Okay, this may sound like a stupid question, but I haven't read anything from the documentation that says it is not possible. Either that, or I overlooked something again.
By multi-dimensional, I mean like arrays. Is something like
vector<vector<double>>
possible? What are the possible drawbacks, at least when compared to arrays?
It's possible, but note that you need a space between the two >s to remove the ambiguity between the right shift operator, i.e.
vector<vector<double> >
Also, I wouldn't call those vectors arrays, since array has a very well-defined meaning in C++:
double matrix[10][10];
edit: As people pointed out, you don't need a space when using C++11.
It is possible.
One of the possible drawbacks could be that it might result in multiple separate allocations from the free store because each vector makes its own allocations. In contrast, a dynamic array allocation is made only once from contiguous memory which is more cache friendly.
What you're describing is absolutely possible, although if you aren't using a C++11 compiler you need to type it as:
vector<vector<double> >
The space between the two > characters being necessary so that the compiler doesn't think you're using the >> operator, as in:
cin >> x;
Of course, with a vector of vectors, you can add and remove elements, either at the top level where the elements are vectors, or at the second level where the elements are doubles. This can be a blessing, a curse, or both, depending on what you are trying to do - note that if you add a double to one of the second-level vectors, the length of that vector is different from all of the others. Because the second-level vectors can have different lengths, I would recommend against using them as a replacement for 2D arrays if fixed dimensions are what you want.
Related
I give online coding contests, where the speed of the program is everything. Over the time I have come across 3 ways to use the concept of array in C++. The questions of the contests usually require us to create a dynamic array of the given size. So its just a one time creation of the dynamic array as per the input and we don't resize the array again.
std::vector
Vectors look the most fancy and everyone tends to love them. But few days back one of the question gave me the TIME_LIMIT_EXCEEDED error when doing it with vectors.When I implemented the same logic with normal arrays, the program was submitted successfully.On researching, I found out that using the push_back() function takes a long time as compared to a normal arr[i]=x;
std::array
I don't have much knowledge about its performance. But it looks like a nicer way to handle arrays.
default arrays in C++
I do the dynamic allocation using int *arr=new int[given_size]; and then use the array normally.Passing an array as argument is not as simple as vectors but its not a big deal.
Apart from this there are also times when I have to work with 2D arrays and I am always unsure about what could be the fastest way. vector<vector<int>> is regarded slow in some forums and so is using multidimensional pointers. So I like to use a 1D array with a typedef function to handle its index but it gets complicated when I have to pass a row to a function.
Most of the answers in forums are based on what the OP was trying to do and this gives different answers. What I want to know is which is the best and long term way to use to have maximum speed/efficiency.
push_back takes a long time compared to arr[i]=x;.
Sorry but you are showing your lack of experience with vectors here, because your examples do two different things.
You are comparing something like this code
vector<int> vec; // vector created with size zero
for (...)
vec.push_back(x); // vector size increases
with this code
int arr[N];
for (...)
arr[i] = x;
The difference is that in the first case the vector has size 0 and it's size increases as you add items to it (this takes extra time), but in the second case the array starts out at it's final size. With an array this is how it must be, but with vectors you have a choice. If you know what the final size of the vector is you should code it like this
vector<int> vec(N); // vector created at size N, note use () not []
for (...)
vec[i] = x;
That is the code you should be comparing with the array code for efficiency,
You might also want to research the resize and reserve methods of a vector. Vectors (if nothing else) are much more flexible than arrays.
I've read that a vector-of-vectors is bad given a fixed 2nd dimension, but I cannot find a clear explanation of the problems on http://www.stackoverflow.com.
Could someone give an explanation of why using 2D indexing on a single vector is preferable to using a vector-of-vectors for a fixed 2nd dimension?
Also, I'm assuming that a vector-of-vectors is the preferable data structure for a 2D array with a variable 2nd dimension? If there is any proof to the contrary I'd love to see that.
For a std::vector the underlying array is dynamically allocated from the heap. If you have e.g. std::vector<std::vector<double>>, then your outer vector would look like
{v1, v2, v3, v4, ... vn}
This looks like each of the inner vectors will be in contiguous memory, and they will, but their underlying arrays will not be contiguous. See the diagram of the memory layout in this post. In other words the you cannot say that
&(v1.back()) + 1 == &(v2.front()) // not necessarily true!
