A generally asked question is whether we should use unordered_map or map for faster access.
The most common( rather age old ) answer to this question is:
If you want direct access to single elements, use unordered_map but if you want to iterate over elements(most likely in a sorted way) use map.
Shouldn't we consider the data type of key while making such a choice?
As hash algorithm for one dataType(say int) may be more collision prone than other(say string).
If that is the case( the hash algorithm is quite collision prone ), then I would probably use map even for direct access as in that case the O(1) constant time(probably averaged over large no. of inputs) for unordered_map map be more than lg(N) even for fairly large value of N.
You raise a good point... but you are focusing on the wrong part.
The problem is not the type of the key, per se, but on the hash function that is used to derive a hash value for that key.
Lexicographical ordering is easy: if you tell me you want to order a structure according to its 3 fields (and they already support ordering themselves) then I'll just write:
bool operator<(Struct const& left, Struct const& right) {
return boost::tie(left._1, left._2, left._3)
< boost::tie(right._1, right._2, right._3);
}
And I am done!
However writing a hash function is difficult. You need some knowledge about the distribution of your data (statistics), you might need to prevent specially crafted attacks, etc... Honestly, I do not expect many people of being able to craft a good hash function. But the worst part is, composition is difficult too! Given two independent fields, combining their hash value right is hard (hint: boost::hash_combine).
So, indeed, if you have no idea what you are doing and you are treating user-crafted data, just stick to a map. It's maybe slower (not sure), but it's safer.
There isn't really such a thing as collision prone object, because this thing is dependent on the hash function you use. Assuming the objects are not identical - there is some feature that can be utilized to create an informative hash function to be used.
Assuming you have some knowledge on your data - and you know it is likely to have a lot of collision for some hash function h1() - then you should find and use a different hash function h2() which is better suited for this task.
That said, there are other issues as well why to favor tree based data structures over hash bases (such as latency and the size of the set), some are covered by my answer in this thread.
There's no point trying to be too clever about this. As always, profile, compare, optimise if useful. There are many factors involved - quite a few of which aren't specified in the Standard and will vary across compilers. Some things may profile better or worse on specific hardware. If you are interested in this stuff (or paid to pretend to be) you should learn about these things a bit more systematically. You might start with learning a bit about actual hash functions and their characteristics. It's extremely rare to be unable to find a hash function that has - for all practical purposes - no more collision proneness than a random but repeatable value - it's just that sometimes it's slower to approach that point than it is to handle a few extra collisions.
Related
I'm trying to create a general memoizator for multiple and arbitrary functions.
For each function std::function<ReturnType(Args...)> that we want to memoize, we unordered_map<Args ..., ReturnType> (I'm keeping things simple on purpose).
The big problem comes when our memoized function has some really big argument Args ...: for example let suppose that our function sort a vector of 10 millions numbers and then returns the sorted vector, so something like std::function<vector<double>(vector<double>)>.
As you can imagine, after having inserted less than 100 vectors, we have already filled 8 GBS of memory. Notice that maybe this is given from the combination of huge vectors and the memory required by the sorting algorithm (I didn't investigate on the causes).
So what about if instead of the structure described above, we define unordered_map<UUID(Args ...), ReturnType> (where UUID= Universally Unique Identifier)? We should relax the deterministic feature (so maybe we return a wrong error), but with a very low probability.
The problem is that since I never used UUIDs, I don't know if there are suitable implementations for this application.
So my question is:
There exists a better solution than UUIDs for this problem?
Which UUID implementation is better suitable for this problem?
boost uuid is a possible candidate?
Unfortunately, the problem could be solved for Args ... but not for ReturnType, so there is a solution for memoized result?
Notice that the UUIDs generated for the object x should be the same even in different runs and machines.
Notice that if we have the same UUID for two different objects (and so we return the wrong value) with a really low probability, then it could be acceptable...let's say that this could be a "probabilistic memoizator".
I know that this application doesn't make sense in a memoization context (what are the odds that an user asks two times to sort the same 10 millions elements vector?), but it's time and memory expensive (so good for benchmarking and to introduce the memory problem that I stated above), so please don't whip and crucify me because this is an absurd memoization application.
Identifying any object is easy. The address is "object identity" in C++. This is also the reason that even empty classes cannot have zero size.
