1. What is Binary Tree Depth?

The depth of a binary tree is the number of edges from the root node to the deepest leaf node. It's a fundamental measure of a tree's structure and complexity.

2. How Does the Calculator Work?

The calculator uses the recursive depth formula:

Where:

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

Explanation: The depth of a tree is determined by its deepest subtree plus one for the current level.

3. Importance of Tree Depth Calculation

Details: Tree depth affects algorithm performance (O(depth) space complexity for recursive algorithms) and is crucial for balanced tree operations.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between depth and height?
A: Depth is measured from root down (root has depth 0), while height is measured from leaves up (leaves have height 0).

Q2: What's the depth of an empty tree?
A: Typically considered -1 or 0 depending on definition. This calculator uses the +1 convention where empty is 0.

Q3: How does this relate to balanced trees?
A: A balanced tree has |depth(left) - depth(right)| ≤ 1 for all nodes.

Q4: What's the time complexity of depth calculation?
A: O(n) for full traversal, but this calculator assumes you already have subtree depths.

Q5: When is maximum depth important?
A: Critical for recursion stack safety and space complexity analysis of tree algorithms.