> For the complete documentation index, see [llms.txt](https://maksimdan.gitbook.io/interview-practice-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://maksimdan.gitbook.io/interview-practice-problems/leetcode_sessions/98-validate-binary-search-tree.md).

# 98 Validate Binary Search Tree

Given a binary tree, determine if it is a valid binary search tree (BST).

Assume a BST is defined as follows:

* The left subtree of a node contains only nodes with keys less than the node's key.
* The right subtree of a node contains only nodes with keys greater than the node's key.
* Both the left and right subtrees must also be binary search trees.

**Example 1:**

```
    2
   / \
  1   3
```

Binary tree \[2,1,3], return true.

**Example 2:**

```
    1
   / \
  2   3
```

Binary tree \[1,2,3], return false

**The Idea:** A BST is valid if the in order traversal of the tree itself follows ascending order. To validate this, we run an inorder traversal, and confirm that the current value in the in order traversal is greater than or equal to the previous element.

**Complexity:** O(N) time and O(|height|) space

```python
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

import sys


class Solution:
    def isValidBST(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """

        is_valid = [True]
        prev = [-sys.maxsize]

        def in_order(root):
            if root and is_valid[0]:
                in_order(root.left)
                if prev[0] >= root.val:
                    is_valid[0] = False
                else:
                    prev[0] = root.val
                in_order(root.right)

        in_order(root)
        return is_valid[0]
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://maksimdan.gitbook.io/interview-practice-problems/leetcode_sessions/98-validate-binary-search-tree.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.