Latency Histograms

A Datadog phone screen often opens with this warm-up, usually the first of two problems before the filesystem walk. The prompt is plain. You get a list of latency measurements, a bucket count, and a bucket width. You count how many latencies land in each range. The first bucket starts at 0, the next covers the following width, and anything past the top range falls into the last bucket. Five lines and you have a histogram.

The five lines are not the point. A histogram is the structure Datadog stores latency in, so the interviewer treats this opener as a doorway into how the real product handles percentiles at scale. The follow-ups walk you from a raw count array toward estimating a p99 from bucket counts alone, switching to log-scale buckets, and merging two histograms from different hosts. Get the bucketing clean, then let the conversation climb.