Now, what you want is value equivalence. That's strictly not in the language domain. It's solidly in the application/library logic domain.
You should consider using something like boost::flyweights. It has precisely this facility, and makes it "easy" to customize the equivalence semantics for your types.
I am looking for some map which has fixed keys (fixed during initialization) and that does faster look-up. It may not support adding/updating elements later. Is there some algorithm which looks the list of keys and formulates a function so that it is faster to look-up later. In my case, keys are strings.
Update:
Keys are not known at compile time. But during initialization time of the application. There wont be any further insertions later but there will be lots of look-ups. So I want look-ups to be optimized.
CMPH may be what you're looking for. Basically this is gperf without requiring the set at compile-time.
Though of course std::unordered_map as by C++11 might just do too, though possibly with a few collisions.
Since you lookup strings, for strings, a trie (any of the different trie flavours, crit-bit or whatever funky names they have) may also be worthwhile to look into, especially if you have many of them. There are a lot of free trie implementations freely available.
The advantage of tries is that they can index-compress strings, so they use less memory, which has a higher likelihood of having data in cache. Also the access pattern is less random, which is also cache-friendly. A hash table must store the value plus the hash, and indexes more or less randomly (not randomly, but unpredictably) into memory. A trie/trie-like structure ideally only needs one extra bit that distinguishes a key from its common prefix in each node.
(Note by the way that O(log(N)) may quite possibly be faster than O(1) in such a case, because big-O does not consider things like that.)
Note that these are distinct things: do you need an upper limit, do you need a fast typical rate, or do you need the fastest lookup ever, no questions asked? The last one will cost you, the first two ones may be conflicting goals.
You could attempt to create a perfect hash function based on the input (i.e. one that does not have collisions of the input set). This is a somehow-solved problem (e.g. this, this). However, they usually generate source code and may spend significant time generating the hash function.
A modification of this would be using a generic hash function (e.g. shift-multiply-add) and do a brute force search over suitable parameters.
This has to be traded off with the cost of a few string comparisons (which aren't that terribly expensive if you don't have to collate).
Another option is to use two distinct hash functions - this increases the cost of a single lookup but makes degradation slightly less likely than aliens stealing your clock cylces. It is rather unlikely that this would be a problem with typical strings and a decent hash function.
Try google-sparsehash: http://code.google.com/p/google-sparsehash/
An extremely memory-efficient hash_map implementation. 2 bits/entry overhead!
The SparseHash library contains several hash-map implementations, including
implementations that optimize for space or speed.
In a similar topic ((number of) items known at compile time) , I produced this one: Lookups on known set of integer keys. Low overhead, no need for perfect hash. Fortunately, it is in C ;-)
Is there a way to write simple hashtable with the key as "strings" and value as the frequency, so that there are NO collisons? There will no be removal from the hashtable, and if the object already exists in the hashtable, then just update its frequency(add them together).
I was thinking there might be a algorithm that can compute a unique number from the string which will be used as the index.
Yes, i am avoiding the use of all STL construct including unordered_map.
You can use any perfect hash generator like gperf
See here for a list: http://en.wikipedia.org/wiki/Perfect_hash_function
PS. You'd still possibly want to use a map instead of flat array/vector in case the mapped domain gets too big/sparse
It really depends on what you mean by 'simple'.
The std::map is a fairly simple class. Still, it uses a red-black tree with all of the insertion, deletion, and balancing nicely hidden away, and it is templated to handle any orderable type as a key and any type as the value. Most map classes use a similar implementation, and avoid any sort of hashing functionality.
Hashing without collisions is not a trivial matter whatsoever. Perhaps the simplest method is Pearson Hashing.
It seems like you have 3 choices:
Implement your own perfect hashing class. This would be a pretty good sized class with a lot of functionality and some decently complex algorithms. I don't think this is simple.
Download and use a perfect hashing library that is already out there. Of course, you have to worry about deployability.
Use STL's map class. It's embedded, well-documented, easy to use, type-flexible, and completely cross-platform. This seems like the 'simplest' solution.
If I may ask, Why are you avoiding STL?
If the set of possible strings is known beforehand, you can use a perfect hash function generator to do this. But otherwise, what you ask is impossible.
