What is the time complexity of Map.containsKey and Map.containsValue in Dart? I'd like to know for the following implementations:
LinkedHashMap
HashMap
SplayTreeMap
I assume for the hash map implementations containsKey is amortized constant time and containsValue is probably linear time. For SplayTreeMap, containsKey is probably logarithmic time while containsValue is probably still linear time. However, the documentation seems to be silent on the issue. The best I could find was for LinkedHashMap, which says:
An insertion-ordered [Map] with expected constant-time lookup.
This doesn't specify if you are looking up the key or the value, but presumably this is referring to the key.
The docs for Set (if you navigate to the implementations), on the other hand, are not silent. They give the time complexity.
I assume this is an oversight in the documentation, but perhaps they are silent because there is no guaranteed time complexity. (That's would be strange, though, because it goes against developer expectations.)
For containsKey, it's the same time as doing a lookup.
HashMap and LinkedHashMap: Expected constant time, worst-case linear time for degenerate hashCodes.
SplayTreeMap, ammortized logarithmic time.
For containsValue, it's linear in the number of elements (at least). It simply does the equivalent of map.values.contains(...). There is no efficient way to find a single value in a map, so there is no better way than looking through all of them in some order.
Some potential HashMap implementations can be extra expensive because they traverse the entire backing store, and if the map had been grown big first, then had a lot of elements removed, then it might have a backing store which is significantly larger than its number of elements. Other implementations auto-shrink, or keep elements in a contiguous area, and won't have that problem.
Very implementation dependent. No promises which implementation Dart uses.
Related
The .split_off method on std::collections::LinkedList is described as having a O(n) time complexity. From the (docs):
pub fn split_off(&mut self, at: usize) -> LinkedList<T>
Splits the list into two at the given index. Returns everything after the given index, including the index.
This operation should compute in O(n) time.
Why not O(1)?
I know that linked lists are not trivial in Rust. There are several resources going into the how's and why's like this book and this article among several others, but I haven't got the chance to dive into those or the standard library's source code yet.
Is there a concise explanation about the extra work needed when splitting a linked list in (safe) Rust?
Is this the only way? And if not why was this implementation chosen?
The method LinkedList::split_off(&mut self, at: usize) first has to traverse the list from the start (or the end) to the position at, which takes O(min(at, n - at)) time. The actual split off is a constant time operation (as you said). And since this min() expression is confusing, we just replace it by n which is legal. Thus: O(n).
Why was the method designed like that? The problem goes deeper than this particular method: most of the LinkedList API in the standard library is not really useful.
Due to its cache unfriendliness, a linked list is often a bad choice to store sequential data. But linked lists have a few nice properties which make them the best data structure for a few, rare situations. These nice properties include:
Inserting an element in the middle in O(1), if you already have a pointer to that position
Removing an element from the middle in O(1), if you already have a pointer to that position
Splitting the list into two lists at an arbitrary position in O(1), if you already have a pointer to that position
Notice anything? The linked list is designed for situations where you already have a pointer to the position that you want to do stuff at.
Rust's LinkedList, like many others, just store a pointer to the start and end. To have a pointer to an element inside the linked list, you need something like an Iterator. In our case, that's IterMut. An iterator over a collection can function like a pointer to a specific element and can be advanced carefully (i.e. not with a for loop). And in fact, there is IterMut::insert_next which allows you to insert an element in the middle of the list in O(1). Hurray!
But this method is unstable. And methods to remove the current element or to split the list off at that position are missing. Why? Because of the vicious circle that is:
LinkedList lacks almost all features that make linked lists useful at all
Thus (nearly) everyone recommends not to use it
Thus (nearly) no one uses LinkedList
Thus (nearly) no one cares about improving it
Goto 1
Please note that are a few brave souls occasionally trying to improve the situations. There is the tracking issue about insert_next, where people argue that Iterator might be the wrong concept to perform these O(1) operations and that we want something like a "cursor" instead. And here someone suggested a bunch of methods to be added to IterMut (including cut!).
Now someone just has to write a nice RFC and someone needs to implement it. Maybe then LinkedList won't be nearly useless anymore.
Edit 2018-10-25: someone did write an RFC. Let's hope for the best!
Edit 2019-02-21: the RFC was accepted! Tracking issue.
