What is the optimal time complexity of solving Diameter 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 Diameter 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 Diameter 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 Diameter 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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Diameter of Binary Tree

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

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Problem Statement

Medium

Given the root of a binary tree, return the length of the diameter of the tree.

The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

The length of a path between two nodes is represented by the number of edges between them.

The tree is represented as a level-order list. Implement a function diameterOfBinaryTree(root: list) -> int.

Constraints

•The number of nodes in the tree is in the range [1, 10000]
•-100 <= Node.val <= 100

Examples

Example 1

Input

[1,2,3,4,5]

Output

Explanation

The longest path is 4->2->1->3 or 5->2->1->3, which has 3 edges.

Example 2

Input

[1,2]

Output

Explanation

The longest path is 2->1, which has 1 edge.

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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