A fun follow up is asking a candidate how to compute the 25th and 75th percentiles or more broadly, the n-th percentile.
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.
To wit, given the unordered set:
[ 5, 1, 3 ]
Oh, you … ;-)
> # implications of sorted() vs numbers.sort()?
I thought references were passed by value in languages like Python? I am not particularly fond of Python, so my experience with and knowledge of the language are quite limited. But, I understand what the question is asking: mutation vs. the creation of a new object.
From the article:
> It can lead to some discussion about statistics and why you might prefer a median to a mean in most cases.
My best example for median vs mean is property prices, where very expensive properties will skew the mean (average value) upwards but the median (middle value) will remain about the same.
I think the lore is that it was a bug in Java?'s binary search lib decades ago?
QuickSelect is average case n, and is, roughly, quick sort where you throw away one of the sides each time and recurse on the other. This has a fat tail for cases where you pick a bad pivot (similar to quicksort), but you can median-of-medians your way out of that problem if someone cares. (Median of medians being where you subdivide the array into, say, 5 arrays, recursively compute the median on those, and pick the middle median as your pivot, which guarantees linear progress per iteration)
Computing a moving average with samples being pumped through an n-element buffer is easy. Doing so for the median requires more thought. It's also very useful e.g. for removing single-sample noise from an audio track, so it's not a meaningless exercise.
Eventually most of those started getting spoiled too lol.
How about something like the beginnings of a spreadsheet engine?
Or.. count the number of distinctly shaped black regions in a bitmap image.
There is also an approximate algorithm that does not keep all the data in memory at the same time.
apricot•1h ago
salamanderman•57m ago