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  • State Monad, why not a tuple?

    - by thr
    I've just wrapped my head around monads (at least I'd like to think I have) and more specifically the state monad, which some people that are way smarter then me figured out, so I'm probably way of with this question. Anyway, the state monad is usually implemented with a M<'a as something like this (F#): type State<'a, 'state> = State of ('state -> 'a * 'state) Now my question: Is there any reason why you couldn't use a tuple here? Other then the possible ambiguity between MonadA<'a, 'b> and MonadB<'a, 'b> which would both become the equivalent ('a * 'b) tuple. Edit: Added example for clarity type StateMonad() = member m.Return a = (fun s -> a, s) member m.Bind(x, f) = (fun s -> let a, s_ = x s in f a s_) let state = new StateMonad() let getState = (fun s -> s, s) let setState s = (fun _ -> (), s) let execute m s = m s |> fst

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  • How to declare a(n) vector/array of reducer objects in Cilk++?

    - by Jin
    Hi All, I had a problem when I am using Cilk++, an extension to C++ for parallel computing. I found that I can't declare a vector of reducer objects: typedef cilk::reducer_opadd<int> T_reducer; vector<T_reducer> bitmiss_vec; for (int i = 0; i < 24; ++i) { T_reducer r; bitmiss_vec.push_back(r); } However, when I compile the code with Cilk++, it complains at the push_back() line: cilk++ geneAttack.cilk -O1 -g -lcilkutil -o geneAttack /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h: In member function ‘void __gnu_cxx::new_allocator<_Tp>::construct(_Tp*, const _Tp&) [with _Tp = cilk::reducer_opadd<int>]’: /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_vector.h:601: instantiated from ‘void std::vector<_Tp, _Alloc>::push_back(const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ geneAttack.cilk:667: instantiated from here /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h:229: error: ‘cilk::reducer_opadd<Type>::reducer_opadd(const cilk::reducer_opadd<Type>&) [with Type = int]’ is private /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/ext/new_allocator.h:107: error: within this context /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h: In member function ‘void std::vector<_Tp, _Alloc>::_M_insert_aux(__gnu_cxx::__normal_iterator<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type::pointer, std::vector<_Tp, _Alloc> >, const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’: /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_vector.h:605: instantiated from ‘void std::vector<_Tp, _Alloc>::push_back(const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ geneAttack.cilk:667: instantiated from here /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h:229: error: ‘cilk::reducer_opadd<Type>::reducer_opadd(const cilk::reducer_opadd<Type>&) [with Type = int]’ is private /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/vector.tcc:252: error: within this context /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_vector.h:605: instantiated from ‘void std::vector<_Tp, _Alloc>::push_back(const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ geneAttack.cilk:667: instantiated from here /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h:230: error: ‘cilk::reducer_opadd<Type>& cilk::reducer_opadd<Type>::operator=(const cilk::reducer_opadd<Type>&) [with Type = int]’ is private /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/vector.tcc:256: error: within this context /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h: In static member function ‘static _BI2 std::__copy_backward<_BoolType, std::random_access_iterator_tag>::__copy_b(_BI1, _BI1, _BI2) [with _BI1 = cilk::reducer_opadd<int>*, _BI2 = cilk::reducer_opadd<int>*, bool _BoolType = false]’: /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_algobase.h:465: instantiated from ‘_BI2 std::__copy_backward_aux(_BI1, _BI1, _BI2) [with _BI1 = cilk::reducer_opadd<int>*, _BI2 = cilk::reducer_opadd<int>*]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_algobase.h:474: instantiated from ‘static _BI2 std::__copy_backward_normal<<anonymous>, <anonymous> >::__copy_b_n(_BI1, _BI1, _BI2) [with _BI1 = cilk::reducer_opadd<int>*, _BI2 = cilk::reducer_opadd<int>*, bool <anonymous> = false, bool <anonymous> = false]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_algobase.h:540: instantiated from ‘_BI2 std::copy_backward(_BI1, _BI1, _BI2) [with _BI1 = cilk::reducer_opadd<int>*, _BI2 = cilk::reducer_opadd<int>*]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/vector.tcc:253: instantiated from ‘void std::vector<_Tp, _Alloc>::_M_insert_aux(__gnu_cxx::__normal_iterator<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type::pointer, std::vector<_Tp, _Alloc> >, const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_vector.h:605: instantiated from ‘void