Maybe I'm misunderstanding your question, but in a linked list, the links of each node have to be followed to proceed to the next node. If you want to get to the third node, you start at the first, follow its link to the second, then finally arrive at the third.
This traversal's complexity is proportional to the target node index n because n nodes are processed/traversed, so it's a linear O(n) operation, not a constant time O(1) operation. The part where the list is "split off" is of course constant time, but the overall split operation's complexity is dominated by the dominant term O(n) incurred by getting to the split-off point node before the split can even be made.
One way in which it could be O(1) would be if a pointer existed to the node after which the list is split off, but that is different from specifying a target node index. Alternatively, an index could be kept mapping the node index to the corresponding node pointer, but it would be extra space and processing overhead in keeping the index updated in sync with list operations.
pub fn split_off(&mut self, at: usize) -> LinkedList<T>
Splits the list into two at the given index. Returns everything after the given index, including the index.
This operation should compute in O(n) time.
The documentation is either:
unclear, if n is supposed to be the index,
pessimistic, if n is supposed to be the length of the list (the usual meaning).
The proper complexity, as can be seen in the implementation, is O(min(at, n - at)) (whichever is smaller). Since at must be smaller than n, the documentation is correct that O(n) is a bound on the complexity (reached for at = n / 2), however such a large bound is unhelpful.
That is, the fact that list.split_off(5) takes the same time if list.len() is 10 or 1,000,000 is quite important!
As to why this complexity, this is an inherent consequence of the structure of doubly-linked list. There is no O(1) indexing operation in a linked-list, after all. The operation implemented in C, C++, C#, D, F#, ... would have the exact same complexity.
Note: I encourage you to write a pseudo-code implementation of a linked-list with the split_off operation; you'll realize this is the best you can get without altering the data-structure to be something else.
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.
I was looking into Core Foundation and CFDictionary, and in the Apple Documentation I found this,
The access time for a value in a CFDictionary object is guaranteed to
be at worst O(log N) for any implementation, but is often O(1)
(constant time). Insertion or deletion operations are typically in
constant time as well, but are O(N*log N) in the worst cases. It is
faster to access values through a key than accessing them directly.
Dictionaries tend to use significantly more memory than an array with
the same number of values
To my surprise, In CFDictionary source , I found this,
The access time for a value in the dictionary is guaranteed to be at
worst O(N) for any implementation, current and future, but will
often be O(1) (constant time). Insertion or deletion operations will
typically be constant time as well, but are O(N*N) in the worst case
in some implementations. Access of values through a key is faster
than accessing values directly (if there are any such operations).
Dictionaries will tend to use significantly more memory than a array
with the same number of values.
Why such difference..? or Am I looking in the wrong place?
Edit: In the apple OpenSource Browser, why are there so many folders which seems like different versions of Core Foundation, is it..? Which out of those is latest/relevant?
"In some implementations". Since you have the source, you can check easily what the worst case is for your implementation. For the worst case, assume that every object in the dictionary returns a hash value of 0 :-)
BTW. Worst case will happen when the hash table gets full and is rebuilt completely. That's why you use at amortised time, not at worst time, unless that worst time for a single insertion is important for you.
I'm pretty sure this is a silly newbie question but I didn't know it so I had to ask...
Why do we use data structures, like Linked List, Binary Search Tree, etc? (when no dynamic allocation is needed)
I mean: wouldn't it be faster if we kept a single variable for a single object? Wouldn't that speed up access time? Eg: BST possibly has to run through some pointers first before it gets to the actual data.
Except for when dynamic allocation is needed, is there a reason to use them?
Eg: using linked list/ BST / std::vector in a situation where a simple (non-dynamic) array could be used.
Each thing you are storing is being kept in it's own variable (or storage location). Data structures apply organization to your data. Imagine if you had 10,000 things you were trying to track. You could store them in 10,000 separate variables. If you did that, then you'd always be limited to 10,000 different things. If you wanted more, you'd have to modify your program and recompile it each time you wanted to increase the number. You might also have to modify the code to change the way in which the calculations are done if the order of the items changes because the new one is introduced in the middle.
Using data structures, from simple arrays to more complex trees, hash tables, or custom data structures, allows your code to both be more organized and extensible. Using an array, which can either be created to hold the required number of elements or extended to hold more after it's first created keeps you from having to rewrite your code each time the number of data items changes. Using an appropriate data structure allows you to design algorithms based on the relationships between the data elements rather than some fixed ordering, giving you more flexibility.
