6 ms·
A curious case of O(N^2) behavior which should be O(N) (2023)
- Sharlin 2y agoMore accidentally quadratic stories: https://www.tumblr.com/accidentallyquadratic https://www.tumblr.com/accidentallyquadratic
- samatman 2y agoA classic. Every time I see that link I read the whole thing starting from the new beginning. ...oops
- dgfitz 2y agoI opened the link and just started reading. I have a really dumb question that may expose common knowledge I don’t have, about this quote: > The total amount of space needed to represent this collection of strings is O(k n^2). I haven’t seen O-notation ever represent ram usage, just algorithm complexity. Is this common?
- nneonneo 2y agoYes, very common. You've seen "time complexity"; it's very common to talk about "space complexity" as well.
- consp 2y agoFun bonus: they can be interchangeable, e.g. increasing space to reduce time.
- dgoldstein0 2y agoYes, but total time is never going to be less than total space, when expressed in big-O notation
- xigoi 2y agoWhy couldn’t it?
- yxhuvud 2y agoBecause it takes n time to access n units of memory. Heavily simplified due to caches etc. To the point where people sometimes measure in cache misses instead as that is usually what actually matters.
- xigoi 2y agoWhat if you allocate a huge chunk of memory and only use a small part of it? For example, checking if a list of numbers contains duplicates using a boolean array.
- Sharlin 2y agoIf your algorithm requires O(n) memory, any O(1) amount of memory can never be enough, no matter how huge. That's the entire point of O notation. And if your implementation of an algorithm allocates more space in the big-oh sense than it can actually touch (eg. O(n) space for O(log n) time or whatever), that's just a wasteful implementation. Doesn't make the algorithm itself require more space than it has time to actually use.
- ajuc 2y agoLet's say you have a lookup table and your algorithm looks up a value and returns it. O(n) space O(1) in time.
- yxhuvud 2y agon is some value depending on the size of the input, so if you have a look up table that is O(n), then that memory needs to be initialized somehow. If you have a fixed size lookup table then it is O(1), even if it is big.
- asboans 2y agoAnd any operation that takes n bits as input can be trivially turned into an O(1) time and O(2^n) space algorithm through tabulation.
- nneonneo 2y agoAssuming you ignore or amortize the time necessary to create the table in the first place, of course. This is the basis for rainbow tables: precomputed tables for mapping hashes to passwords, with a space-saving “hash chaining” trick to effect a constant factor reduction in table size. Such tables are the reason why passwords must be hashed with a unique salt when stored in a database.
- masklinn 2y ago> Is this common? Very. For instance if you look at sorting algorithms on wikipedia they pretty much all list performance (best, worst, average) but also worst-case space complexity, in O notation.
- itronitron 2y agoIs there a way to do that without signing in?
- Liftyee 2y agoNeat find! This proves to me a huge benefit of open source software: individual developers can satisfy their curiosity towards particular issues (with additional motivation from being personally affected) and improve the package for everyone once it's fixed.
- bla3 2y agoExcept it wasn't improved in this case, if I'm reading the gist correctly. The author didn't like their fix enough to make a pull request.
- EdSchouten 2y agoJust like “this entire meeting could have been an email”, all this effort writing this gist could have been spent creating a PR.
- dmitrygr 2y agoWhy not just change the “%s.%u” to “%s.%010u” and no code changes?
- andrelaszlo 2y agoIf I understood the article correctly it caused problems when the same file was imported multiple times, or when another file with the same base name was imported. https://gist.github.com/bssrdf/397900607028bffd0f8d223a7acdce7e#solution https://gist.github.com/bssrdf/397900607028bffd0f8d223a7acdc...
- dmitrygr 2y agoYes, TFA says the issue is because "12345" sorts before "9888" My solution avoids that.
- consp 2y agoYou just created a fix up to a large, but arbitrary, number just pushing the problem down the road instead of fixing it.
- nrdvana 2y agoWhy was the solution not to get rid of the linked list and replace it with a red/black tree?
