# LeetCode 98. Validate Binary Search Tree

## Description

https://leetcode.com/problems/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

Input: [2,1,3]
Output: true
```

Example 2:

```    5
/ \
1   4
/ \
3   6

Input: [5,1,4,null,null,3,6]
Output: false
Explanation: The root node's value is 5 but its right child's value is 4.```

## Explanation

The idea is to compare the node value with its upper and lower limits if they are available. Then one repeats the same step recursively for left and right subtrees.

## Python Solution

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

class Solution:
def isValidBST(self, root: TreeNode) -> bool:
return self.validBST_helper(root, sys.maxsize, -sys.maxsize)

def validBST_helper(self, root, max_value, min_value):
if root == None:
return True

if root.val >= max_value or root.val <= min_value:
return False

return self.validBST_helper(root.left, root.val, min_value) and self.validBST_helper(root.right, max_value, root.val)``````
• Time complexity: O(N).
• Space complexity: O(N).