# 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
```

Binary tree \[2,1,3], return true.

**Example 2:**

```
    1
   / \
  2   3
```

Binary tree \[1,2,3], return false

**The Idea:** A BST is valid if the in order traversal of the tree itself follows ascending order. To validate this, we run an inorder traversal, and confirm that the current value in the in order traversal is greater than or equal to the previous element.

**Complexity:** O(N) time and O(|height|) space

```python
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

import sys


class Solution:
    def isValidBST(self, root):
        """
        :type root: TreeNode
        :rtype: bool
        """

        is_valid = [True]
        prev = [-sys.maxsize]

        def in_order(root):
            if root and is_valid[0]:
                in_order(root.left)
                if prev[0] >= root.val:
                    is_valid[0] = False
                else:
                    prev[0] = root.val
                in_order(root.right)

        in_order(root)
        return is_valid[0]
```


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