# 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:

``````Input:

2
/ \
1   3

Output:
true
``````

Example 2:

``````    5
/ \
1   4
/ \
3   6

Output:
false

Explanation:
The input is: [5,1,4,null,null,3,6]. The root node's value
is 5 but its right child's value is 4.
``````

## Analysis

``````  3
/ \
1   5
/ \
2   6
``````

``````boolean isValidSubtree (TreeNode root, Integer min, Integer max)
``````

## Solution

``````/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
class Solution {
public boolean isValidBST(TreeNode root) {
if (root == null) return true;
return isValidSubtree(root, null, null);
}
boolean isValidSubtree (TreeNode root, Integer min, Integer max) {
if (root == null) return true;
if ((min != null && root.val <= min) ||  (max != null && root.val >= max)) return false;
return isValidSubtree (root.left, min, root.val) && isValidSubtree(root.right, root.val, max);
}
}
``````

Time Complexity -- O(n)

Space Complexity - O(n) (recursive call stack)