- thayne 2y agoOr hash table, or any other kind of tree. My guess would be because it was implemented in c, where the usual practice if you need a container type other than a fixed size array is to implement it yourself. IME, c code tends to use linked lists for a lot of things that in most other languages would be implemented using a better suited, and more performent, container type from the standard library. One way that other languages can outperform c, is it is easier to use the right data structure.
- masklinn 2y agoBlender's not even in C (the snippets are clearly C++), I wonder what the logic of having a sorted doubly linked list is: unless it's a skip list it's not like you can do bisection searches. I guess a flat array could still be debatable if you're usually inserting near but not at the end, as it'll still need to move all the following elements. But it seems dubious.
- Epa095 2y agoI got the impression that the expected performance of the double linked list insertion is actually O(1), since in most cases the elements arrive in sorted order. It's been a time since my algorithm courses, but I think all the 'normal' trees have log(n) insertion in that case.
- nrdvana 2y agoO(n) is generally indistinguishable from O(log n) so if there is any chance of different behavior than the expected optimum, go with the better algorithm.
- deleted 2y ago[deleted]
- geuis 2y ago"Now, it should be clear that most of the time (28s-53s on the time line) of importing that particular USD file is spent in id_sort_by_name". Luckily there's a graph screenshot. But the graph it displays is incomprehensible. Without "id_sort_by_name" being on the one bar, I wouldn't even know what I'm looking at.
- wtallis 2y agoThe timeline view in the upper screenshot is fairly straightforward: the region of 28-53s is selected, other parts of the timeline are grayed out, and the statistics for the selected time region down below show 94.4% of "Total CPU" being in id_sort_by_name. The lower screenshot is a flame graph. If you haven't encountered one of those before, it's totally reasonable to not know how to read it. But it's a standard and common way to present this sort of data. See https://www.brendangregg.com/flamegraphs.html https://www.brendangregg.com/flamegraphs.html for more information.
- ojbyrne 2y ago“alphebatically” is used 3 times, and otherwise no typos that I noticed. So I wondered if it’s a term I’m not familiar with.
- purplesyringa 2y agoAh yes, the most reliable solution to a wrong choice of a data structure: add data-specific hacks until it works. For the life of me I can't figure out why people never consider replacing linked lists. Even without worst-case O(n) insertion, they usually behave worse than vectors, deques, or hives.
- mjevans 2y agoThere's also the choice of data structure that appears to force multiple copies of the same thing rather than thin references and ideally copy on modify.
- xigoi 2y agoWhat is a hive in the context of data structures?
- masklinn 2y agoI assume it's an autocorrect of heap.
- purplesyringa 2y agoI meant something close to https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p0447r15.html https://www.open-std.org/jtc1/sc22/wg21/docs/papers/2021/p04... Perhaps a simple way to look at it is that it's like a dynamic array, but when the capacity is exceeded, you don't reallocate the array, just just allocate a new (exponentially larger) chunk and keep the old one as-is. Then just link the chunks in a (very short) linked list, or keep a separate small list of chunks (you're never gonna need more than 48, so you can just have a fixed allocation for it), or what have you. The bonus here is that it reduces latency on pushing and has more predictable performance.
- rokkamokka 2y agoWhile taking a computational complexity course I wrote some python code that should have run in O(n) but was closer to O(n^2). After asking StackOverflow and some more experimentation it turns out the garbage collector turned it O(n^2) - turning it off manually yielded the correct O(n) runtime
- eska 2y ago2 questions I would look into before anything else: 1. Does this have to be sorted? 2. Why is it sorted alphabetically instead of naturally?
- Neywiny 2y agoI had something like this. I was making a script that would parse a standardized file describing a molecule and create the atoms and bonds and whatnots. I found out that they time an object is added it iterates through all the objects to update them of the addition. This was very noticable even around 1k objects. I later grouped all the duplicated objects (such as all the oxygens) into 1 discontinuous object, leading to O(1 [the bonds] + #elements) instead of O(#bonds * #atoms). In the end I still lost out to another package that did the same function a lot faster. May be interesting to look back to see how they did it.