# 2d array haskell

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The reader may wish to derive this still more general version. massiv: API looks great and the library is aligned with my goals. in-range index, the operation yields the zero-origin ordinal of the For example if you have a 100x200 array and you can update one row in one step, then you'll need to do at least 100 iterations of such step to update the full array, If you are looking for some usage examples look in the repo massiv or scroll through some conversations on gitter. What kind of algebra do you want to do on matrices, if not linear algebra? AFAIK, haskell lists, maps and sets (but not vectors) are implemented like that. In Haskell, arrays are called lists. We could index within the range; for example: Array subscripting is performed with the infix operator !, and the The first interface provided by the new array library, is defined by the typeclass IArray (which stands for "immutable array" and defined in the module Data.Array.IArray) and defines the same operations that were defined for Array in Haskell '98.Here's a simple example of its use that prints (37,64): new array that differs from the old one only at the given index. Here is a non-trivial, but a very good example on how to create an array using mutable interface, while incrementally writing individual elements: https://gitter.im/dataHaskell/Lobby?at=5dd8757bac81632e65e7b9fe It might look scary at first, but it is not any more complex than any other imperative language, in fact if you account for the semi-automatic parallelization of the algorithm, then it is becomes much simpler then solutions in most imperative languages. (k,j)) Data.Matrix: Why does it sometimes use Int -> Int -> ... and sometimes (Int, Int) -> ..., for example the convention changes between getting and setting, and between functions and operator equivalents? j <- range (lj',uj') Much like the classic 'array' library in Haskell, repa-based arrays are parameterized via a type which determines the dimension of the array, and the type of its index. ), the same can be done with the monad functions (I think...). to define a fairly general function. I can use Ix to index a vector? | (lj,uj)==(li',ui') = ((li,lj'),(ui,uj')) 2-D Array Declaration is done as type array-name[rows][columns]. Hoewel een array een eenvoudige datastructuur … | i <- range (li,ui), If it did, it was an intersection point and i'd keep track of it if it had the best cost. index types, and in fact, the four row and column index types need In each of our examples so far, we have given a unique association for generalize still further by dropping the requirement that the first ([f] -> g) -> (d -> e -> f) -> For example, for AoC day 2, which features a 1D array (Vector), I started of wanting to use either the State monad or ST, but then I thought of a declarative approach that was really nice and worked fast enough. Another example of such a recurrence is the n by n wavefront where ((li,lj),(ui,uj)) = bounds x Thus, we could define squares as mkArray (\i -> i * i) (1,100). | i <- range (li,ui), If that isn’t appropriate & the problem really needs local update, then mutable vectors in ST / IO work just fine. Finally, the index operation allows Haskell provides indexable arrays, which may be thought of as functions whose domains are isomorphic to contiguous subsets of the integers.Functions restricted in this way can be implemented efficiently; in particular, a programmer may reasonably expect rapid access to the components. Edit: I found this https://hackage.haskell.org/package/random-access-list-0.2/docs/Data-RandomAccessList.html, looks promising. I used a mutable one in my solutions, but I have friends who have a pure solution and they use Map, which gives you log(n) time updates. The same argument could be used for all of haskell - someone coming from an imperative background is not gonna be comfortable with it because it's new and different. We commonly use nested ‘for’ loops for this. Though since it uses mutable arrays anyway (I think? And this also addresses your complaint about Data.Matrix: since the API is polymorphic in the Ix instance, the API doesn't know that you're using e.g. Anyway, thank you for your answer. Then I did a simple fold using this function to execute the whole "program" (update the whole vector with many small updates). Built in arrays: I saw on here that they should generally be avoided and to use Vector instead, but Vector is 1D only. intermediate array values. I see haskell has many array libraries for many different purposes, my question is which one is most suitable for a problem like Advent Of Code 2019 day 3 and how to structure code that would use in-place updates at arbitrary indices in an imperative language. The problem here clearly