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

Learn how to solve the 'Invert 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, invert the tree, and return its root.

Inverting a binary tree means swapping the left and right children of every node in the tree.

The tree is represented as a level-order list where None represents a missing node. Implement a function invertTree(root: list) -> list that returns the inverted tree in level-order.

Constraints

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

Examples

Example 1

Input

[4,2,7,1,3,6,9]

Output

[4,7,2,9,6,3,1]

Explanation

The root stays 4. Its children swap: left becomes 7, right becomes 2. Their children also swap recursively.

Example 2

Input

[2,1,3]

Output

[2,3,1]

Explanation

The root stays 2. Left child 1 and right child 3 are swapped.

Example 3

Input

[]

Output

[]

Explanation

An empty tree inverted is still empty.

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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