Use Trie or SortedSet for Dictionary? - memory

I had some questions about usage of Tries/SortedSets for a dictionary.
Which is more efficient for lookups?
Which is more efficient for virtual memory?
Are there any other advantages/disadvantages of either structure when utilized for a dictionary?
No need to answer all three, just looking for some good responses and source material if you have any. Thanks.

Lookups in a Trie are blazing fast, as they just require O(length of key) comparisons, and are almost as fast as it's possible to be. A SortedSet is generally implemented using balanced binary search trees, which would perform many more comparisons, in the worst case O(height of tree) string comparisons. So the Trie is the clear winner here.
Virtual memory efficiency can be seen as how fast the data structure can be loaded into memory. SortedSet takes up space proportional to the number of elements. It's implemented using pointers, which can be bad for the loading efficiency. That can be improved by serializing it and storing it in an array, but that increases the space needed. A Trie in its most simple form takes a lot of memory. It's also implemented using pointers, which is again bad for loading efficiency. Even if serialized, it takes a large amount of memory. But there are interesting alternatives here, which compress the trie and give the same performance. Radix Tries take significantly less amount of memory. Even better, a DAWG (directed acyclid word graph) overlaps common suffixes and prefixes and compresses the dictionary by a huge amount. After compression, the DAWG could take less space than your dictionary itself. It is implemented using an array, so it's fast to load too. At the end, if you have a static dictionary, DAWG would be the best way to go, otherwise it depends.
A trie sees keys as sequences. It is a prefix tree. You can get all words starting from a prefix very fast. Using a trie, you can perform auto completion and auto correction efficiently. Some keys like floating point numbers, could lead to long chains in the trie, which is bad. A SortedSet sees keys as comparable items. So it is easily possible to partition the elements. Both SortedSet and Trie can offer the keys in alphabetical order, but I guess SortedSet would be much faster.

Related

Using something other than a Swift array for mutable fixed-size thread-safe data passed to OpenGL buffer

I am trying to squeeze every bit of efficiency out of my application I am working on.
I have a couple arrays that follow the following conditions:
They are NEVER appended to, I always calculate the index myself
The are allocated once and never change size
It would be nice if they were thread safe as long as it doesn't cost performance
Some hold primitives like floats, or unsigned ints. One of them does hold a class.
Most of these arrays at some point are passed into a glBuffer
Never cleared just overwritten
Some of the arrays individual elements are changed entirely by = others are changed by +=
I currently am using swift native arrays and am allocating them like var arr = [GLfloat](count: 999, repeatedValue: 0) however I have been reading a lot of documentation and it sounds like Swift arrays are much more abstract then a traditional C-style array. I am not even sure if they are allocated in a block or more like a linked list with bits and pieces thrown all over the place. I believe by doing the code above you cause it to allocate in a continuous block but i'm not sure.
I worry that the abstract nature of Swift arrays is something that is wasting a lot of precious processing time. As you can see by my above conditions I dont need any of the fancy appending, or safety features of Swift arrays. I just need it simple and fast.
My question is: In this scenario should I be using some other form of array? NSArray, somehow get a C-style array going, create my own data type?
Im looking into thread safety, would a different array type that was more thread safe such as NSArray be any slower?
Note that your requirements are contradictory, particularly #2 and #7. You can't operate on them with += and also say they will never change size. "I always calculate the index myself" also doesn't make sense. What else would calculate it? The requirements for things you will hand to glBuffer are radically different than the requirements for things that will hold objects.
If you construct the Array the way you say, you'll get contiguous memory. If you want to be absolutely certain that you have contiguous memory, use a ContiguousArray (but in the vast majority of cases this will give you little to no benefit while costing you complexity; there appear to be some corner cases in the current compiler that give a small advantage to ContinguousArray, but you must benchmark before assuming that's true). It's not clear what kind of "abstractness" you have in mind, but there's no secrets about how Array works. All of stdlib is open source. Go look and see if it does things you want to avoid.
For certain kinds of operations, it is possible for other types of data structures to be faster. For instance, there are cases where a dispatch_data is better and cases where a regular Data would be better and cases where you should use a ManagedBuffer to gain more control. But in general, unless you deeply know what you're doing, you can easily make things dramatically worse. There is no "is always faster" data structure that works correctly for all the kinds of uses you describe. If there were, that would just be the implementation of Array.
None of this makes sense to pursue until you've built some code and started profiling it in optimized builds to understand what's going on. It is very likely that different uses would be optimized by different kinds of data structures.
It's very strange that you ask whether you should use NSArray, since that would be wildly (orders of magnitude) slower than Array for dealing with very large collections of numbers. You definitely need to experiment with these types a bit to get a sense of their characteristics. NSArray is brilliant and extremely fast for certain problems, but not for that one.
But again, write a little code. Profile it. Look at the generated assembler. See what's happening. Watch particularly for any undesired copying or retain counting. If you see that in a specific case, then you have something to think about changing data structures over. But there's no "use this to go fast." All the trade-offs to achieve that in the general case are already in Array.