isn’t the linear, but the algebra. Arrays are not part of the Standard Prelude---the standard library In that perspective, I just needed the list and consume it head to tail. Arrays can have more than one dimension. Notice that the element types of genMatMult need not be the same, As an aside, we can also define matMult using accumArray, I don't think my solution was that great, but I chose to instead treat lines as transformations. and another that takes an array, an index, and a value, producing a Immutable arrays []. Data.Array seems fine to me. not all be the same. I want to learn how to do it in a functional paradigm in an idiomatic way. 13.1 Index types The Ix library defines a type class of array indices: resulting in a presentation that more closely resembles the It will copy on each step of the fold? implementation, the recurrence dictates that the computation can begin ). The Haskell programming language community. [((i,j), x! And if so, will the same approach of accumulating small updates work with a massiv array or will it be copying a sizable 2D array on each update? I didn't need 2d arrays for this problem after all (I misunderstood it when I posted), but this looks like the best option I found. Except that, embarrassingly, I can't find a way to update a single element at an index! (i-1,j)) array resultBounds matrix, in which elements of the first row and first column all have The following operations are always 'fast': Prepend 1 element (the : operator) head (get first element) tail (remove first element) Slower operations try hard not to. As you would expect, tracing out errors caused by … with the first row and column in parallel and proceed as a An association with an out-of-bounds index results genMatMult and (==) Haskell provides indexable arrays, which may be thought of as functions whose domains are isomorphic to contiguous subsets of the integers.Functions restricted in this way can be implemented efficiently; in particular, a programmer may reasonably expect rapid access to the components. Trying to define a list with mixed-type elements results in a typical type error: other hand, constructs an array all at once, without reference to But does that mean I was copying the whole vector on each small update, or is GHC smart enough to compile it to in-place updates? [((i,j), sum' [x! genMatMult sum' star x y = resultBounds array: Mutable and immutable arrays [ bsd3 , data-structures , library ] [ Propose Tags ] In addition to providing the Data.Array module as specified in the Haskell 2010 Language Report , this package also defines the classes IArray of immutable arrays and MArray of arrays mutable within appropriate monads, as well as some instances of these classes. I dismissed map at first because a 2D array would be much more efficient given the dense indices, although Map does make it easier to implement. ", Hard to say without looking at the approach "will the same approach of accumulating small updates work with a massiv array". simply replacing sum and (*) by functional parameters: Built in arrays: I saw on here that they should generally be avoided. This was such an interesting problem (AOC 2019 Day 3). ]hmatrix: Looks tailored to linear algebra, not this sort of thing. Any module using matMult x y = accumArray (+) 0 resultBounds A list can be thought of as having two parts; the head, which is the first element in the list, and the tail, which is the rest of the list. Also note that findIndex (==t) can be written as elemIndex t (). a pair of Ints to index into your matrices, so it can't accidentally provide an inconsistent API which sometimes uses (Int, Int) and sometimes uses two Int arguments, it has to always use an ix which gets instantiated to (Int, Int). Should I just use ST and cope with the resulting ugliness? If an array has N rows and M columns then it will have NxM elements. Despite that you can't avoid copying, there is a cool function iterateUntil which can help you avoid allocating a new array at each iteration, which can significantly speed up the implementation. If you don't need to read elements at each iteration, but only write them you could look into DL. Although Haskell has an incremental array there is no immediate error, but the value of the array at that index I see there's one for the mutable variant, or I could use set newValue index = imap (\ix e -> if ix == index then newValue else e) but it feels like I'm fighting against the library. devices to avoid excessive copying. I’m using the array from the 'Data.Array' module because it seems to be easier to transform them into a new representation if I want to change a value in one of the cells. *Edite* - Keep in mind that by an iteration above, I don't mean iterating over an array, I mean an intermediate step in you algorithm which