Instead if you used a single vector with striding then you would gain data locality, and it would inherently be more cache friendly as all your data is contiguous.
For the sake of completeness, I would use neither of these methods if your matrix was sparse, as there are more elegant and efficient storage schemes than straight 1D or 2D arrays. Though since you mentioned you have a "fixed 2nd dimension" I will assume that is not the case here.
I shall answer with a simple analogy.
What is "better" in general out of the two things?
A telephone book where each entry is a code referring to a different book that you have to find and read to discover someone's telephone number
A telephone book that lists people's telephone numbers
Keeping all your data in a single big blob is more simple, more sensible, and easier on your computer's cache. A vector with N vectors inside it is much more operationally complex (remember, each of those requires a dynamic allocation and size management operations!); one vector is, well, one vector. You haven't multiplied the workload by N.
The only downside really is that to simulate 2D array access with a 1D underlying data store, you need to write a facade. Fortunately, this is very easy.
Now for the subjective part: on balance I'd say that it's worthwhile unless you're really in a rush and your code quality doesn't particularly matter.
Using a vector of vectors:
Is inefficient in terms of memory allocation, due to multiple blocks being allocated.
Models a jagged right hand edge, so bugs can creep in.
Using a single vector is, in general, better as the memory management is simpler. But you can encounter problems if your matrix is large as it can be difficult to acquire a large contiguous block.
If your array is resizeable, then I'd still stick to a single vector: the resize complexity can be isolated in a single function that you can optimise.
The best solution of all is, of course, to use something like the linear algebra library (BLAS), available in Boost. That also handles large sparse matrices beautifully.
I have an assignment in which I must read a list of 4000 names from a text file and sort then into a C style array as they're being read in (rather than reading them all then sorting). Since this is going involve a lot elements changing indices would it be possible to use bitshifting to rearrange large quantities of elements simultaneously?For example,
declare a heap based array of 20 size
place variable x index 10
perform a bitshift on index 9 with the size of the array data type so that x is now in index 11
Also, if you have any tips on the task in general I'd appreciate it.
No, that doesn't sound at all like something you'd use bitshifting for.
You will have distinct elements (the names) stored in an array, and you need to change the order of entire elements. This is not what bitshifting is used for; it is used to move the bits in a single integer to the left or to the right.
You should just learn qsort().
Not sure about the "sort as they're being read in" requirement, but the easiest solution would be to just call qsort() as each name is added. If that's not allowed or deemed too expensive, think about how to do a "sorted insert" against an array.
By the way, a typical approach in C would be to work with an array of pointers to strings, rather than an array of actual strings. This is good, since sorting an array of pointers is much easier.
So you would have:
char *names[4000];
instead of
char names[4000][64 /* or whatever */];
This would require you to dynamically allocate space for each name as it's loaded though, which isn't to hard. Especially not if you have strdup(). :)
If using qsort() is not allowed(would be pretty stupid to do so after every insert), you could write your own insertion sort. It's not exactly a very efficient way of sorting large arrays but I suppose it's what your teacher is expecting for.
i want to store some kind of distance-matrix (2D), where each entry has some alternatives (different coordinates). So i want to access the distance for example x=1 with x_alt=3 and y=3 with y_alt=1, looking in a 4-dim multi-array with array[1][3][3][1].
The important thing to notice is the following: the 2 most inner arrays/vectors don't have the same size for different values of the outer ones.
After a first init step, where i calculate the values, no more modifying is needed!
This should be easily possible with the use of stl-vectors:
vector<vector<vector<vector<double> > > >`extended_distance_matrix;
where i can dynamically iterate over the outer 2 dimensions and fill only as much alternatives to the inner 2 dimensions as i need (e.g. with push_back()).
Questions:
Is this kind of data-structure definition possible with Boost.MultiArray? How?
Is it a good idea to use Boost.MultiArray instead of the nested vectors? Performance (especially lookups! (Memory-layout))? Easy of use?
Thanks for any input!
sascha
PS: The boost documentation didn't help me. Maybe one can use multi_array_ref to get already sized arrays into the whole 4D-structure?