Storing data with large input

There is a problem in a competitive programming site(hackerrank) in which the input number is of the range 10^18.So,is it possible to store (10^18) in java?If yes then which data type should be used?
For some easy HackerRank problems, BigInteger or BigDecimal do work for extremely large inputs,but they usually don't work in moderate/difficult problems as they tend to reduce performance & a high number of test-cases of extremely large inputs can cause a timeout.
In such cases,you will need go for different storage techniques e.g. an array of int,each element of the array representing a digit of the large input. You will then need to do digit-based arithmetic on the array for your computations.
BigInteger.valueOf(10).pow(10000)
No real need not be careful, as the BigInteger.valueOf(long) method will give you a compilation error if you try to write a literal that exceeds Long.MAX_VALUE. Furthermore, it's easy to construct a BigInteger much greater, say BigInteger.valueOf(10).pow(10000)

Linked List in OpenCL

I have 1000 float datas in an array. I want to separate into different classes, lets say 4 classes. Their sizes are unpredictable. I could easily hold them in a linked list in a CPU implementation, but in OpenCL kernel, is there an opportunity like that? In my mind there are 3 solution to this problem.
First, arrays with length 1000 constructed in number of classes, which is memory costly.
Second, I allocate an array with length 1000 and separate them into parts. However, I may transport the values from and index into different index, becuase I don't know the size of each classes and they may exceed the size which I provided for each.
Third, and better in my opinion, I get two different array with same length. One of them stores data, the other one stores pointers. For example, in i-th index of data array, the value is stored which belongs to 2nd class. Additionally in i-th index of pointer to the next data which belongs to 2nd class. But this is good for just atomic type (like int, float, char etc) linked lists.
I am new in OpenCL. I haven't known lots of features of it yet. If there is a better way, please don't share with me and others.
Using pointers on GPU is usually very bad idea. Major amount of data resides in global memory, and to fetch it quickly the access should be coalesced. Using pointers breaks the access pattern totally, making it essentially random. It's not very good on CPUs too since it cause a lot of cache misses, but CPUs have larger caches and "smarter" internal logic, so it's usually not so important, but sometimes cache-aware memory access pattern can increase CPU application's speed by nearly order of magnitude. On GPUs coalesced global memory access is one of most important optimizations, and pointers can't provide it.
If you are not extremely short on memory, I'd suggest to use first way and preallocate arrays large enough to hold all data. If you are really short on memory, you could use textures to store your data and pointer arrays, but it depends on the algorithm whether it would provide any benefits or not.

