Validate Binary Search Tree

Binary Tree Level Order Traversal

Same Tree

Check whether a binary tree satisfies strict BST ordering.

Return true if every node in `root` satisfies the strict binary-search-tree ordering rule.

## Example
```json
Input: {"root":[2,1,3]}
Output: true
```

## Constraints
- 1 <= number of nodes <= 10000
- -2^31 <= node value <= 2^31 - 1

## Follow-up
Why is checking only each node's immediate children insufficient?

The key pattern is: DFS carries the full valid value range. 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.