std::vector<_Tp, _Alloc>::push_back(const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ geneAttack.cilk:667: instantiated from here /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h:230: error: ‘cilk::reducer_opadd<Type>& cilk::reducer_opadd<Type>::operator=(const cilk::reducer_opadd<Type>&) [with Type = int]’ is private /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_algobase.h:433: error: within this context /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h: In function ‘void std::_Construct(_T1*, const _T2&) [with _T1 = cilk::reducer_opadd<int>, _T2 = cilk::reducer_opadd<int>]’: /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_uninitialized.h:87: instantiated from ‘_ForwardIterator std::__uninitialized_copy_aux(_InputIterator, _InputIterator, _ForwardIterator, std::__false_type) [with _InputIterator = cilk::reducer_opadd<int>*, _ForwardIterator = cilk::reducer_opadd<int>*]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_uninitialized.h:114: instantiated from ‘_ForwardIterator std::uninitialized_copy(_InputIterator, _InputIterator, _ForwardIterator) [with _InputIterator = cilk::reducer_opadd<int>*, _ForwardIterator = cilk::reducer_opadd<int>*]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_uninitialized.h:254: instantiated from ‘_ForwardIterator std::__uninitialized_copy_a(_InputIterator, _InputIterator, _ForwardIterator, std::allocator<_Tp>) [with _InputIterator = cilk::reducer_opadd<int>*, _ForwardIterator = cilk::reducer_opadd<int>*, _Tp = cilk::reducer_opadd<int>]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/vector.tcc:275: instantiated from ‘void std::vector<_Tp, _Alloc>::_M_insert_aux(__gnu_cxx::__normal_iterator<typename std::_Vector_base<_Tp, _Alloc>::_Tp_alloc_type::pointer, std::vector<_Tp, _Alloc> >, const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_vector.h:605: instantiated from ‘void std::vector<_Tp, _Alloc>::push_back(const _Tp&) [with _Tp = cilk::reducer_opadd<int>, _Alloc = std::allocator<cilk::reducer_opadd<int> >]’ geneAttack.cilk:667: instantiated from here /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/cilk++/reducer_opadd.h:229: error: ‘cilk::reducer_opadd<Type>::reducer_opadd(const cilk::reducer_opadd<Type>&) [with Type = int]’ is private /usr/local/cilk/bin/../lib/gcc/x86_64-unknown-linux-gnu/4.2.4/../../../../include/c++/4.2.4/bits/stl_construct.h:81: error: within this context make: *** [geneAttack] Error 1 jinchen@galactica:~/workspace/biometrics/genAttack$ make cilk++ geneAttack.cilk -O1 -g -lcilkutil -o geneAttack geneAttack.cilk: In function ‘int cilk cilk_main(int, char**)’: geneAttack.cilk:670: error: expected primary-expression before ‘,’ token geneAttack.cilk:670: error: expected primary-expression before ‘}’ token geneAttack.cilk:674: error: ‘bitmiss_vec’ was not declared in this scope make: *** [geneAttack] Error 1 The Cilk++ manule says it supports array/vector of reducers, although there are performance issues to consider: "If you create a large number of reducers (for example, an array or vector of reducers) you must be aware that there is an overhead at steal and reduce that is proportional to the number of reducers in the program. " Anyone knows what is going on? How should I declare/use vector of reducers? Thank you

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  • Naming Suggestions For A Function Providing Method Chaining In A Different Way

    - by sid3k
    I've coded an experimental function which makes passed objects chainable by using high order functions. It's name is "chain" for now, and here is a usage example; chain("Hello World") (print) // evaluates print function by passing "Hello World" object. (console.log,"Optional","Parameters") (returnfrom) // returns "Hello World" It looks lispy but behaves very different since it's coded in a C based language, I don't know if there is a name for this idiom and I couldn't any name more suitable than "chain". Any ideas, suggestions?

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  • Is there a Java equivalent to libevent?

    - by JoelPM
    I've written a high-throughput server that handles each request in its own thread. For requests coming in it is occasionally necessary to do RPCs to one or more back-ends. These back-end RPCs are handled by a separate queue and thread-pool, which provides some bounding on the number of threads created and the maximum number of connections to the back-end (it does some caching to reuse clients and save the overhead of constantly creating connections). Having done all this, though, I'm beginning to think an event-based architecture would be more efficient. In searching around I haven't found any equivalents to libevent for Java, but maybe I'm not looking in the right place? Mina-statemachine from Apache was the closest thing I found, but it looks more verbose than I need and there's no real release available. Any suggestions?