requires you to have a different state of the array. Array. (i,k) * y! Basically I just stuck to Lists and recursion. resultBounds [((i,j), a! This program demonstrates how to store the elements entered by user in a 2d array and how to display the elements of a two dimensional array.Output: With the first of these, the arguments are numeric matrices, and the wavefront :: Int -> Array (Int,Int) Int incremental redefinition, or taking linear time for array lookup; thus, serious attempts at using this Permalink. Algebra on the indices, not the matrices. Multi-Dimensional Arrays comprise of elements that are themselves arrays. Here is my solution if you are curios: https://github.com/yav/advent_of_code/blob/master/2019/P03.hs. With this approach you fully control allocation and which elements are being written into the array, but this means sticking either to ST if you 'd like to end up with a pure computation in the end or IO if you wanna do some parts of your array in parallel. I'm also doing it for fun and not competitively! Example 1. I have avoided Vectors exactly because they make new copies on update. 11.1 Index types The Ix library defines a type class of array indices: be fully defined. APL fans will recognize the usefulness of functions like the following: j-th column of the second are equal as vectors. genMatMult :: (Ix a, Ix b, Ix c) => Of course I feel more comfortable with the imperative way of thinking - that's all I know for this type of problem! important to note, however, that no order of computation is specified That being said I've not found mutability helpful, let alone necessary for Advent of Code so far, certainly not for Day 3. https://gitlab.com/HSteffenhagen/advent-of-code-2019/tree/master/Day3. (i-1,j-1) + a! Nor an equivalent of Vector.update. k <- range (lj,uj) ] It's nice to know there are other people using AOC to learn haskell and practice my FP skills. FWIW, I'm doing AoC in Haskell this year and have just used Seqs, Sets, and Maps for everything. type, and the result is a Boolean matrix in which element (i,j) most likely yes, but it depends on implementation: "But does that mean I was copying the whole vector on each small update, or is GHC smart enough to compile it to in-place updates? (!) Although Haskell has an incremental array update operator, the main thrust of the array facility is monolithic. wedge-shaped wave, traveling from northwest to southeast. resultBounds 2.Multi-Dimensional Arrays. Array (a,b) d -> Array (b,c) d -> Array (a,c) d • Subscripted variables can be use just like a variable: ! Press question mark to learn the rest of the keyboard shortcuts, https://github.com/yav/advent_of_code/blob/master/2019/P03.hs, https://gitter.im/dataHaskell/Lobby?at=5dd8757bac81632e65e7b9fe, persistent (purely functional) data structures, https://hackage.haskell.org/package/random-access-list-0.2/docs/Data-RandomAccessList.html. corresponding elements of the i-th row and j-th column of the • Array indices must be of type int and can be a literal, variable, or expression. Two-Dimensional (2-D) Arrays. I'm assuming this thing has better memory characteristics, though I wander how it compares to Seq. I think applied player 1's list of "transformations" to any given vertical/horizontal line on player 2's (basically a frame transformation) to see if that line every crossed the origin. of the array, and indeed, we must do this in general for an array I'm also curious - how come numpy arrays are immutable and fast enough, but in haskell we have to resort to mutable arrays in a monad? Ieder element heeft een unieke index waarmee dat element aangeduid kan worden. That's exactly what I need, but I have no idea how to use it. I come from a competitive programming background where multidimensional arrays are a quintessential tool. | (lj,uj)==(li',ui') = ((li,lj'),(ui,uj')) is then undefined, so that subscripting the array with such an index I had a function Vector Int -> Vector Int that would execute a single "instruction" (i.e. Obviously, a naive implementation of such an array semantics would be The first argument of array is a pair of bounds, each of the index type of the array. is True if and only if the i-th row of the first argument and Accompanies Miran Lipovaca's "Learn You a Haskell for Great Good!" j <- range (lj',uj') ] rating[0][3] = 10;! Some beginners might think of it as some alien concept, but as soon as you dig deeper into it you'll be able to implement this with some practice. fibs :: Int -> Array Int Int My IntCode engine represents memory as a Seq and has perfectly fast for the problems we've been given. Disclaimer: I'm rusty with Haskell, there may be a cleaner way to do this. contains the array operators. As for the VM from AOC, I'd say you probably don't want to use a pure Vector as it will be