What is the optimal time complexity of solving Binary Tree Level Order Traversal?

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 Binary Tree Level Order Traversal?

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 Binary Tree Level Order Traversal?

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 Binary Tree Level Order Traversal?

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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Binary Tree Level Order Traversal

Learn how to solve the 'Binary Tree Level Order Traversal' 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 level order traversal of its nodes' values. (i.e., from left to right, level by level).

The tree is represented as a level-order list. Implement a function levelOrder(root: list) -> list that returns a list of lists, where each inner list contains the values at that level.

Constraints

•The number of nodes in the tree is in the range [0, 2000]
•-1000 <= Node.val <= 1000

Examples

Example 1

Input

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

Output

[[3],[9,20],[15,7]]

Explanation

Level 0: [3]. Level 1: [9,20]. Level 2: [15,7].

Example 2

Input

[1]

Output

[[1]]

Explanation

Only one node at level 0.

Example 3

Input

[]

Output

[]

Explanation

Empty tree has no levels.

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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