer" strategy using recursion. Being able to explain why picking the middle element as the root leads to a balanced tree is a key part of the interview.

Algorithmic pattern used

The core pattern is Divide and Conquer.

1. Find the middle element of the current array range.
2. Make this middle element the root of your (sub)tree.
3. Recursively repeat the process for the left half of the array to build the left subtree.
4. Recursively repeat for the right half of the array to build the right subtree.

Example explanation

Input Array: [1, 2, 3, 4, 5]

1. Find middle: index 2, value 3. 3 is the root.
2. Left half: [1, 2]. Middle is 1. 1 becomes the left child of 3.
3. Right child of 1 is 2.
4. Right half: [4, 5]. Middle is 4. 4 becomes the right child of 3.
5. Right child of 4 is 5. This results in a perfectly balanced tree.

Common mistakes candidates make

• Incorrect Midpoint Calculation: Using (left + right) / 2 might cause integer overflow in some languages; left + (right - left) / 2 is safer.
• Off-by-one errors: Passing the wrong boundaries to the recursive calls (e.g., including the middle element in the sub-ranges).
• Not understanding balance: Thinking any BST will work, when the problem specifically requires a height-balanced tree.

Interview preparation tip

Practice visualizing the tree structure as you step through the recursion. If the array length is even, it doesn't matter if you pick the "left-middle" or "right-middle" element; both will result in a balanced tree.