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98\. Validate Binary Search Tree

Medium

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:**

![](https://assets.leetcode.com/uploads/2020/12/01/tree1.jpg)

**Input:** root = [2,1,3]

**Output:** true 

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/12/01/tree2.jpg)

**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

To solve the "Validate Binary Search Tree" problem in Java with the Solution class, follow these steps:

1. Define a method `isValidBST` in the `Solution` class that takes the root of a binary tree as input and returns true if the tree is a valid binary search tree (BST), and false otherwise.
2. Implement a recursive approach to validate if the given binary tree is a valid BST:
   - Define a helper method `isValidBSTHelper` that takes the root node, a lower bound, and an upper bound as input parameters.
   - In the `isValidBSTHelper` method, recursively traverse the binary tree nodes.
   - At each node, check if its value is within the specified bounds (lower bound and upper bound) for a valid BST.
   - If the node's value violates the BST property, return false.
   - Otherwise, recursively validate the left and right subtrees by updating the bounds accordingly.
   - If both the left and right subtrees are valid BSTs, return true.
3. Call the `isValidBSTHelper` method with the root node and appropriate initial bounds to start the validation process.

Here's the implementation of the `isValidBST` method in Java:

```java
class Solution {
    public boolean isValidBST(TreeNode root) {
        return isValidBSTHelper(root, null, null);
    }
    
    private boolean isValidBSTHelper(TreeNode node, Integer lower, Integer upper) {
        if (node == null) {
            return true;
        }
        
        int val = node.val;
        if ((lower != null && val <= lower) || (upper != null && val >= upper)) {
            return false;
        }
        
        return isValidBSTHelper(node.left, lower, val) && isValidBSTHelper(node.right, val, upper);
    }
}
```

This implementation recursively validates whether the given binary tree is a valid BST in O(n) time complexity, where n is the number of nodes in the tree.