0098.md

98. Validate Binary Search Tree

Level:

Topic:

Question

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.

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.

Intuition

Recursive:

• use helper function to keep track of low and high value
• any node value that's <= high or <= low, it's not a BST

Code

Time: O(n)
Space: O(n)

Recursive

public boolean isValidBST(TreeNode root) {
    return isValid(root, null, null);
}

private boolean isValid(TreeNode root, Integer low, Integer high) {
    if (root == null)
        return true;

    if (low != null && root.val <= low)
        return false;

    if (high != null && root.val >= high)
        return false;

    return isValid(root.left, low, root.val) && isValid(root.right, root.val, high);
}