"""
98. Validate Binary Search Tree
Difficulty: Medium
https://leetcode.com/problems/validate-binary-search-tree/

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

A valid BST is defined as follows:

• The left subtree of a node contains only nodes with keys strictly
less than the node's key.

• The right subtree of a node contains only nodes with keys strictly
greater than the node's key.

        • Both the left and right subtrees must also be binary search trees.



Example 1:

Input: root = [2,1,3]
Output: true

Example 2:

Input: root = [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.



Constraints:

        • The number of nodes in the tree is in the range [1, 10^4].

        • -2^31 <= Node.val <= 2^31 - 1
"""


# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def isValidBST(self, root: Optional[TreeNode]) -> bool:
        def valid(node, low, high):
            if not node:
                return True

            if not (low < node.val < high):
                return False

            return valid(node.left, low, node.val) and valid(node.right, node.val, high)

        return valid(root, float("-inf"), float("inf"))