Validate A Binary Search Tree

In the previous post we solved a LeetCode problem that required us to create a height-balance binary search tree from a sorted array. In this problem we are going to look at another LeetCode problem. This time we are validating that a binary tree is a valid binary search tree.

Problem

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.

Solution

In order to solve this problem we do an in-order traversal of the binary tree updating a global minimum value as we go along. Once we find a node that is less than (or equal) the minimum we know it’s not a valid binary search tree since in-order traversal visits the nodes in ascending order. The time complexity of this algorithm is \(O(n)\) while the space complexity is \(O(h)\) where \(h\) is the height of the tree. Here’s the code:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
public class Solution {
    public bool IsValidBST(TreeNode root) {
        var min = Int64.MinValue;
        return CheckValidity(root, ref min);
    }

    private bool CheckValidity(TreeNode node, ref Int64 min){
        if (node is null){
            return true;
        }


        if (!CheckValidity(node.left, ref min)){
            return false;
        }

        if (node.val <= min){
            return false;
        }

        min = node.val;

        return CheckValidity(node.right, ref min);
    }
}

In this post we solved another LeetCode problem that required us to check if a binary tree is a valid binary search tree. Again, I used the code I submitted to LeetCode so there’s nothing on the GitHub repository. Till next time, thanks for reading and don’t hesitate to leave a comment below.