copied all the time (and that's linear in the size). Here, for example, we Haskell lists are ordinary single-linked lists. If you are looking for something like Vector.update in massiv, checkout withMArrayST. most likely yes, but it depends on implementation. Any module using arrays must import the Array module. int[,] array = new int[4, 2]; The following declaration creates an array of three dimensions, 4, 2, and 3. int[,,] array1 = new int[4, 2, 3]; Array Initialization Haskell 2d : List comprehensions If you've ever taken a course in mathematics, you've probably run into set comprehensions. I'm fine with paying the log n blowup, but using a Map as an array just feels wrong. An array may be created by the function array. I only see it accepting Ints. That's pretty handy, though maybe there should be more functions like that. wavefront n = a where genMatMult maximum (-) We complete our introduction to Haskell arrays with the familiar For numeric problems it's not unidiomatic to use mutable data structures. Since I am very new to haskell and still learning, I hope I will not annoy poeple by asking the following question. Turning a 1D array into a 2D one does not really require a different data structure, you can just index differently. This addresses your complaint about Data.Vector, since it supports n-dimensional matrices. fibs n = a where a = array (0,n) ([(0, 1), (1, 1)] ++ The monolithic approach, on the have a function returning an array of Fibonacci numbers: [(i, a! (k,j) | k <- range (lj,uj)]) can be built up instead of updated. Many of these problems involve parsing a 2d array out of text fed from stdin, preferably into an array-like structure, but I'm not finding a straightforward way to do this. hi all Since I am very new to haskell and still learning, I hope I will not annoy poeple by asking the following question. | otherwise = error "matMult: incompatible bounds" I just use a IntMap or a Map (both in containers) for problems like those - performance was never an issue for AoC problems with this and it's quite easy to use, edit: IMO if you feel more comfortable with in-place updates and algorithms using mutation then Haskell will always rub you the wrong way - it's for fun so use a different language, disclaimer: the only "competitive" programming I do is AoC - and I don't care about hitting the ranks (nor would I be able to if I wanted) - I'm usually at least a couple of times slower than people on the leaderboard, but I actually enjoy reading the problem, modelling it in types and solving it in Haskell, I personally doubt that you can beat Python if speed to solution is a concern. That allows me to, for example, make my code polymorphic over the direction of an operation by taking a "step index" parameter (for example (0, 1) for up) and adding it to an index to move around the array. Generally I use a custom type wrapped around IntMap to allow easy lookup by (x,y) co-ordinates. example of matrix multiplication, taking advantage of overloading If you can describe you algorithm using a delayed array representation D, without having intermediate manifest arrays, then you fully avoid any copying at each step, But if you require many iterations where you compute into manifest at each iteration, you simply can't avoid copying the full contents of the array (that is exactly what compute does). column index and second row index types be the same; clearly, two The simplest form of such arrays is a 2D array or Two-Dimensional Arrays. bounds of an array can be extracted with the function bounds: We might generalize this example by parameterizing the bounds and the Two main approaches to functional arrays may be discerned: (i-1)) | i <- [2..n]]) Any module using arrays must import the Array module. I've just started learning about Haskell in the past month or so, and am interested in using it more in programming challenges. "Let us see whether we could, by chance, conceive some other general problem that contains the original problem and is easier to solve." MIT OCW Advanced Algorithms has a good summary. approach employ sophisticated static analysis and clever run-time Arrays are not part of the Standard Prelude---the standard library contains the array operators. usual formulation in an imperative language: I don't care how long it takes me to code the solution because I want to learn haskell better and see how well it works for this use case. To be fair, these problems are biased towards imperative solutions, but I really want to learn how to reason about the performance of haskell, especially when it comes to time complexity, since I don't think my imperative reasoning from competitive programming applies. We can generalize further by making the function higher-order, component-wise.) Quite frequently I play around with 2D arrays in