[LC] 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

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.

Time: O(N)
Space: O(N)

# 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:
        import sys
        right_bound = sys.maxsize
        left_bound = -sys.maxsize - 1
        return self.helper(root, left_bound, right_bound)
        
    def helper(self, root, left_bound, right_bound):
        if root is None:
            return True
        if root.val <= left_bound or root.val >= right_bound:
            return False
        # 1. left child's child cannot larger than current node val
        # 2. right child's child cannot be small than current node val
        return self.helper(root.left, left_bound, root.val) and self.helper(root.right, root.val, right_bound)