Now, it IS possible to make the likelihood of collisions extremely low by using a good hash function and making sure your table is huge. You basically need a big enough table to make the likelihood of invoking the Birthday Paradox low enough to suit you. Then you just use n bits of output from SHA-1, and 2^n will be your table size.
I'm also wondering if maybe you could use a Bloom filter and have an actual counter instead of bits. Keep a list of all the words you've stuffed into the bloom filter and what entries they've incremented (which will be the same each time) and you have yourself a gigantic linear function that you might be able to solve to get all the individual counts back out again.
I'm developing game. I store my game-objects in this map:
std::map<std::string, Object*> mObjects;
std::string is a key/name of object to find further in code. It's very easy to point some objects, like: mObjects["Player"] = .... But I'm afraid it's to slow due to allocation of std::string in each searching in that map. So I decided to use int as key in that map.
The first question: is that really would be faster?
And the second, I don't want to remove my current type of objects accesing, so I found the way: store crc string calculating as key. For example:
Object *getObject(std::string &key)
{
int checksum = GetCrc32(key);
return mObjects[checksum];
}
Object *temp = getOject("Player");
Or this is bad idea? For calculating crc I would use boost::crc. Or this is bad idea and calculating of checksum is much slower than searching in map with key type std::string?
Calculating a CRC is sure to be slower than any single comparison of strings, but you can expect to do about log2N comparisons before finding the key (e.g. 10 comparisons for 1000 keys), so it depends on the size of your map. CRC can also result in collisions, so it's error prone (you could detect collisions relatively easily detect, and possibly even handle them to get correct results anyway, but you'd have to be very careful to get it right).
You could try an unordered_map<> (possibly called hash_map) if your C++ environment provides one - it may or may not be faster but won't be sorted if you iterate. Hash maps are yet another compromise:
the time to hash is probably similar to the time for your CRC, but
afterwards they can often seek directly to the value instead of having to do the binary-tree walk in a normal map
they prebundle a bit of logic to handle collisions.
(Silly point, but if you can continue to use ints and they can be contiguous, then do remember that you can replace the lookup with an array which is much faster. If the integers aren't actually contiguous, but aren't particularly sparse, you could use a sparse index e.g. array of 10000 short ints that are indices into 1000 packed records).
Bottom line is if you care enough to ask, you should implement these alternatives and benchmark them to see which really works best with your particular application, and if they really make any tangible difference. Any of them can be best in certain circumstances, and if you don't care enough to seriously compare them then it clearly means any of them will do.
For the actual performance you need to profile the code and see it. But I would be tempted to use hash_map. Although its not part of the C++ standard library most of the popular implentations provide it. It provides very fast lookup.
The first question: is that really would be faster?
yes - you're comparing an int several times, vs comparing a potentially large map of strings of arbitrary length several times.
checksum: Or this is bad idea?
it's definitely not guaranteed to be unique. it's a bug waiting to bite.
what i'd do:
use multiple collections and embrace type safety:
// perhaps this simplifies things enough that t_player_id can be an int?
std::map<t_player_id, t_player> d_players;
std::map<t_ghoul_id, t_ghoul> d_ghouls;
std::map<t_carrot_id, t_carrot> d_carrots;
faster searches, more type safety. smaller collections. smaller allocations/resizes.... and on and on... if your app is very trivial, then this won't matter. use this approach going forward, and adjust after profiling/as needed for existing programs.
good luck
If you really want to know you have to profile your code and see how long does the function getObject take. Personally I use valgrind and KCachegrind to profile and render data on UNIX system.
I think using id would be faster. It's faster to compare int than string so...
In one of the applications I work on, it is necessary to have a function like this:
bool IsInList(int iTest)
{
//Return if iTest appears in a set of numbers.
}
The number list is known at app load up (But are not always the same between two instances of the same application) and will not change (or added to) throughout the whole of the program. The integers themselves maybe large and have a large range so it is not efficient to have a vector<bool>. Performance is a issue as the function sits in a hot spot. I have heard about Perfect hashing but could not find out any good advice. Any pointers would be helpful. Thanks.
p.s. I'd ideally like if the solution isn't a third party library because I can't use them here. Something simple enough to be understood and manually implemented would be great if it were possible.
I would suggest using Bloom Filters in conjunction with a simple std::map.
