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 tree structure in computer science.

2. How Does the Calculator Work?

The calculator uses the recursive 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 level.

3. Importance of Tree Height Calculation

Details: Tree height affects time complexity of operations (O(h) for BST operations) and is crucial for balancing trees (AVL, Red-Black trees).

4. Using the Calculator

Tips: Enter the heights of left and right subtrees. The calculator will determine the full tree height. Values must be non-negative integers.

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 has height 0.

Q2: How does this relate to tree depth?
A: Height is measured from leaves to root, while depth is from root to nodes. For the whole tree, height and max depth are equal.

Q3: What's the time complexity of height calculation?
A: O(n) for a complete traversal, but this calculator provides O(1) calculation when subtree heights are known.

Q4: How is this used in balanced trees?
A: AVL trees use height difference (balance factor) between subtrees to determine rotation needs.

Q5: What's the minimum height of a binary tree?
A: Minimum height is ⌊log₂n⌋ for a tree with n nodes (complete binary tree).