String to Byte [delphi]

I need to store my data into memory. My type data of my data is string. I want to minimize the memory usage. I guess I have to change string into byte. Am I right? If I convert string to byte, that means I have to convert string to TMemoryStream?
If you really want to convert it then this code will get it done
var
BinarySize: Integer;
InputString: string;
StringAsBytes: array of Byte;
begin
BinarySize := (Length(InputString) + 1) * SizeOf(Char);
SetLength(StringAsBytes, BinarySize);
Move(InputString[1], StringAsBytes[0], BinarySize);
But as already stated this will not save you memory. The ammount of it used will be practically the same. You will gain nothing from this alone. If you are having to many strings take a different approach. Like something from this list of choices:
Use a dictionary and only store each same string once
Only hold a portion of all strings in memory. Some sort of cache. Have others on hard drive and use streams to load them
If you have very large string consider compressing them.
If you are reading from file and you target is binary data, skip the string in the middle. Read the source directly into a byte buffer.
It is hard to give further help without knowing more about the problem.
EDIT:
If you really want a minimum memory footprint and you can live with a little lower speed (but still very fast) you can use Suffix Trie or B-Tree or event a simple Binary Tree. They can work directly from hard drive and can be very fast for searching. If you then cache a subset of the data to RAM, you get the optimal solution memory vs. speed wise.
Anyway given the ammount of data you claim to have it seems no memory optimization is needed at all. 22MB of RAM is hardly an issue and not worth optimizing.
Are you certain this is an optimization that is needed?
2000 lines that are 10 characters long is only 20000 characters.
In most environments, that's tiny. Most machines have considerably more RAM than that. Most disks are considerably larger than that. And, usually, sending and receiving that much information is trivial over the web.
Perhaps your situation is unique. Maybe you have large number of 20000 character data sets, or very slow web access over which to transmit this date, etc. But, I'd encourage you to consider whether you aren't perhaps trying to optimize something that even if you are very successful in implementing, won't significantly change your application's performance in the real world.
Make your storage type tutf8string. It can be simply assigned from tunicodestring, and conversion should be safe.

TStringList, Dynamic Array or Linked List in Delphi?