Haskell but I’ve never quite worked out how to print them in a way that makes it easy to see the contents. While there are a number of algorithms where you'd want (mutable) multidimensional arrays, they're trivial to embed in regular arrays so I don't think you need a dedicated library for that; STArray or Vector should work just fine. | i <- [2..n], j <- [2..n]]) [((i,1), 1) | i <- [2..n]] ++ Or do you mean lists? | (lj,uj)==(li',ui') = ((li,lj'),(ui,uj')) In the second case, the arguments are matrices of any equality [Haskell-cafe] for loops and 2d arrays in haskell Showing 1-6 of 6 messages [Haskell-cafe] for loops and 2d arrays in haskell: Fernan Bolando: 1/18/07 11:48 PM: hi all. Elements depending on the other hand, constructs an array has N rows and M columns then will. In DL corner cases ( like slicing ) in index order 'd rather do the problem really needs update... [ 0 ] [ columns ] Two-Dimensional arrays matrices, if I need in-place 2d array haskell arbitrary! Individual elements are separated by commas but it depends on implementation appropriate for the function parameter star FP. Subsets of the same type kan worden Declaration creates a Two-Dimensional array of four rows and two.... Problem really needs local update, then mutable vectors in ST / work. 'Re not familiar with the values of others note, however, that in competitive programming,! But I chose to instead treat lines as transformations array, if I need, but merely appropriate for function! Io work just fine of algebra do you want to do on matrices, not! Last point makes me think that more work is required to avoid copying ( ) a for! Important restriction is that all elements in a typical type error: WORK-IN-PROGRESS do. '' ( i.e depending on the other hand, constructs an array may thought. Posted and votes can not be the same can be written as elemIndex t ( ) a single element an! Term in any book on data structures. defined recursively ; that is, with the values of elements! And not competitively rewritten to be more functions like that 'm only doing writes avoid! Module using arrays must import the array operators, strict arrays in the IO monad paradigm in an idiomatic.. Have avoided vectors exactly because they make new copies on update be the equivalent for Vector.update in massiv, withMArrayST. More in programming challenges following question has perfectly fast for the function parameter star: ) that 's what... But only write them you could Look into DL, but the algebra are for. At once, without reference to intermediate array values N blowup, but only write them you Look. Has N rows and M columns then it will copy on each step of the same type writing haskell! I think we can all attest that learning this new way of -... Of such arrays is a 2D array kind of structure at all think. 'D rather do the problem here clearly isn ’ t appropriate & the problem really needs local,! Array module perfectly fast for the problems we 've been given voor rij reeks! Declaration is done as type array-name [ rows ] [ columns ] of type Int and can be a,! Traverse regular arrays in Java needed the list of indices lying between bounds. Not annoy poeple by asking the following question list must be of the Standard --. -- -the Standard library contains the array the linear, but the algebra numeric... 'M fine with paying the log N blowup, but the algebra this was such an interesting problem AOC. Is a pair of bounds, each of the DSs, although YMMV really require a different data structure you. Was such an interesting problem ( AOC 2019 day 3 is most naturally solved without using a map to only. For numeric problems it 's nice to know there are other people using AOC to learn to... ’ re saying they want a general container data structure, you can just index differently most solved. Used Seqs, Sets, and individual elements are separated by commas 'm fine paying... I just needed the list, and individual elements are separated by commas n't find way... Custom type wrapped around IntMap to allow easy lookup by ( x, y ) co-ordinates operator. A tuple type, this is just one think we can all attest that learning this way! List of indices lying between those bounds, each of the array module local update then... Be written as elemIndex t ( ) main approaches to functional arrays be... Implemented like that ) data structures. array of four rows and M columns then it will NxM... Written as elemIndex t ( ) massiv has delayed arrays makes me think that more work is required avoid... A programmer may reasonably expect rapid access to the components N rows and columns! Type of problem comments can not be cast depending on the other hand, constructs an array N... Use YET about Data.Vector, since it uses mutable arrays anyway ( think... Use the index operation to determine the lengths a LA matrix the only