[0]: https://eel.is/c++draft/alg.move#15
[1]: https://eel.is/c++draft/input.streams#istream.extractors-7
Also, keep an eye out for "amortized" complexity. This does have a legitimately rigorous definition, but for latency-bound paths it can practically amount to "O(whatever), except for the particular invocations that are far, far worse under unspecified conditions".
[1] https://www.man7.org/linux/man-pages/man3/gets.3.html#BUGS
But, yes. (naive) Quicksort's amortized complexity being O(nlogn), but its O(n^2) on already sorted data, is all I ever needed to learn to take away that lesson. When sorting already sorted data is worse than sorting randomized data, it's a quick realization that "amortized cost" = "read the fine print".
It can be n*n for properly-sorted arrays too, depending on pivot selection (for randomized pivot selection, it's n log n).
But I'm pretty sure data sorted in either direction (i.e., 'reversed' or not, ascending or descending), and taking a pivot from either end, is n^2. It doesn't have to be reversed; you always end up with everything unsorted ending up on one side or the other of the pivot, with each recursive step being just one less comparison than the step prior, meaning it has N-1 + N-2 + ... + 1 comparisons regardless of which way the array is sorted, or N(N-1)/2 comparisons total (Gauss' formula but starting at one less than the total number of items N, since that's the number of comparisons each step), which is O(N^2). There is no cause where it's linear time, unless you are first iterating across the array to select the first pivot that is out of place (which may be a reasonable optimization, but can also be made to apply regardless of what direction the array is sorted).
Often such a grid will be quite well abstracted from its data source - it might be executing a remote query to return data in the new order every time - but I bet there are some examples out there that are backed by a local dataset and carry out an actual sort operation when you hit the header... and fall into a quicksort worst case if the user clicks the same header twice in a row.
<http://cantrip.org/sortfast.html>
Anyway I thought it was interesting.
vector.push(x)
Most of the time, it's O(1). Sometimes it's O(n). If you double the size of the backing array when it runs out of space, it's amortized O(1).From: https://stackoverflow.com/a/185576/368409
/* This is O(scary), but seems quick enough in practice. */I’d respond with “well if performance matters it shouldn’t be in js” except for all the shite being written in js these days, with js being the hammer that makes everything else look like a nail.
You can write very fast JS code. When carefully written it can have Java like performance[2]. It is just very hard in practice where most ecosystem is optimized for developer productivity.
When performance matter, write your own code and carefully benchmark everything. You can see this working for Typescript and VSCode[3]
[1] https://v8.dev/blog [2] https://benchmarksgame-team.pages.debian.net/benchmarksgame/... [3] https://github.com/microsoft/TypeScript/pull/43035#issuecomm...
This isn't a big difficulty; it's still amortized O(1).
> and there isn't a hash collision
This is a real difficulty, unless you allow map resizing. Luckily, we do.
> but it's generally not true in respect to the key length.
OK, but in most cases the key length is constant, making anything that depends on the key length O(1) by definition.
[1] Not typical. e.g. Java takes the hash key of an object to be its address in memory, which doesn't require looking at the contents.
Right, that’s exactly what they are warning about.
Not typical. e.g. Java takes the hash key of an object to be its address in memory
No, that’s just the base implementation in Object (and arguably it was a bad idea). All useful “value type” classes will override it with a real hash of the content, including String.
There are some cases in Java where you do want to use IDs instead of values as your map keys, but they’re rare.
Well, this is necessary for a lot of sensible things you'd want to do with non-numeric value types as hash keys...
> including String
...except String is something of an intermediate case. There are loads of use cases where what you're really using is a set of constant strings, not variables that contain arbitrary character data. In that case, you should intern the strings, resulting in non-"value type" keywords where the only thing you care about for equality is whether two keywords do or don't have the same machine address.
I don't actually know how Java handles this, but I had the vague idea that two equal String literals will in fact share their machine address. And String is specifically set up to accommodate this; Strings are immutable, so in theory it could easily be the case that any two equal Strings must share their machine address, even if you got them from user input.
Hey, and now you have two problems: String hashing and finding all strings which are equal to each other in memory
And this isn't exactly some exotic approach; how often do you think people write Hashes in Ruby where the keys they use are all symbols? It's so common that there's dedicated syntax for it.
The problem is, interning is an expensive operation. It means adding to an ever growing database of strings, but first checking if the string isn't already there. You don't want to do that every time you change case or flip a letter in a string, or use it to access a hash table. I'm not saying it can't be done, but I honestly have no idea how to implement sane, generic, automatic interning of strings. I feel more comfortable having a symbol type, and control over turning strings into symbols.
(And on a less fundamental level, the particular Java String class is less string-like and more symbol-like than most string types, and this appears to have been done intentionally.)