I have a choice.
I have a number of already ordered strings that I need to store and access. It looks like I can choose between using:
A TStringList
A Dynamic Array of strings, and
A Linked List of strings (singly linked)
and Alan in his comment suggested I also add to the choices:
TList<string>
In what circumstances is each of these better than the others?
Which is best for small lists (under 10 items)?
Which is best for large lists (over 1000 items)?
Which is best for huge lists (over 1,000,000 items)?
Which is best to minimize memory use?
Which is best to minimize loading time to add extra items on the end?
Which is best to minimize access time for accessing the entire list from first to last?
On this basis (or any others), which data structure would be preferable?
For reference, I am using Delphi 2009.
Dimitry in a comment said:
Describe your task and data access pattern, then it will be possible to give you an exact answer
Okay. I've got a genealogy program with lots of data.
For each person I have a number of events and attributes. I am storing them as short text strings but there are many of them for each person, ranging from 0 to a few hundred. And I've got thousands of people. I don't need random access to them. I only need them associated as a number of strings in a known order attached to each person. This is my case of thousands of "small lists". They take time to load and use memory, and take time to access if I need them all (e.g. to export the entire generated report).
Then I have a few larger lists, e.g. all the names of the sections of my "virtual" treeview, which can have hundreds of thousands of names. Again I only need a list that I can access by index. These are stored separately from the treeview for efficiency, and the treeview retrieves them only as needed. This takes a while to load and is very expensive memory-wise for my program. But I don't have to worry about access time, because only a few are accessed at a time.
Hopefully this gives you an idea of what I'm trying to accomplish.
p.s. I've posted a lot of questions about optimizing Delphi here at StackOverflow. My program reads 25 MB files with 100,000 people and creates data structures and a report and treeview for them in 8 seconds but uses 175 MB of RAM to do so. I'm working to reduce that because I'm aiming to load files with several million people in 32-bit Windows.
I've just found some excellent suggestions for optimizing a TList at this StackOverflow question:
Is there a faster TList implementation?
Unless you have special needs, a TStringList is hard to beat because it provides the TStrings interface that many components can use directly. With TStringList.Sorted := True, binary search will be used which means that search will be very quick. You also get object mapping for free, each item can also be associated with a pointer, and you get all the existing methods for marshalling, stream interfaces, comma-text, delimited-text, and so on.
On the other hand, for special needs purposes, if you need to do many inserts and deletions, then something more approaching a linked list would be better. But then search becomes slower, and it is a rare collection of strings indeed that never needs searching. In such situations, some type of hash is often used where a hash is created out of, say, the first 2 bytes of a string (preallocate an array with length 65536, and the first 2 bytes of a string is converted directly into a hash index within that range), and then at that hash location, a linked list is stored with each item key consisting of the remaining bytes in the strings (to save space---the hash index already contains the first two bytes). Then, the initial hash lookup is O(1), and the subsequent insertions and deletions are linked-list-fast. This is a trade-off that can be manipulated, and the levers should be clear.
A TStringList. Pros: has extended functionality, allowing to dynamically grow, sort, save, load, search, etc. Cons: on large amount of access to the items by the index, Strings[Index] is introducing sensible performance lost (few percents), comparing to access to an array, memory overhead for each item cell.
A Dynamic Array of strings. Pros: combines ability to dynamically grow, as a TStrings, with the fastest access by the index, minimal memory usage from others. Cons: limited standard "string list" functionality.
A Linked List of strings (singly linked). Pros: the linear speed of addition of an item to the list end. Cons: slowest access by the index and searching, limited standard "string list" functionality, memory overhead for "next item" pointer, spead overhead for each item memory allocation.
TList< string >. As above.
TStringBuilder. I does not have a good idea, how to use TStringBuilder as a storage for multiple strings.
Actually, there are much more approaches:
linked list of dynamic arrays
hash tables
databases
binary trees
etc
The best approach will depend on the task.
Which is best for small lists (under
10 items)?
Anyone, may be even static array with total items count variable.
Which is best for large lists (over 1000 items)?
Which is best for huge lists (over 1,000,000 items)?
For large lists I will choose:
- dynamic array, if I need a lot of access by the index or search for specific item
- hash table, if I need to search by the key
- linked list of dynamic arrays, if I need many item appends and no access by the index
Which is best to minimize memory use?
dynamic array will eat less memory. But the question is not about overhead, but about on which number of items this overhead become sensible. And then how to properly handle this number of items.
Which is best to minimize loading time to add extra items on the end?
dynamic array may dynamically grow, but on really large number of items, memory manager may not found a continous memory area. While linked list will work until there is a memory for at least a cell, but for cost of memory allocation for each item. The mixed approach - linked list of dynamic arrays should work.
Which is best to minimize access time for accessing the entire list from first to last?
dynamic array.
On this basis (or any others), which data structure would be preferable?
For which task ?
If your stated goal is to improve your program to the point that it can load genealogy files with millions of persons in it, then deciding between the four data structures in your question isn't really going to get you there.
Do the math - you are currently loading a 25 MB file with about 100000 persons in it, which causes your application to consume 175 MB of memory. If you wish to load files with several millions of persons in it you can estimate that without drastic changes to your program you will need to multiply your memory needs by n * 10 as well. There's no way to do that in a 32 bit process while keeping everything in memory the way you currently do.
