1. What is Binary Tree Height?

The height of a binary 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 complexity.

2. How Does the Calculator Work?

The calculator uses the binary tree height formula:

Where:

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

Explanation: The height of a tree is determined by the taller of its two subtrees plus one for the current level.

3. Importance of Tree Height Calculation

Details: Tree height is crucial for analyzing algorithm complexity (O(h) operations), balancing trees (AVL, Red-Black), and optimizing search operations.

4. Using the Calculator

Tips: Enter the heights of left and right subtrees in levels (must be non-negative integers). The calculator will compute the total tree height.

5. Frequently Asked Questions (FAQ)

Q1: What's the height of an empty tree?
A: Typically -1 or 0, depending on definition. This calculator uses the +1 convention where empty tree is -1.

Q2: How does this relate to tree balancing?
A: Balanced trees maintain height difference ≤1 between subtrees (AVL property) to ensure O(log n) operations.

Q3: What's the height of a perfect binary tree?
A: For a perfect tree with n levels, height is n-1 (root at level 0) or n (root at level 1).

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

Q5: Why add 1 in the formula?
A: The +1 accounts for the current node's level in the path from leaf to root.