# Binary Search Tree Validation - Amazon Top Interview Questions

### Problem Statement :

Given a binary tree root, return whether it's a binary search tree. A binary tree node is a binary search tree if :

All nodes on its left subtree are smaller than node.val
All nodes on its right subtree are bigger than node.val
All nodes hold the these properties.
Constraint

n ≤ 100,000 where n is the number of nodes in root

Example 1

Input

root = [3, [2, null, null], [9, [7, [4, null, null], [8, null, null]], [12, null, null]]]

Output

True

Example 2

Input

root = [3, [1, null, null], [5, [4, null, [7, null, null]], [6, null, null]]]

Output

False

Explanation

This is not a binary search tree because the 7 is not smaller than 5.

### Solution :

Solution in C++ :

bool isBST(Tree* root, int lo, int hi) {
if (root == NULL) return 1;
if (root->val < lo or root->val > hi) return 0;

return isBST(root->left, lo, root->val) and isBST(root->right, root->val, hi);
}

bool solve(Tree* root) {
return isBST(root, INT_MIN, INT_MAX);
}

Solution in Python :

# class Tree:
#     def __init__(self, val, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
def solve(self, root):
def inorder(root):
if root is None:
return True
nonlocal l
left = inorder(root.left)
if (l > root.val) or not left:
return False
l = root.val
return inorder(root.right)

l = -float("inf")
return inorder(root)

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