K-th Smallest Latency Value | Dataford Interview Questions

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Problem

TikTok Shop monitors server response times to detect latency regressions. Given an array of latency values and an integer k, return the k-th smallest latency, where k = 1 represents the smallest value.

Use an algorithm that avoids sorting the entire array when k is much smaller than the number of latency measurements.

Formal Specification

Implement kth_smallest_latency(latencies, k).

Input: latencies, a non-empty list of integers representing response times in milliseconds, and k, a 1-indexed integer.
Output: The integer latency that would appear at index k - 1 after sorting latencies in ascending order.
Duplicate latency values count as separate elements.

Constraints

1 <= len(latencies) <= 10^5
1 <= k <= len(latencies)
0 <= latencies[i] <= 10^9
Duplicate latency values are allowed

Function Signature

def kth_smallest_latency(latencies, k):