Validate Binary Search Tree

Published: Jan 16, 2023

Medium Binary Search Tree Depth-First Search

Problem Description

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.

Constraints: The number of nodes in the tree is in the range [1, 10**4].

  • -2**31 <= Node.val <= 2**31 - 1


Example 1
Input: root = [2,1,3]
Output: true
  /   \
1      3
Example 2
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.
  /   \
1      4
     /   \
    3     6

How to Solve

Check each node value is less than upper bound and greater than lower bound. Start from a minimum value as a lower bound and a maximum value as a upper bound. The solution here took depth-first search (recursive). When it goes to a left subtree, lower bound is from previous one and upper bound is a parent node value. When it goes to a right subtree, lower bound is a parent node value and upper bound is from previous one. If all node values are valid, the tree is a valid BST.


 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
class ValidateBinarySearchTree {
  bool helper(TreeNode* root, long long low, long long high)
    if (!root)
      return true;
    if (root->val <= low || root->val >= high)
      return false;
    return helper(root->left, low, root->val) && helper(root->right, root->val, high);
    bool isValidBST(TreeNode* root) {
        return helper(root, LLONG_MIN, LLONG_MAX);

# 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 ValidateBinarySearchTree:
    def isValidBST(self, root: Optional[TreeNode]) -> bool:
        def helper(root: Optional[TreeNode], low, high)-> bool:
            if not root:
                return True
            if root.val <= low or root.val >= high:
                return False
            return helper(root.left, low, root.val) and\
                helper(root.right, root.val, high)

        return helper(root, float('-inf'), float('inf'))
# Definition for a binary tree node.
# class TreeNode
#     attr_accessor :val, :left, :right
#     def initialize(val = 0, left = nil, right = nil)
#         @val = val
#         @left = left
#         @right = right
#     end
# end
def helper(root, low, high)
    if !root
        return true
    if root.val <= low || high <= root.val
        return false
    return helper(root.left, low, root.val) && helper(root.right, root.val, high)

# @param {TreeNode} root
# @return {Boolean}
def is_valid_bst(root)
    return helper(root, -2**31-1, 2**31)


  • Time: O(n)
  • Space: O(h) – h: height of the tree