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Leetcode
Medium
Trees
Recursion
Binary Search
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Microsoft
Validate Binary Search Tree

Determine whether a binary tree satisfies the binary search tree ordering rules.

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Problem Statement

Given the root of a binary tree, determine whether it is a valid binary search tree (BST).

A binary tree is a valid BST if for every node:

  • all values in its left subtree are strictly smaller than the node's value
  • all values in its right subtree are strictly larger than the node's value
  • both subtrees are also valid BSTs

Your task is to return whether the entire tree obeys these rules.

Input Format

  • A binary tree root is provided as the input.
  • The tree nodes contain integer values.
  • Null children indicate missing nodes.

Output Format

  • Return true if the tree is a valid BST.
  • Return false otherwise.

Constraints

  • The tree may be empty.
  • Node values are integers.
  • Duplicate values are not allowed in a valid BST.
  • Focus on correctness for all subtree boundary constraints, not just immediate parent-child comparisons.
Examples
Sample cases returned by the problem API.

Example 1

Input

root = [2,1,3]

Output

true

Explanation

Left child 1 is smaller than 2, and right child 3 is larger than 2, so the tree is a valid BST.

Example 2

Input

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

Output

false

Explanation

The node 3 is in the right subtree of 5, but 3 is less than 5, so the tree is not a valid BST.

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