Edit:
At the moment i'm thinking of another approach: flattening the alternatives -> one bigger matrix with all the distances between the alternatives. Then i only need to calc the number of alternatives per node, build up the prefix sum (which is describing the matrix position/shift) and can then access the information in a 2-step-way.
But my questions are still open.
it sounds like you need:
multi_array<ublas::matrix<type>,2>
Boost.MultiArray deals with contiguous memory (arranged logically in many dimensions) so it is difficult to add elements in the inner dimensions. MultiArrays can be dynamically resized, e.g. to add elements in any dimension, but this is a costly operation that almost certainly need (internally) reallocation and copying.
Because of that requirement MultiArray is not the best option. But from what you say it looks like a combination of the two would be appropriate to you.
boost::multi_array<std::vector<std::vector<type>>, 2> data
The very nice thing is that the indexing interface doesn't change with respect to boost::multi_array<type, 4>. For example data[1][2][3][4] still makes sense.
I don't know from your post how you handle the inner dimension but it could even make sense to use this:
boost::multi_array<boost::multi_array<type>, 2>, 2> data
In any case, unless you really need to do linear algebra I would stay away from boost::ublas::array, or at most use it for the internal array if type is numeric. boost::multi_array<boost::ublas::array<type>, 2> data which is mentioned in the other answer.
This is my little big question about containers, in particular, arrays.
I am writing a physics code that mainly manipulates a big (> 1 000 000) set of "particles" (with 6 double coordinates each). I am looking for the best way (in term of performance) to implement a class that will contain a container for these data and that will provide manipulation primitives for these data (e.g. instantiation, operator[], etc.).
There are a few restrictions on how this set is used:
its size is read from a configuration file and won't change during execution
it can be viewed as a big two dimensional array of N (e.g. 1 000 000) lines and 6 columns (each one storing the coordinate in one dimension)
the array is manipulated in a big loop, each "particle / line" is accessed and computation takes place with its coordinates, and the results are stored back for this particle, and so on for each particle, and so on for each iteration of the big loop.
no new elements are added or deleted during the execution
First conclusion, as the access on the elements is essentially done by accessing each element one by one with [], I think that I should use a normal dynamic array.
I have explored a few things, and I would like to have your opinion on the one that can give me the best performances.
As I understand there is no advantage to use a dynamically allocated array instead of a std::vector, so things like double** array2d = new ..., loop of new, etc are ruled out.
So is it a good idea to use std::vector<double> ?
If I use a std::vector, should I create a two dimensional array like std::vector<std::vector<double> > my_array that can be indexed like my_array[i][j], or is it a bad idea and it would be better to use std::vector<double> other_array and acces it with other_array[6*i+j].
Maybe this can gives better performance, especially as the number of columns is fixed and known from the beginning.
If you think that this is the best option, would it be possible to wrap this vector in a way that it can be accessed with a index operator defined as other_array[i,j] // same as other_array[6*i+j] without overhead (like function call at each access) ?
Another option, the one that I am using so far is to use Blitz, in particular blitz::Array:
typedef blitz::Array<double,TWO_DIMENSIONS> store_t;
store_t my_store;
Where my elements are accessed like that: my_store(line, column);.
I think there are not much advantage to use Blitz in my case because I am accessing each element one by one and that Blitz would be interesting if I was using operations directly on array (like matrix multiplication) which I am not.
Do you think that Blitz is OK, or is it useless in my case ?
These are the possibilities I have considered so far, but maybe the best one I still another one, so don't hesitate to suggest me other things.
Thanks a lot for your help on this problem !
Edit:
From the very interesting answers and comments bellow a good solution seems to be the following:
Use a structure particle (containing 6 doubles) or a static array of 6 doubles (this avoid the use of two dimensional dynamic arrays)
Use a vector or a deque of this particle structure or array. It is then good to traverse them with iterators, and that will allow to change from one to another later.
In addition I can also use a Blitz::TinyVector<double,6> instead of a structure.
So is it a good idea to use std::vector<double> ?
Usually, a std::vector should be the first choice of container. You could use either std::vector<>::reserve() or std::vector<>::resize() to avoid reallocations while populating the vector. Whether any other container is better can be found by measuring. And only by measuring. But first measure whether anything the container is involved in (populating, accessing elements) is worth optimizing at all.