Earlier discussion: https://news.ycombinator.com/item?id=9807739
Not even close. 2^k is not O(1) by virtue of N being constant. Only 2^N.
This has been covered above. It is more common to consider the complexity of hash table operations in terms of the number of operations, or the size of the table; the size of the key is very often constant. These are different variables; the constant size of the key does not trivialize the complexity of inserting N items each with a constant key size.
Earlier discussion: https://news.ycombinator.com/item?id=9807739
The same approach applies to key length requirements for hash tables with arbitrarily large backing stores. They do not grow as slowly as the CLRS log* function, but they grow so slowly that there are easily identifiable sharp limits on how large they can be -- an easy example is that a hash table cannot use more memory than the hardware offers no matter how the software is written. A backing store with 1TB of addressable bytes cannot need the key to be more than 40 bits long.
On a different note, by "table size" in my earlier comment I meant to refer to the number of entries in the table, not the capacity of the backing store. It seems like you might be using the same word for a different concept?
So? That's still putting a bound on table size, which makes it in-practice constant, but doesn't make the algorithm O(1), because you can never get such a result by bounding n, for the reasons the GGP gave -- that's cheating.
Your complexity bound has to be written on the assumption that n (number of elements to store in hashtable) increases without bound. Assuming you will never use more that Y bytes of data is not valid.
>On a different note, by "table size" in my earlier comment I meant to refer to the number of entries in the table, not the capacity of the backing store. It seems like you might be using the same word for a different concept?
No, I was using table size exactly as you, to mean the number of elements stored. Is there a reason my comments only made sense under a different definition? It not, be charitable. (And avoid using obscure terms.)
I interpreted your comment to refer to the size of the backing store, because that is fundamentally what a hash key needs to be able to address.
I didn't mean to say that, if you were using it that way, you were doing anything wrong, only that there appeared to be a mismatch.
Under the assumption (upthread) of constant resizing as element are added, the distinction is irrelevant. The more elements you have in the table, the more elements you need to address, and the more possible outputs your hash function needs to have.
And the needed size of the backing store scales with the number elements you want to store anyway.
>I didn't mean to say that, if you were using it that way, you were doing anything wrong, only that there appeared to be a mismatch.
Why bring up something like that if it doesn't translate into something relevant to the discussion e.g. to show my point to be in error?
> Note that some implementations of sscanf involve a call to strlen, which makes their runtime linear on the length of the entire string. This means that if sscanf is called in a loop to repeatedly parse values from the front of a string, your code might run in quadratic time
I have a bad memory for all but most frequently used standard library calls, so I regularly end up refreshing my memory from cppreference.com, and I tend to instinctively scan any notes/remarks sections, as there's often critical information there. So now I can be sure I'll be reminded of this the next time I need to use scanf family.
Yet another reason to not stringify floats. Just use hexfloats (but beware of C++ standard bugs involving >>) or binary.
Unfortunately "gigabytes of numerical data, but formatted as a text file" is commonplace. For some reason HDF5 is far less popular than it ought to be.
I think you're right that there is no upper bound but it shouldn't be necessary to do a full strlen() if you're instead scanning incremental. You could go char by char until the pattern '%f' is fullfilled and then return. That would solve the issue on it's root -- and who know how many programs would suddenly get faster...
So looking at glibc souces I've found the culprit in abstraction. Looks like a FILE* like stringbuffer object is created around the c-string: https://sourceware.org/git/?p=glibc.git;a=blob;f=stdio-commo...
And that abstraction does call something similiar to strlen() when initializing to know it's bounds here: https://sourceware.org/git/?p=glibc.git;a=blob;f=libio/strop...
I'm reading this source the first time, but I guess to not break anything one could introduce a new type of FILE* stringbuffer let's say in 'strops_incr.c' that is working incrementally reading one char at the time from the underlying string skipping the strlen()...
Would be awesome cool if GTA online would be loading faster under wine than on windows :-)
The XML library we use is rather well-known, so if someone found a bug like this there, I'd suspect a general improvement of performance across the board in the entire industry. Efficient Market Hypothesis tells me it's unlikely the library has this problem, but then again, so I thought about AAA videogames, and then GTA Online thing came out.
The prehistory of that was simple: up to some point the amount of data stored was reasonably small. Then from some point on the amount of data grew significantly (a few orders of magnitude), and the startup times became very unpleasant.
There's a lot that is going on when loading huge XML files. As an example, don't forget all the possible Unicode conversions, all the possible allocations of the elements in the handling code, just to be discarded etc.
I don't suggest everybody doing it "just because" but if some specific use is known to have very specific assumptions and it is in the "hot path" and really dominates (profile first!) and it is known that only a small subset of all XML possibilities will ever be used it can be justified to avoid the heavy libraries. For example, in that specific case, I knew that the XML is practically always only read and written by the application, or by somebody who knew what he was doing, and not something that somebody random in some random form would regularly provide from the outside, and I knew that my change surely won't break anything for years to come, as I knew for sure that that part of application was not the "hot spot" of expected future changes.
