validate_binary_search_tree.py

"""
https://leetcode.com/problems/validate-binary-search-tree/

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 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:
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, 104].
-231 <= Node.val <= 231 - 1
"""

from typing import Optional


class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right


def is_valid_binary_search_tree(root: Optional[TreeNode]) -> bool:
    if not root:
        return True

    q = [(root, float("-inf"), float("inf"))]

    while q:
        node, left, right = q.pop()
        if not (left < node.val < right):
            return False
        if node.left:
            q.append((node.left, left, node.val))
        if node.right:
            q.append((node.right, node.val, right))

    return True