Is Kth Smallest Element in a BST easy or hard?

The problem is rated Medium because recognizing the in-order traversal property of BSTs is the key insight. Once that observation is made, the implementation is straightforward, but interviewers may ask follow-ups such as reducing space to O(1) using Morris traversal.

Kth Smallest Element in a BST Python/Java solution

Python and Java implementations typically use recursive in-order traversal with a global or reference counter. Each node visit increments the counter until the kth node is found. The same logic works in C++, JavaScript, and other languages because it depends only on tree traversal order.

How to solve Kth Smallest Element in a BST in O(n)?

Perform an in-order traversal of the BST and maintain a counter for visited nodes. Increment the counter each time a node is processed. When the counter equals k, return that node’s value. This guarantees O(n) time because each node is visited at most once.

What is the best approach for Kth Smallest Element in a BST?

In-order traversal is the best approach because a Binary Search Tree outputs nodes in sorted order when traversed left → root → right. Counting nodes during traversal allows you to stop once the kth node is reached. This method runs in O(n) time and O(h) space where h is the tree height.

Is Kth Smallest Element in a BST asked at Google/Amazon/Meta?

Kth Smallest Element in a BST appears frequently in interviews at companies like Amazon, Google, and Meta. It tests understanding of BST ordering, depth-first traversal, and the ability to optimize space using techniques such as Morris traversal.

What data structure is used in Kth Smallest Element in a BST?

The core data structure is a Binary Search Tree. Solutions rely on depth-first traversal, usually in-order traversal, and may use recursion stacks or pointer threading (Morris traversal) to navigate the tree efficiently.

What is the time complexity of Kth Smallest Element in a BST?

Most solutions run in O(n) time because in the worst case you may need to visit every node. Recursive in-order traversal uses O(h) space for the recursion stack, while Morris traversal reduces extra space to O(1) by temporarily modifying tree pointers.

Description Hints 4 Solution Video 10:56

230. Kth Smallest Element in a BST

Medium77.2% acceptance12 companies

Given the root of a binary search tree, and an integer k, return the k^th smallest value (1-indexed) of all the values of the nodes in the tree.

Example 1:

Input: root = [3,1,4,null,2], k = 1
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
Output: 3

Constraints:

The number of nodes in the tree is n.
1 <= k <= n <= 10⁴
0 <= Node.val <= 10⁴

Follow up: If the BST is modified often (i.e., we can do insert and delete operations) and you need to find the kth smallest frequently, how would you optimize?