Binary Search Tree Height Calculator Code

BST Height Formula:

\[ Height = \max(Height(left), Height(right)) + 1 \]

BST Height:

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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 time complexity.

2. How Does the Calculator Work?

The calculator uses the BST height formula:

\[ Height = \max(Height(left), Height(right)) + 1 \]

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 efficiency (O(h) time complexity). Balanced trees (minimum height) provide optimal performance.

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.

Q2: How does height relate to balance factor?
A: Balance factor is the difference between left and right subtree heights. AVL trees maintain |balance| ≤ 1.

Q3: What's the minimum height of a BST with n nodes?
A: Minimum height is ⌊log₂n⌋, achieved by a complete binary tree.

Q4: What's the worst-case height?
A: Worst-case height is n-1 (degenerate tree where each node has only one child).

Q5: How is height used in tree rotations?
A: Rotation operations maintain/restore balance by reducing overall tree height.