98. Validate Binary Search Tree

Medium

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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 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

Solution 1 : Without Any Space

# 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 recursion(root, floor = -float("inf"), ceil = float("inf")):
            if root is None:
                return True
            if root.val <= floor or root.val >= ceil:
                return False
            return recursion(root.left, floor , root.val) and recursion(root.right, root.val, ceil)
        return recursion(root)

class Solution:
    def isValidBST(self, root: Optional[TreeNode], floor = -float("inf"), ceil = float("inf")) -> bool:
        if root is None:
                return True
        if root.val <= floor or root.val >= ceil:
            return False
        return self.isValidBST(root.left, floor , root.val) and self.isValidBST(root.right, root.val, ceil)

Solution 2 : With Space

# 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:
        arr = []
        self.inorder(root, arr)
        for index in range(1, len(arr)):
            if arr[index] <= arr[index-1]:
                return False
        return True
        
    def inorder(self, root, arr):
        if not root:
            return
        self.inorder(root.left, arr)
        arr.append(root.val)
        self.inorder(root.right, arr)