Is K-th Smallest in Lexicographical Order easy or hard?

LeetCode classifies this problem as Hard because the optimal solution requires recognizing the implicit lexicographical tree and implementing prefix counting correctly. The algorithm itself is short but the insight behind skipping entire numeric ranges makes it challenging.

K-th Smallest in Lexicographical Order Python/Java solution

Implementations in Python or Java typically use a helper function that counts how many numbers exist between two prefixes (for example between 1 and 2, then 10 and 20, etc.). The algorithm repeatedly moves to the next prefix or deeper into the tree until the k-th number is reached.

How to solve K-th Smallest in Lexicographical Order in O(n)?

A naive solution could generate all numbers from 1 to n, convert them to strings, sort them lexicographically, and pick the k-th element. That approach costs O(n log n) time and O(n) space. Efficient solutions avoid full generation and instead traverse the implicit prefix tree in about O((log n)^2) time.

What is the best approach for K-th Smallest in Lexicographical Order?

The most efficient approach treats numbers from 1 to n as a lexicographical prefix tree and performs a controlled traversal. At each prefix, a counting function determines how many numbers exist under that prefix so entire subtrees can be skipped. This avoids generating all numbers and runs in about O((log n)^2) time with constant space.

Is K-th Smallest in Lexicographical Order asked at Google/Amazon/Meta?

This problem style appears in interviews at large tech companies because it tests prefix reasoning, number ranges, and tree-like traversal without building a full data structure. Variants involving lexicographical ranking or prefix counting have appeared in interviews at Google and Amazon.

What data structure is used in K-th Smallest in Lexicographical Order?

The solution conceptually uses a trie-like prefix tree where each node represents a numeric prefix. The tree is not built explicitly; instead, prefix ranges are counted mathematically to simulate traversal of this structure.

What is the time complexity of K-th Smallest in Lexicographical Order?

The optimal solution runs in O((log n)^2) time and O(1) space. Each step computes how many numbers lie between two lexicographical prefixes, which costs O(log n), and this counting is performed across roughly log n traversal steps.

Description Solution Video 19:06

440. K-th Smallest in Lexicographical Order

Hard46.2% acceptance7 companies

Given two integers n and k, return the k^th lexicographically smallest integer in the range [1, n].

Example 1:

Input: n = 13, k = 2
Output: 10
Explanation: The lexicographical order is [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9], so the second smallest number is 10.

Example 2: