| I got that recently, I really didn't like that question. For the n-th percentile version, the obvious solution is sorting and it takes 10 seconds to get to that point, 5 minutes of implementation with tests. Good. It's all downhill from here. Then you get hit with the "it's a data stream" and you realize you have to implement a balanced tree on the spot which I wouldn't describe as fun. You may or may not be able to implement that. I did not. Blabbered something about Rust having sorted B-Trees and I don't think Python has them -- they do not on the standard library. Then the interviewer leaned heavily on the "reduce memory usage" and I couldn't come up with a solution (no shit it's Ω(n) and he didn't even tell me to go fetch for a randomized algorithm). I later understood he expected the reservoir sampling solution which is basically keeping a representative group of size K that is a good proxy of the whole stream, it goes like this: keep the K first elements, any elements after that replaces any element of our sample at random. What I did after 10 minutes of weird silence is to assume the data stream follows a normal distribution and computing the P-percentiles by computing the running mean and standard deviation. I felt frustrated at the end of the interview because it really felt like a big gotcha of either you know the reservoir sampling "leetcode trivia" or you don't. |
RS is really interesting to me. many people you talk to can realize you can compute the mean of a data stream (https://www.geeksforgeeks.org/web-tech/expression-for-mean-a...) without knowing the exact formulation. And it's not far from that to think of a sampling strategy to decide if a new sample should go into a fixed-size reservoir. (for all of these, I know specific hints that will usually help people get to the next step).
The only reason I know RS is because it was in the google3 monorepo and I was looking for interesting codes to use and found it. There was an associated Sharding class, LexicographicRangeSharding (https://www.mongodb.com/docs/manual/core/ranged-sharding/) which you could use to find near-optimal split points in sorted string tables so your mappers didn't end up with hotspots. If you had shown me Algorithm R in a stats class, I don't think I would have appreciated it at all, but seeing the code implementation and a useful example made it click.