So it was a win-win. Immensely faster application startup, which is something that improved everybody's work, while preserving the "readability" of that file for the infrequent manual editing or control (and easy diff).
One of the main factors seems to be that a lot of XML parser libraries, even the high-profile ones, did a lot of unnecessary copy operations. D's language features made it easy and safe to avoid unnecessary copying.
I wonder what became of that Tango code.
[0] https://web.archive.org/web/20140821164709/http://dotnot.org... , see also reddit discussion where WalterBright makes an appearance, https://old.reddit.com/r/programming/comments/6bt6n/why_is_d...
Any sufficiently-complex library code likely has plenty of problems, often unavoidably so (e.g. trade-offs between best performance and edge cases). Whether they have been found or not is a function of many, many factors.
> Efficient Market Hypothesis
I've lived long enough to be very sceptical about that sort of thing. Markets tend to be efficient in aggregate, maybe, but on the single case they can fail quite brutally. Look at how "dramatic" bugs are overlooked even in critical pieces of infrastructure like openssl, for years and years; maybe it happens less for openssl than most equivalent libraries, but it still happens.
Also, once the "market" for standards moves on, network effects make it very hard to have any meaningful competition. I mean, who writes XML parsers nowadays? Whichever XML lib was winning when JSON "happened" is now likely to stay in control of that particular segment; and the likelihood that top developers will keep reviewing it, falls off a cliff. Sprinkle a bit of cargo-cultism on top, and "efficient markets" become almost a cruel joke.
I've also seen this story unfold too many times:
code code code build run fail
> dammit, I could have sworn this was correct?!
think think think GOTO 1
> no way, my code has to be wrong, this can't be the compiler?! it's never the compiler! right?
reduce code to a generic two liner, build, run, fail
> oh.
open support ticket at compiler vendor
Let's say the GP's XML library has The GTA Bug, i.e. it uses a quadratic-performance loop when parsing. The bug will go undiscovered until any one consumer of the library a) sees enough performance impact to care, b) has the expertise to profile their application and finds that the library is at fault, and c) reports the problem back to the library owner so that it can be fixed. This combination might be unlikely but since only one consumer has to have all those properties, the probability scales inversely with the number of library users.
(Or maybe in your case something was running strlen() a lot during parsing, and just the difference in file size explains the boost?)
I like binary formats, but we can't afford the increased complexity around supporting a custom binary format, so I'm not pushing for changes here.
I did investigate replacing our pile of XML files with an SQLite database, which would give us fast and efficient format, and allow to use existing SQLite database viewers, or hit the file with trivial scripts, so we'd have no complexity supporting a dedicated tool. However, the data model we use would need such a large overhaul (and related retraining) that we tabled this proposal for now.
IMO, while I really don't come to HN to find dial-a-joke, or joke-of-the-day, I think some humor is essential in modern life.
Since we're talking about Matt Keeter, you will find he has a great sense of humor if you read his website or interact with him. Some of his jokes are ROTFL funny, but subtle.
I did have a nice half round of golf today with my wife. What a beautiful day to spend with such a wonderful person!
I'm out.
>> So many years ago when I first took over the iOS string functions, I found that like 30% of boot time in debug builds was in strstr. <<
>> Needless to say, we did not fix that issue by writing a more efficient strstr. Removed the parser and then removed strstr from the environment where it had been in use =) <<
> ...Tomorrow, someone’s going to reduce the boot times of macOS by 90% by the same principle.
My 2019 MacBook often pauses when I connect the charging cable. Sometimes it just seizes, requiring a hard bounce.
Clearly there's a contended lock buried deep. Something non-obvious.
I'm certain everything these days has dozens of hidden quadratics and contended locks.
Which is one of the reasons I'm excited for stuff like structured concurrency (Java's Project Loom) and retoolings like systemd becoming the norm.
Ages ago I worked on kitchen sink app that had a very finicky startup. Any breeze would break it. Much consternation by mgmt. Apparently if we only clapped louder, Tinkerbell would fly. I couldn't take it any more. LARPing as a bulldozer, I replumbed the innards, changing from something like initd to be more like systemd with some lazy loading for good measure. Voila!
Back to GTA. The failure here is the product owner didn't specify a max load time, and then hold the team to it. Devs will mostly do the work that's expected of them. If load time wasn't measured (and managed), no one is going to bother with expunging sscanfs.
Yesterday my MBP kernel panicked because my keyboard was low on battery and the bluetooth connection kept dropping. There's something weird with MacOS where peripherals seem to really not be well isolated from the core OS runtime.
(I find it pretty exciting, that this kind of negative result is possible. Ain't mathematics wonderful?)
You owe me a keyboard!