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  • how to use quad core CPU in application

    - by Mayank
    For using all the cores of a quad core processor what do I need to change in my code is it about adding support of multi threading or is it which is taken care by OS itself. I am having FreeBSD and language I am using is C++. I want to give complete CPU cycles to my application at least 90%.

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  • Suggestions for a PHP programmer wanting to create a timer app for an internet cafe

    - by grokker
    Hi, I was asked by a friend to make a timer app for his small internet cafe. He wants to have timers on each client PCs. The timers indicate how much time has been spent by the customer. On the PC that he uses, there's another program that has the overview of all the timers and there's a button for each client PCs that allows him to blacken out the screen. It's not automatic hence the button. The problem is I haven't done any desktop apps before so that's why I'm asking you guys (the awesome people at SO) for suggestions/advice on what language/tool to use. A little info about me: I did Java but haven't tried Swing though. I know a bit about Python and Ruby too. I don't mind learning new languages as long as I get to finish or get a prototype up and running. He doesn't mind if I could show him a prototype, it's actually for me. It gives me satisfaction to see I'm progressing. I'm not planning on asking him to pay me for doing this. Whatever he gives me is fine. P.S. He's using Windows XP

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  • Do you have any tips for commenting code?

    - by Rob Wells
    G'day, I've read both of Steve McConnell's excellent Code Complete books "Code Complete" and "Code Complete 2" and was wondering if people have any other suggestions for commenting code.co My commenting mantra could be summed up by the basic idea of expressing "what the code below cannot say". While enjoying this interesting blog post by Jeff about commenting I was still left wondering "When coding, when do you feel a comment is required?"

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  • Subroutine & GoTo design

    - by sub
    I have a strange question concerning subroutines: As I'm creating a minimal language and I don't want to add high-level loops like while or for I was planning on just adding gotos to keep it Turing-Complete. Now I thought, eww - gotos - I wouldn't want to program in that language if I had to use gotos so often. So I thought about adding subroutines instead. I see the difference as the following: gotos Go to (captain obvious) a previously defined point and continue executing the program from there. Leads to hardly understandable and buggy code, I think that's a fact. subroutines Similiar: You define their starting point somewhere, as you call them the program jumps there - but the subroutine can go back to the point it was called from with return. Okay. Why didn't I just add the more function-like, nice looking subroutines? Because: In order to make return work if I call subroutines from within subroutines from within other subroutines, I'd have to use a stack containing the point where the currently running subroutine came from at top. That would then mean that I would, if I create loops using the subroutines, end up with an extremely memory-eating, overflowing stack with return locations. Not good. Don't think of my subroutines as functions. They are just gotos that return to the point they were called from, they don't actually give back values like the return x; statement in nearly all today's languages. Now to my actual questions: How can I solve the above problem with the stack overflow on loops with subroutines? Do I have to add a separate goto language construct without the return option? Assembler doesn't have loops but as I have seen myJumpPoint:, jnz, jz, retn. That means to me that there must also be a stack containing all the return locations. Am I right with that? What about long running loops then? Don't they overflow the stack/eat memory then? Am I getting the retn symbol in assembler totally wrong? If yes, please explain it to me.

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  • How well do zippers perform in practice, and when should they be used?

    - by Rob
    I think that the zipper is a beautiful idea; it elegantly provides a way to walk a list or tree and make what appear to be local updates in a functional way. Asymptotically, the costs appear to be reasonable. But traversing the data structure requires memory allocation at each iteration, where a normal list or tree traversal is just pointer chasing. This seems expensive (please correct me if I am wrong). Are the costs prohibitive? And what under what circumstances would it be reasonable to use a zipper?

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  • Using TTMessageController with Multiple Data Sources

    - by PF1
    Hi Everyone: I am wondering if there is some way to set a separate .datasource for each custom field in a TTMessageController. Right now I am using a TTMessageController subclass (and referencing the data source controller delegate) and simply setting the data source of the message controller to self. But I only believe this will work for one field with one set of options. Thanks for any help!

