K-th Smallest Element

Problem

Return the k-th smallest value of the list (k counts from 1). Quickselect finds it in average O(n) time without sorting everything.

Implement kth_smallest(numbers, k).

numbers: The list of integers. k: Which smallest value to return, starting at 1.

Return the k-th smallest value.

1 ≤ k ≤ length ≤ 200,000

Example 1

Input:
k = 3
numbers = [7, 10, 4, 3, 20, 15]

Expected output:
expected = 7

Input:
long long k = 3;
std::vector<long long> numbers = {7, 10, 4, 3, 20, 15};

Expected output:
long long expected = 7;

Input:
long k = 3;
long[] numbers = new long[] {7, 10, 4, 3, 20, 15};

Expected output:
long expected = 7;

Sorted: 3, 4, 7, 10, 15, 20; the 3rd smallest is 7.

Example 2

Input:
k = 2
numbers = [5, 5, 1]

Expected output:
expected = 5

Input:
long long k = 2;
std::vector<long long> numbers = {5, 5, 1};

Expected output:
long long expected = 5;

Input:
long k = 2;
long[] numbers = new long[] {5, 5, 1};

Expected output:
long expected = 5;

Sorted: 1, 5, 5; the 2nd smallest is 5 (duplicates count).

Try on your own first, then open one hint at a time.

Hint 1

You only need the element that would sit in position k after sorting, not the fully sorted list.

Hint 2

Partition around a pivot and recurse or iterate only into the side that can still contain the target rank.

Hint 3

Remember that k is one-based, and duplicates must still count as separate positions.

Expected complexity

O(n) average time, O(1) extra space

This challenge is adapted for CodeUtility. Follow the statement and constraints above.