You basically have two options:
Not keeping everything in memory at once, instead using a database, or a file-based solution which you load data from when you need it. I remember you had other questions about this already, and probably decided against it, so I'll leave it at that.
Keep everything in memory, but in the most space-efficient way possible. As long as there is no 64 bit Delphi this should allow for a few million persons, depending on how much data there will be for each person. Recompiling this for 64 bit will do away with that limit as well.
If you go for the second option then you need to minimize memory consumption much more aggressively:
Use string interning. Every loaded data element in your program that contains the same data but is contained in different strings is basically wasted memory. I understand that your program is a viewer, not an editor, so you can probably get away with only ever adding strings to your pool of interned strings. Doing string interning with millions of string is still difficult, the "Optimizing Memory Consumption with String Pools" blog postings on the SmartInspect blog may give you some good ideas. These guys deal regularly with huge data files and had to make it work with the same constraints you are facing.
This should also connect this answer to your question - if you use string interning you would not need to keep lists of strings in your data structures, but lists of string pool indexes.
It may also be beneficial to use multiple string pools, like one for names, but a different one for locations like cities or countries. This should speed up insertion into the pools.
Use the string encoding that gives the smallest in-memory representation. Storing everything as a native Windows Unicode string will probably consume much more space than storing strings in UTF-8, unless you deal regularly with strings that contain mostly characters which need three or more bytes in the UTF-8 encoding.
Due to the necessary character set conversion your program will need more CPU cycles for displaying strings, but with that amount of data it's a worthy trade-off, as memory access will be the bottleneck, and smaller data size helps with decreasing memory access load.
One question: How do you query: do you match the strings or query on an ID or position in the list?
Best for small # strings:
Whatever makes your program easy to understand. Program readability is very important and you should only sacrifice it in real hotspots in your application for speed.
Best for memory (if that is the largest constrained) and load times:
Keep all strings in a single memory buffer (or memory mapped file) and only keep pointers to the strings (or offsets). Whenever you need a string you can clip-out a string using two pointers and return it as a Delphi string. This way you avoid the overhead of the string structure itself (refcount, length int, codepage int and the memory manager structures for each string allocation.
This only works fine if the strings are static and don't change.
TList, TList<>, array of string and the solution above have a "list" overhead of one pointer per string. A linked list has an overhead of at least 2 pointers (single linked list) or 3 pointers (double linked list). The linked list solution does not have fast random access but allows for O(1) resizes where trhe other options have O(lgN) (using a factor for resize) or O(N) using a fixed resize.
What I would do:
If < 1000 items and performance is not utmost important: use TStringList or a dyn array whatever is easiest for you.
else if static: use the trick above. This will give you O(lgN) query time, least used memory and very fast load times (just gulp it in or use a memory mapped file)
All mentioned structures in your question will fail when using large amounts of data 1M+ strings that needs to be dynamically chaned in code. At that Time I would use a balances binary tree or a hash table depending on the type of queries I need to maken.
From your description, I'm not entirely sure if it could fit in your design but one way you could improve on memory usage without suffering a huge performance penalty is by using a trie.
Advantages relative to binary search tree
The following are the main advantages
of tries over binary search trees
(BSTs):
Looking up keys is faster. Looking up a key of length m takes worst case
O(m) time. A BST performs O(log(n))
comparisons of keys, where n is the
number of elements in the tree,
because lookups depend on the depth of
the tree, which is logarithmic in the
number of keys if the tree is
balanced. Hence in the worst case, a
BST takes O(m log n) time. Moreover,
in the worst case log(n) will approach
m. Also, the simple operations tries
use during lookup, such as array
indexing using a character, are fast
on real machines.
Tries can require less space when they contain a large number of short
strings, because the keys are not
stored explicitly and nodes are shared
between keys with common initial
subsequences.
Tries facilitate longest-prefix matching, helping to find the key
sharing the longest possible prefix of
characters all unique.
Possible alternative:
I've recently discovered SynBigTable (http://blog.synopse.info/post/2010/03/16/Synopse-Big-Table) which has a TSynBigTableString class for storing large amounts of data using a string index.
Very simple, single layer bigtable implementation, and it mainly uses disc storage, to consumes a lot less memory than expected when storing hundreds of thousands of records.
As simple as:
aId := UTF8String(Format('%s.%s', [name, surname]));
bigtable.Add(data, aId)
and
bigtable.Get(aId, data)
One catch, indexes must be unique, and the cost of update is a bit high (first delete, then re-insert)
TStringList stores an array of pointer to (string, TObject) records.
TList stores an array of pointers.
TStringBuilder cannot store a collection of strings. It is similar to .NET's StringBuilder and should only be used to concatenate (many) strings.
Resizing dynamic arrays is slow, so do not even consider it as an option.
I would use Delphi's generic TList<string> in all your scenarios. It stores an array of strings (not string pointers). It should have faster access in all cases due to no (un)boxing.
You may be able to find or implement a slightly better linked-list solution if you only want sequential access. See Delphi Algorithms and Data Structures.
Delphi promotes its TList and TList<>. The internal array implementation is highly optimized and I have never experienced performance/memory issues when using it. See Efficiency of TList and TStringList

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