How do you solve K-th Smallest in Lexicographical Order on LeetCode?

K-th Smallest in Lexicographical Order (LeetCode #440) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(log n) time complexity and O(1) space complexity. Key insight: Understanding the structure of numbers can help optimize the search for the k-th smallest.

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

The optimal solution for K-th Smallest in Lexicographical Order runs in O(log n) time and uses O(1) space. The time complexity is O(log n) due to the logarithmic depth of the tree we traverse, and the space complexity is O(1) since we only use a few variables.

What is the brute force solution for K-th Smallest in Lexicographical Order?

The brute force approach for K-th Smallest in Lexicographical Order is Brute Force, with O(n log n) time complexity and O(n) space complexity. The brute-force approach involves generating all numbers from 1 to n, converting them to strings, and then sorting them to find the k-th smallest in lexicographical order. This is straightforward but inefficient for large values of n. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve K-th Smallest in Lexicographical Order?

K-th Smallest in Lexicographical Order uses the following concepts: Trie. The recommended patterns to study are: Prefix Tree, Counting.

What are the interview tips for K-th Smallest in Lexicographical Order?

Always clarify the constraints and edge cases before diving into coding. Think about the efficiency of your approach, especially with large inputs. Explain your thought process clearly as you code to demonstrate your understanding.

What are common mistakes when solving K-th Smallest in Lexicographical Order?

Confusing lexicographical order with numerical order. Not considering the constraints of large n when choosing an approach.

#440

K-th Smallest in Lexicographical Order

Hard

TriePrefix TreeCounting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n log n)	O(log n)
Space	O(n)	O(1)

💡

Intuition

Time O(log n)Space O(1)

Instead of generating all numbers, we can use a prefix-based counting approach. By treating the numbers as a tree, we can count how many numbers exist under a given prefix and navigate through this tree to find the k-th smallest number efficiently.

⚙️

Algorithm

5 steps

1Step 1: Initialize current prefix as 1.
2Step 2: Count how many numbers exist with the current prefix in the range [1, n].
3Step 3: If the count is less than k, move to the next prefix (current prefix + 1).
4Step 4: If the count is greater than or equal to k, move down the tree (current prefix * 10).
5Step 5: Repeat until k-th number is found.

solution.py18 lines

1def findKthNumber(n, k):
2    current = 1
3    k -= 1
4    while k > 0:
5        count = 0
6        first = current
7        last = current + 1
8        while first <= n:
9            count += min(n + 1, last) - first
10            first *= 10
11            last *= 10
12        if count <= k:
13            current += 1
14            k -= count
15        else:
16            current *= 10
17            k -= 1
18    return current

ℹ

Complexity note: The time complexity is O(log n) due to the logarithmic depth of the tree we traverse, and the space complexity is O(1) since we only use a few variables.

1Understanding the structure of numbers can help optimize the search for the k-th smallest.
2Using a prefix tree-like approach allows us to count efficiently without generating all numbers.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.