What is the optimal time complexity of solving Maximum Depth of Binary Tree?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Maximum Depth of Binary Tree?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Maximum Depth of Binary Tree?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Maximum Depth of Binary Tree?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Maximum Depth of Binary Tree

Learn how to solve the 'Maximum Depth of Binary Tree' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

Given the root of a binary tree, return its maximum depth.

A binary tree's maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

The tree is represented as a level-order list where None represents a missing node. Implement a function maxDepth(root: list) -> int.

Constraints

•The number of nodes in the tree is in the range [0, 10000]
•-100 <= Node.val <= 100

Examples

Example 1

Input

[3,9,20,None,None,15,7]

Output

Explanation

The tree has 3 levels: root [3], second level [9,20], third level [15,7]. The longest path is 3->20->15 or 3->20->7, both of depth 3.

Example 2

Input

[1,None,2]

Output

Explanation

The tree has root 1 with only a right child 2. Depth is 2.

Example 3

Input

[]

Output

Explanation

An empty tree has depth 0.

Need a Hint?

Perform a recursive tree traversal (DFS) or level-order traversal (BFS) using a queue/stack.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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