# Validate Binary Search Tree: A Comprehensive Guide

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## Chapter 1: Understanding the Problem

In this chapter, we will delve into the problem statement of LeetCode 98, which asks us to verify whether a given binary tree is a valid binary search tree (BST). A valid BST adheres to specific rules:

- The left subtree of any node contains only nodes with values less than that node.
- The right subtree consists solely of nodes with values greater than the node.
- Both subtrees must also be valid binary search trees.

## Example Cases

Let's examine two examples to clarify the concept:

**Example 1:**- Input: root = [2,1,3]
- Output: true

**Example 2:**- Input: root = [5,1,4,null,null,3,6]
- Output: false
- Explanation: Here, the root node's value is 5, but its right child has the value 4, which violates the BST rules.

## Constraints

The tree can contain between 1 and 10,000 nodes, with node values ranging from -2^31 to 2^31 - 1.

Understanding the constraints helps us develop an efficient solution.

## Chapter 2: Unpacking the Explanation

While the problem may seem straightforward at first glance, there are subtleties that can lead to confusion. A crucial aspect to grasp is the definition of a valid BST. When recursively validating the tree, each node's left child, along with its entire subtree, must contain values less than the current node's value. Conversely, the right child must contain values greater than the current node's value.

One common pitfall is failing to account for the infinite potential of left and right paths. Thus, as we validate each node, we need to keep track of a minimum and maximum value that the node's value must adhere to. If any node's value falls outside this range, we can conclude that the tree is invalid.

## The Python Solution

To implement the solution in Python, we start by defining the minimum and maximum possible values for the root node as negative and positive infinity, respectively. The base case for our recursive function is straightforward: if a node is null, it doesn't violate any BST rules, so we return true.

If the node's value lies outside the designated range, we return false. A key insight is that when checking the left child, we maintain the initial minimum value because it cannot be updated without moving right. The maximum value is updated to the current node's value. Conversely, when checking the right child, we update the minimum value to the current node's value while keeping the maximum unchanged. This logic allows us to effectively solve the problem.

The first video titled "Validate Binary Search Tree - Depth First Search - Leetcode 98 - YouTube" offers an insightful overview of using depth-first search to validate binary search trees.

The second video titled "Leetcode - Validate Binary Search Tree (Python) - YouTube" provides a detailed walkthrough of implementing the solution in Python.

## Python Code Implementation

# 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 check(node, left, right):

if not node:

return True

if not (left < node.val < right):

return False

return check(node.left, left, node.val) and check(node.right, node.val, right)

return check(root, float('-inf'), float('inf'))

The code leverages a recursive helper function to validate the binary search tree structure efficiently.