A simple analogy might help to understand. You could, for example, organize all of your important papers by putting each of them into separate filing cabinet. If you did that you'd have to memorize (i.e., hard-code) the cabinet in which each item can be found in order to use them effectively. Alternatively, you could store each in the same filing cabinet (like a generic array). This is better in that they're all in one place, but still not optimum, since you have to search through them all each time you want to find one. Better yet would be to organize them by subject, putting like subjects in the same file folder (separate arrays, different structures). That way you can look for the file folder for the correct subject, then find the item you're looking for in it. Depending on your needs you can use different filing methods (data structures/algorithms) to better organize your information for it's intended use.
I'll also note that there are times when it does make sense to use individual variables for each data item you are using. Frequently there is a mixture of individual variables and more complex structures, using the appropriate method depending on the use of the particular item. For example, you might store the sum of a collection of integers in a variable while the integers themselves are stored in an array. A program would need to be pretty simple though before the introduction of data structures wouldn't be appropriate.
Sorry, but you didn't just find a great new way of doing things ;) There are several huge problems with this approach.
How could this be done without requring programmers to massively (and nontrivially) rewrite tons of code as soon as the number of allowed items changes? Even when you have to fix your data structure sizes at compile time (e.g. arrays in C), you can use a constant. Then, changing a single constant and recompiling is sufficent for changes to that size (if the code was written with this in mind). With your approach, we'd have to type hundreds or even thousands of lines every time some size changes. Not to mention that all this code would be incredibly hard to read, write, maintain and verify. The old truism "more lines of code = more space for bugs" is taken up to eleven in such a setting.
Then there's the fact that the number is almost never set in stone. Even when it is a compile time constant, changes are still likely. Writing hundreds of lines of code for a minor (if it exists at all) performance gain is hardly ever worth it. This goes thrice if you'd have to do the same amount of work again every time you want to change something. Not to mention that it isn't possible at all once there is any remotely dynamic component in the size of the data structures. That is to say, it's very rarely possible.
Also consider the concept of implicit and succinct data structures. If you use a set of hard-coded variables instead of abstracting over the size, you still got a data structure. You merely made it implicit, unrolled the algorithms operating on it, and set its size in stone. Philosophically, you changed nothing.
But surely it has a performance benefit? Well, possible, although it will be tiny. But it isn't guaranteed to be there. You'd save some space on data, but code size would explode. And as everyone informed about inlining should know, small code sizes are very useful for performance to allow the code to be in the cache. Also, argument passing would result in excessive copying unless you'd figure out a trick to derive the location of most variables from a few pointers. Needless to say, this would be nonportable, very tricky to get right even on a single platform, and liable to being broken by any change to the code or the compiler invocation.
Finally, note that a weaker form is sometimes done. The Wikipedia page on implicit and succinct data structures has some examples. On a smaller scale, some data structures store much data in one place, such that it can be accessed with less pointer chasing and is more likely to be in the cache (e.g. cache-aware and cache-oblivious data structures). It's just not viable for 99% of all code and taking it to the extreme adds only a tiny, if any, benefit.
The main benefit to datastructures, in my opinion, is that you are relationally grouping them. For instance, instead of having 10 separate variables of class MyClass, you can have a datastructure that groups them all. This grouping allows for certain operations to be performed because they are structured together.
Not to mention, having datastructures can potentially enforce type security, which is powerful and necessary in many cases.
And last but not least, what would you rather do?
string string1 = "string1";
string string2 = "string2";
string string3 = "string3";
string string4 = "string4";
string string5 = "string5";
Console.WriteLine(string1);
Console.WriteLine(string2);
Console.WriteLine(string3);
Console.WriteLine(string4);
Console.WriteLine(string5);
Or...
List<string> myStringList = new List<string>() { "string1", "string2", "string3", "string4", "string5" };
foreach (string s in myStringList)
Console.WriteLine(s);
the erlang documentation says:
erlang:now()
[...] It is also guaranteed that subsequent calls to this BIF returns continuously increasing values. Hence, the return value from now() can be used to generate unique time-stamps, and if it is called in a tight loop on a fast machine the time of the node can become skewed. [...]
I find this a little strange (especially considering that the granularity is microsecond). Why was it specced this way?
Because it can then be used to uniquely generate timestamp numbers. The os module has a variant which does not do that.