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Validate Binary Search Tree

medium
Blind 75NeetCode 150treesbstrecursion

Problem

Given the root of a binary tree, decide whether it is a valid binary search tree, meaning every node's value is greater than all values in its left subtree and smaller than all in its right subtree.

Examples

Input: [2, 1, 3]
Output: true
Left child smaller, right child larger.
Input: [5, 1, 4, null, null, 3, 6]
Output: false
The value 3 violates the upper bound set by its ancestors.

Constraints

  • • 1 <= number of nodes <= 10^4
  • • -2^31 <= node value <= 2^31 - 1
Hints(tap to reveal)
  • 1. Comparing only direct children is not enough.
  • 2. Pass down an allowed value range to each node.
Optimal approach(spoiler)
  1. Recurse with a lower and upper bound, initially unbounded.
  2. Each node's value must lie strictly within its bounds.
  3. Recurse left with the node's value as the new upper bound.
  4. Recurse right with the node's value as the new lower bound.
  5. O(n) time, O(h) space.

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