Invert Binary Tree

Same Tree

Subsets

Swap every binary-tree node's left and right children.

Given the root of a binary tree, invert it in place and return the root.

## Example
```json
Input: {"root":[4,2,7,1,3,6,9]}
Output: [4,7,2,9,6,3,1]
```

## Constraints
- 0 <= number of nodes <= 1000
- -100 <= node value <= 100

## Follow-up
Can you implement both recursive DFS and iterative BFS?

The key pattern is: DFS swaps children at every node. Identify the state and invariant before coding.

Recognize the Pattern

Advance one state transition at a time. Mark or update state before exploring dependent work.

Build the Algorithm

Test empty or minimal input, skewed shapes, duplicates where allowed, and impossible outcomes.

Check Edge Cases

Time: O(n). Space: O(h).

Java/Go/Rust below are reference solutions for learning the pattern in those languages; only Python and JavaScript can be run and submitted for this problem, since the remote judge doesn't support the TreeNode structure yet.