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  • How to return the output of a recursive function in Clojure

    - by Silanglaya Valerio
    Hi everyone! I'm new to functional languages and clojure, so please bear with me... I'm trying to construct a list of functions, with either random parameters or constants. The function that constructs the list of functions is already working, though it doesn't return the function itself. I verified this using println. Here is the snippet: (def operations (list #(- %1 %2) #(+ %1 %2) #(* %1 %2) #(/ %1 %2))) (def parameters (list \u \v \w \x \y \z)) (def parameterlistcount 6) (def paramcount 2) (def opcount 4) (defn generateFunction "Generates a random function list" ([] (generateFunction 2 4 0.5 0.6 '())) ([pc maxdepth fp pp function] (if (and (> maxdepth 0) (< (rand) fp)) (dotimes [i 2] (println(conj (generateFunction pc (dec maxdepth) fp pp function) {:op (nth operations (rand-int opcount))}))) (if (and (< (rand) pp) (> pc 0)) (do (dec pc) (conj function {:param (nth parameters (rand-int parameterlistcount))})) (conj function {:const (rand-int 100)}))))) Any help will be appreciated, thanks!

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  • How to simply this logic/code?

    - by Tattat
    I want to write an apps that accepts user command. The user command is used in this format: command -parameter For example, the app can have "Copy", "Paste", "Delete" command I am thinking the program should work like this : public static void main(String args[]){ if(args[0].equalsIgnoreCase("COPY")){ //handle the copy command } else if(args[0].equalsIgnoreCase("PASTE")){ //handle the copy command }/** code skipped **/ } So, it works, but I think it will become more and more complex when I have more command in my program, also, it is different to read. Any ideas to simply the logic?

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  • getting started with lex

    - by cambr
    I need to format some hexdump like this: 00010: 02 03 04 05 00020: 02 03 04 08 00030: 02 03 04 08 00010: 02 03 04 05 00020: 02 03 04 05 02 03 04 05 02 03 04 08 to 02 03 04 05 02 03 04 08 02 03 04 02 03 04 05 02 03 04 05 02 03 04 05 02 03 04 a) remove the address fields, if present b) remove any 08 at the end of a paragraph (followed by an empty line) c) remove any empty lines How can this be done using lex? thanks!

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  • How do programmers work together on a project?

    - by Laith J
    Hello, I've always programmed alone, I'm still a student so I never programmed with anyone else, I haven't even used a version control system before. I'm working on a project now that requires knowledge of how programmers work together on a piece of software in a company. How is the software compiled? Is it from the version control system? Is it by individual programmers? Is it periodic? Is it when someone decides to build or something? Are there any tests that are done to make sure it "works"? Anything will do. Thanks.

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  • scripts on Cshell

    - by lego69
    hello, I've got some problem, I have list of data in the file: 053-37878 03828008 Moskovitch James 500 052-34363 01234567 Mendelson Kippi 450 053-32322 03828008 Jameson Shula 350 054-39238 03333333 Merden Moshe 300 is it possible rewrite this list in the same file (without using temporary file) but without last number thanks in advance for any help (I'm talking about C-Shell scripts)

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  • Practices for Foreground/Background threads in .NET

    - by Andrei Taptunov
    I work with in-house legacy communication framework which exposes some high level abstractions. These abstractions are wrappers with some logic around .NET threads. When I looked at code I've noticed that some abstractions are wrappers around foreground threads while others are wrappers around background threads. The sad thing is that I don't see any logic why in some cases foreground threads are used and background in other cases. Are there any guidelines or patterns & practices when it's better to choose one over another on server side and client side (I believe there should be some difference)?

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  • How Search Engine Bots Crawl Forums?

    - by Waleed Eissa
    If I have a forums site with a large number of threads, will the search engine bot crawl the whole site every time? Say I have over 1,000,000 threads in my site, will they get crawled every time the bot crawls my site? or how does it work? I want my website to be indexed but I don't want the bot to kill my website! In other words I don't want the bot to keep crawling the old threads again and again every time it crawls my website. Also, what about the pages crawled before? Will the bot request them every time it crawls my website to make sure they are still on the site? I'm asking this because I only link to the latest threads, i.e. there's a page that contains a list of all the latest threads, but I don't link to the older threads, they have to be explicitly requested by URL, e.g. http://www.mysite.com/showthread.aspx?threadid=7 , will this work to stop the bot from bringing my site down and consuming all my bandwidth? P.S. The site is still under development but I want to know in order to design the site so that search engine bots don't bring it down. Thanks

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  • How do I compile a module in User Mode Linux

    - by Zach
    Having a tough time compiling a module for User Mode Linux. I just need a basic way to compile a very basic module in user mode linux and cannot seem to get it to work. I checked out the how-to on sourceforge for UML but had no luck. Anyone have a working example of what it takes? Thanks!

