1. What is Binary Search Tree Height?

The height of a binary search tree is the number of edges on the longest path from the root node to a leaf node. It's a fundamental measure of a tree's structure and affects search efficiency.

2. How Does the Calculator Work?

The calculator uses the recursive BST height formula:

Where:

• \( Height(left) \) — Height of left subtree
• \( Height(right) \) — Height of right subtree

Explanation: The height of a tree is determined by its tallest subtree plus one for the current node.

3. Importance of BST Height Calculation

Details: Tree height directly impacts search performance (O(height) time complexity) and helps determine if the tree is balanced.

4. Using the Calculator

Tips: Enter the heights of left and right subtrees (0 if subtree is empty). The calculator will compute the total height of the BST.

5. Frequently Asked Questions (FAQ)

Q1: What's the height of an empty tree?
A: The height of an empty tree (null node) is typically considered -1 or 0, depending on definition. This calculator uses 0 as base case.

Q2: How does height relate to tree balance?
A: A balanced BST has heights of left and right subtrees differing by at most 1 at every node.

Q3: What's the time complexity of height calculation?
A: O(n) for full traversal, but this calculator assumes you already have subtree heights.

Q4: How is this different from depth?
A: Height is measured from leaf to root (bottom-up), while depth is from root to node (top-down).

Q5: What's the minimum possible height for n nodes?
A: Minimum height is ⌊log₂n⌋ for a perfectly balanced tree.