Unfortunately the bloom filter is not part of the standard library, so you'll have to implement it yourself. However it turns out to be quite a simple structure!
A Bloom Filter is a data structure that is specialized in the question: Is this element part of the set, but does so with an incredibly tight memory requirement, and quite fast too.
The slight catch is that the answer is... special: Is this element part of the set ?
No
Maybe (with a given probability depending on the properties of the Bloom Filter)
This looks strange until you look at the implementation, and it may require some tuning (there are several properties) to lower the probability but...
What is really interesting for you, is that for all the cases it answers No, you have the guarantee that it isn't part of the set.
As such a Bloom Filter is ideal as a doorman for a Binary Tree or a Hash Map. Carefully tuned it will only let very few false positive pass. For example, gcc uses one.
What comes to my mind is gperf. However, it is based in strings and not in numbers. However, part of the calculation can be tweaked to use numbers as input for the hash generator.
integers, strings, doesn't matter
http://videolectures.net/mit6046jf05_leiserson_lec08/
After the intro, at 49:38, you'll learn how to do this. The Dot Product hash function is demonstrated since it has an elegant proof. Most hash functions are like voodoo black magic. Don't waste time here, find something that is FAST for your datatype and that offers some adjustable SEED for hashing. A good combo there is better than the alternative of growing the hash table.
#54:30 The Prof. draws picture of a standard way of doing perfect hash. The perfect minimal hash is beyond this lecture. (good luck!)
It really all depends on what you mod by.
Keep in mind, the analysis he shows can be further optimized by knowing the hardware you are running on.
The std::map you get very good performance in 99.9% scenarios. If your hot spot has the same iTest(s) multiple times, combine the map result with a temporary hash cache.
Int is one of the datatypes where it is possible to just do:
bool hash[UINT_MAX]; // stackoverflow ;)
And fill it up. If you don't care about negative numbers, then it's twice as easy.
A perfect hash function maps a set of inputs onto the integers with no collisions. Given that your input is a set of integers, the values themselves are a perfect hash function. That really has nothing to do with the problem at hand.
The most obvious and easy to implement solution for testing existence would be a sorted list or balanced binary tree. Then you could decide existence in log(N) time. I doubt it'll get much better than that.
For this problem I would use a binary search, assuming it's possible to keep the list of numbers sorted.
Wikipedia has example implementations that should be simple enough to translate to C++.
It's not necessary or practical to aim for mapping N distinct randomly dispersed integers to N contiguous buckets - i.e. a perfect minimal hash - the important thing is to identify an acceptable ratio. To do this at run-time, you can start by configuring a worst-acceptible ratio (say 1 to 20) and a no-point-being-better-than-this-ratio (say 1 to 4), then randomly vary (e.g. changing prime numbers used) a fast-to-calculate hash algorithm to see how easily you can meet increasingly difficult ratios. For worst-acceptible you don't time out, or you fall back on something slower but reliable (container or displacement lists to resolve collisions). Then, allow a second or ten (configurable) for each X% better until you can't succeed at that ratio or reach the no-pint-being-better ratio....
Just so everyone's clear, this works for inputs only known at run time with no useful patterns known beforehand, which is why different hash functions have to be trialed or actively derived at run time. It is not acceptible to simple say "integer inputs form a hash", because there are collisions when %-ed into any sane array size. But, you don't need to aim for a perfectly packed array either. Remember too that you can have a sparse array of pointers to a packed array, so there's little memory wasted for large objects.
Original Question
After working with it for a while, I came up with a number of hash functions that seemed to work reasonably well on strings, resulting in a unique - perfect hashing.
Let's say the values ranged from L to H in the array. This yields a Range R = H - L + 1.
Generally it was pretty big.
I then applied the modulus operator from H down to L + 1, looking for a mapping that keeps them unique, but has a smaller range.
In you case you are using integers. Technically, they are already hashed, but the range is large.
It may be that you can get what you want, simply by applying the modulus operator.
It may be that you need to put a hash function in front of it first.
It also may be that you can't find a perfect hash for it, in which case your container class should have a fall back position.... binary search, or map or something like that, so that
you can guarantee that the container will work in all cases.
A trie or perhaps a van Emde Boas tree might be a better bet for creating a space efficient set of integers with lookup time bring constant against the number of objects in the data structure, assuming that even std::bitset would be too large.