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  • How can I use functools.partial on multiple methods on an object, and freeze parameters out of order

    - by Joseph Garvin
    I find functools.partial to be extremely useful, but I would like to be able to freeze arguments out of order (the argument you want to freeze is not always the first one) and I'd like to be able to apply it to several methods on a class at once, to make a proxy object that has the same methods as the underlying object except with some of its methods parameter being frozen (think of it as generalizing partial to apply to classes). I've managed to scrap together a version of functools.partial called 'bind' that lets me specify parameters out of order by passing them by keyword argument. That part works: >>> def foo(x, y): ... print x, y ... >>> bar = bind(foo, y=3) >>> bar(2) 2 3 But my proxy class does not work, and I'm not sure why: >>> class Foo(object): ... def bar(self, x, y): ... print x, y ... >>> a = Foo() >>> b = PureProxy(a, bar=bind(Foo.bar, y=3)) >>> b.bar(2) Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: bar() takes exactly 3 arguments (2 given) I'm probably doing this all sorts of wrong because I'm just going by what I've pieced together from random documentation, blogs, and running dir() on all the pieces. Suggestions both on how to make this work and better ways to implement it would be appreciated ;) One detail I'm unsure about is how this should all interact with descriptors. Code follows. from types import MethodType class PureProxy(object): def __init__(self, underlying, **substitutions): self.underlying = underlying for name in substitutions: subst_attr = substitutions[name] if hasattr(subst_attr, "underlying"): setattr(self, name, MethodType(subst_attr, self, PureProxy)) def __getattribute__(self, name): return getattr(object.__getattribute__(self, "underlying"), name) def bind(f, *args, **kwargs): """ Lets you freeze arguments of a function be certain values. Unlike functools.partial, you can freeze arguments by name, which has the bonus of letting you freeze them out of order. args will be treated just like partial, but kwargs will properly take into account if you are specifying a regular argument by name. """ argspec = inspect.getargspec(f) argdict = copy(kwargs) if hasattr(f, "im_func"): f = f.im_func args_idx = 0 for arg in argspec.args: if args_idx >= len(args): break argdict[arg] = args[args_idx] args_idx += 1 num_plugged = args_idx def new_func(*inner_args, **inner_kwargs): args_idx = 0 for arg in argspec.args[num_plugged:]: if arg in argdict: continue if args_idx >= len(inner_args): # We can't raise an error here because some remaining arguments # may have been passed in by keyword. break argdict[arg] = inner_args[args_idx] args_idx += 1 f(**dict(argdict, **inner_kwargs)) new_func.underlying = f return new_func

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  • Efficient algorithm to generate all solutions of a linear diophantine equation with ai=1

    - by Ben
    I am trying to generate all the solutions for the following equations for a given H. With H=4 : 1) ALL solutions for x_1 + x_2 + x_3 + x_4 =4 2) ALL solutions for x_1 + x_2 + x_3 = 4 3) ALL solutions for x_1 + x_2 = 4 4) ALL solutions for x_1 =4 For my problem, there are always 4 equations to solve (independently from the others). There are a total of 2^(H-1) solutions. For the previous one, here are the solutions : 1) 1 1 1 1 2) 1 1 2 and 1 2 1 and 2 1 1 3) 1 3 and 3 1 and 2 2 4) 4 Here is an R algorithm which solve the problem. library(gtools) H<-4 solutions<-NULL for(i in seq(H)) { res<-permutations(H-i+1,i,repeats.allowed=T) resum<-apply(res,1,sum) id<-which(resum==H) print(paste("solutions with ",i," variables",sep="")) print(res[id,]) } However, this algorithm makes more calculations than needed. I am sure it is possible to go faster. By that, I mean not generating the permutations for which the sums is H Any idea of a better algorithm for a given H ?

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