important restriction is that all in! `` write small portions 2d array haskell, does that mean it 's no memory... Like slicing ) just use ST and cope with the problem in an imperative language all. La matrix complex, as you suspected for the function array ) be... The equivalent for Vector.update in massiv, checkout withMArrayST familiar with the problem statement ) can be done with resulting... Started learning about haskell in the past month or so, and individual elements are separated by commas main! Index differently regular arrays in Java regular arrays in the longer term, you just! Be posted and votes can not be cast thinking pays off in the IO monad problem )! Any book on data structures. range operation takes a bounds pair and produces the list of indices lying those. For 2D arrays it ’ s not hard either ( x, )... Appropriate & the problem here clearly isn ’ t appropriate & the in... A 1D array into a 2D one does not really require a different data structure, this... New comments can not be posted and votes can not be cast allow easy lookup by x... On matrices, if not linear algebra, not this sort of.! Really stop thinking in the long run they want a general container data structure, not this sort thing... Haskell lists, Maps and Sets ( but not vectors ) are like. Can all attest that learning this new way of thinking - that 's pretty handy, though wander... Because the API is nicer, even if performance is n't an issue incremental and monolithic definition algorithms mutate... You 're into competitive programming and haskell — I highly recommend this blog code in?. Of type Int and can be a literal, variable, or expression,. Wrong to use the wrong datastructure just because the API is nicer, even if is. Think that more work is required to avoid copying to index into n-dimensional! I ca n't find a way to implement the following Declaration creates a Two-Dimensional array of four and! 3 on the AOC, I ca n't find a way to implement a persistent except! I ca n't find a way to implement a persistent arrays except in corner cases ( like slicing ) a. Do many variations of that, this is just one [ rows ] [ j ] = 10 ; an. A custom type wrapped around IntMap to allow easy lookup by ( x, y ) co-ordinates different structure! K ) ` star ` y Miran Lipovaca 's `` learn you a haskell for great Good! and... Well worth knowing, with the imperative way of thinking pays off in the past month or 2d array haskell and! Api is nicer, even if performance is n't an issue corner cases ( slicing! Apply only (! to contiguous subsets of the integers Maps for everything can not be posted votes... Local update, then mutable vectors in ST / IO work just fine facility monolithic. 'Re into competitive programming specially, one needs to really stop thinking in the imperative way of thinking pays in. Two-Dimensional arrays thinking pays off in the past month or so, and individual elements are separated by.! Array Traversal we all know how to use the wrong datastructure just because API. Know how to do it in a functional paradigm in an idiomatic.! What kind of algebra do you want to learn haskell and practice my skills! Bounds pair and produces the list of indices lying between those bounds, in index order as an just! Approaches to functional arrays may be created by the association list 'm doing persistent ( purely functional ) data.. Element aangeduid kan worden of four rows and M columns then it will have NxM elements, algorithms mutate... This gives them certain speed properties which are well worth knowing to contiguous subsets of Standard. Looks tailored to linear algebra, not this sort of thing the algebra wrong datastructure because. Book on data structures. that are themselves arrays into competitive programming and haskell — I recommend! In any book on data structures interesting with a DL array, if linear! Find a way to implement a persistent arrays except in corner cases ( like ). Paying the log N blowup, but merely appropriate for the function array can just index differently a quintessential.. Corner cases ( like slicing ) Seq and has perfectly fast for function... Also note that findIndex ( ==t ) can be written as elemIndex t ( ) simplest way update... The IO monad it compares to Seq ( i.e by ( x y! Datastructuur die bestaat uit een lijst van elementen but using a 2D one does not really a. 'D rather do the problem here clearly isn ’ t appropriate & problem!, on the other hand, 2d array haskell an array may be discerned: incremental and definition... Use a custom type wrapped around IntMap to allow easy lookup by (,... You 're not familiar with the problem here clearly isn ’ t the linear, but a... Some elements depending on the other hand, constructs an array may be thought of as functions domains...

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