If I use a std::vector, should I create a two dimensional array like std::vector<std::vector<double> > [...]?
No. IIUC, you are accessing your data per particle, not per row. If that's the case, why not use a std::vector<particle>, where particle is a struct holding six values? And even if I understood incorrectly, you should rather write a two-dimensional wrapper around a one-dimensional container. Then align your data either in rows or columns - what ever is faster with your access patterns.
Do you think that Blitz is OK, or is it useless in my case?
I have no practical knowledge about blitz++ and the areas it is used in. But isn't blitz++ all about expression templates to unroll loop operations and optimizing away temporaries when doing matrix manipulations? ICBWT.
First of all, you don't want to scatter the coordinates of one given particle all over the place, so I would begin by writing a simple struct:
struct Particle { /* coords */ };
Then we can make a simple one dimensional array of these Particles.
I would probably use a deque, because that's the default container, but you may wish to try a vector, it's just that 1.000.000 of particles means about a single chunk of a few MBs. It should hold but it might strain your system if this ever grows, while the deque will allocate several chunks.
WARNING:
As Alexandre C remarked, if you go the deque road, refrain from using operator[] and prefer to use iteration style. If you really need random access and it's performance sensitive, the vector should prove faster.
The first rule when choosing from containers is to use std::vector. Then, only after your code is complete and you can actually measure performance, you can try other containers. But stick to vector first. (And use reserve() from the start)
Then, you shouldn't use an std::vector<std::vector<double> >. You know the size of your data: it's 6 doubles. No need for it to be dynamic. It is constant and fixed. You can define a struct to hold you particle members (the six doubles), or you can simply typedef it: typedef double particle[6]. Then, use a vector of particles: std::vector<particle>.
Furthermore, as your program uses the particle data contained in the vector sequentially, you will take advantage of the modern CPU cache read-ahead feature at its best performance.
You could go several ways. But in your case, don't declare astd::vector<std::vector<double> >. You're allocating a vector (and you copy it around) for every 6 doubles. Thats way too costly.
If you think that this is the best option, would it be possible to wrap this vector in a way that it can be accessed with a index operator defined as other_array[i,j] // same as other_array[6*i+j] without overhead (like function call at each access) ?
(other_array[i,j] won't work too well, as i,j employs the comma operator to evaluate the value of "i", then discards that and evaluates and returns "j", so it's equivalent to other_array[i]).
You will need to use one of:
other_array[i][j]
other_array(i, j) // if other_array implements operator()(int, int),
// but std::vector<> et al don't.
other_array[i].identifier // identifier is a member variable
other_array[i].identifier() // member function getting value
other_array[i].identifier(double) // member function setting value
You may or may not prefer to put get_ and set_ or similar on the last two functions should you find them useful, but from your question I think you won't: functions are prefered in APIs between parts of large systems involving many developers, or when the data items may vary and you want the algorithms working on the data to be independent thereof.
So, a good test: if you find yourself writing code like other_array[i][3] where you've decided "3" is the double with the speed in it, and other_array[i][5] because "5" is the the acceleration, then stop doing that and give them proper identifiers so you can say other_array[i].speed and .acceleration. Then other developers can read and understand it, and you're much less likely to make accidental mistakes. On the other hand, if you are iterating over those 6 elements doing exactly the same things to each, then you probably do want Particle to hold a double[6], or to provide an operator[](int). There's no problem doing both:
struct Particle
{
double x[6];
double& speed() { return x[3]; }
double speed() const { return x[3]; }
double& acceleration() { return x[5]; }
...
};
BTW / the reason that vector<vector<double> > may be too costly is that each set of 6 doubles will be allocated on the heap, and for fast allocation and deallocation many heap implementations use fixed-size buckets, so your small request will be rounded up t the next size: that may be a significant overhead. The outside vector will also need to record a extra pointer to that memory. Further, heap allocation and deallocation is relatively slow - in you're case, you'd only be doing it at startup and shutdown, but there's no particular point in making your program slower for no reason. Even more importantly, the areas on the heap may just around in memory, so your operator[] may have cache-faults pulling in more distinct memory pages than necessary, slowing the entire program. Put another way, vectors store elements contiguously, but the pointed-to-vectors may not be contiguous.