Tutorial :Factorial Algorithms in different languages


I want to see all the different ways you can come up with, for a factorial subroutine, or program. The hope is that anyone can come here and see if they might want to learn a new language.


  • Procedural
  • Functional
  • Object Oriented
  • One liners
  • Obfuscated
  • Oddball
  • Bad Code
  • Polyglot

Basically I want to see an example, of different ways of writing an algorithm, and what they would look like in different languages.

Please limit it to one example per entry. I will allow you to have more than one example per answer, if you are trying to highlight a specific style, language, or just a well thought out idea that lends itself to being in one post.

The only real requirement is it must find the factorial of a given argument, in all languages represented.

Be Creative!

Recommended Guideline:

  # Language Name: Optional Style type       - Optional bullet points        Code Goes Here    Other informational text goes here  

I will ocasionally go along and edit any answer that does not have decent formatting.


Polyglot: 5 languages, all using bignums

So, I wrote a polyglot which works in the three languages I often write in, as well as one from my other answer to this question and one I just learned today. It's a standalone program, which reads a single line containing a nonnegative integer and prints a single line containing its factorial. Bignums are used in all languages, so the maximum computable factorial depends only on your computer's resources.

  • Perl: uses built-in bignum package. Run with perl FILENAME.
  • Haskell: uses built-in bignums. Run with runhugs FILENAME or your favorite compiler's equivalent.
  • C++: requires GMP for bignum support. To compile with g++, use g++ -lgmpxx -lgmp -x c++ FILENAME to link against the right libraries. After compiling, run ./a.out. Or use your favorite compiler's equivalent.
  • brainf*ck: I wrote some bignum support in this post. Using Muller's classic distribution, compile with bf < FILENAME > EXECUTABLE. Make the output executable and run it. Or use your favorite distribution.
  • Whitespace: uses built-in bignum support. Run with wspace FILENAME.

Edit: added Whitespace as a fifth language. Incidentally, do not wrap the code with <code> tags; it breaks the Whitespace. Also, the code looks much nicer in fixed-width.

char //# b=0+0{- |0*/; #>>>>,----------[>>>>,--------  #define	a/*#--]>>>>++<<<<<<<<[>++++++[<------>-]<-<<<  #Perl	><><><>	 <> <> <<]>>>>[[>>+<<-]>>[<<+>+>-]<->  #C++	--><><>	<><><><	> < > <	+<[>>>>+<<<-<[-]]>[-]  #Haskell >>]>[-<<<<<[<<<<]>>>>[[>>+<<-]>>[<<+>+>-]>>]  #Whitespace	>>>>[-[>+<-]+>>>>]<<<<[<<<<]<<<<[<<<<  #brainf*ck > < ]>>>>>[>>>[>>>>]>>>>[>>>>]<<<<[[>>>>*/  exp; ;//;#+<<<<-]<<<<]>>>>+<<<<<<<[<<<<][.POLYGLOT^5.  #include <gmpxx.h>//]>>>>-[>>>[>>>>]>>>>[>>>>]<<<<[>>  #define	eval int	main()//>+<<<-]>>>[<<<+>>+>->  #include <iostream>//<]<-[>>+<<[-]]<<[<<<<]>>>>[>[>>>  #define	print std::cout	<< // >	<+<-]>[<<+>+>-]<<[>>>  #define	z std::cin>>//<< +<<<-]>>>[<<<+>>+>-]<->+++++  #define c/*++++[-<[-[>>>>+<<<<-]]>>>>[<<<<+>>>>-]<<*/  #define	abs int $n //><	<]<[>>+<<<<[-]>>[<<+>>-]]>>]<  #define	uc mpz_class fact(int	$n){/*<<<[<<<<]<<<[<<  use bignum;sub#<<]>>>>-]>>>>]>>>[>[-]>>>]<<<<[>>+<<-]  z{$_[0+0]=readline(*STDIN);}sub fact{my($n)=shift;#>>  #[<<+>+>-]<->+<[>-<[-]]>[-<<-<<<<[>>+<<-]>>[<<+>+>+*/  uc;if($n==0){return 1;}return $n*fact($n-1);	}//;#  eval{abs;z($n);print fact($n);print("\n")/*2;};#-]<->  '+<[>-<[-]]>]<<[<<<<]<<<<-[>>+<<-]>>[<<+>+>-]+<[>-+++  -}--	<[-]]>[-<<++++++++++<<<<-[>>+<<-]>>[<<+>+>-++  fact 0	= 1 -- ><><><><	> <><><	]+<[>-<[-]]>]<<[<<+ +  fact	n=n*fact(n-1){-<<]>>>>[[>>+<<-]>>[<<+>+++>+-}  main=do{n<-readLn;print(fact n)}-- +>-]<->+<[>>>>+<<+  {-x<-<[-]]>[-]>>]>]>>>[>>>>]<<<<[>+++++++[<+++++++>-]  <--.<<<<]+written+by+++A+Rex+++2009+.';#+++x-}--x*/;}  



sorry I couldn't resist xD



This is one of the faster algorithms, up to 170!. It fails inexplicably beyond 170!, and it's relatively slow for small factorials, but for factorials between 80 and 170 it's blazingly fast compared to many algorithms.

curl http://www.google.com/search?q=170!  

There's also an online interface, try it out now!

Let me know if you find a bug, or faster implementation for large factorials.


This algorithm is slightly slower, but gives results beyond 170:

curl http://www58.wolframalpha.com/input/?i=171!  

It also simplifies them into various other representations.


C++: Template Metaprogramming

Uses the classic enum hack.

template<unsigned int n>  struct factorial {      enum { result = n * factorial<n - 1>::result };  };    template<>  struct factorial<0> {      enum { result = 1 };  };  


const unsigned int x = factorial<4>::result;  

Factorial is calculated completely at compile time based on the template parameter n. Therefore, factorial<4>::result is a constant once the compiler has done its work.



     	.   .   	.  		.    	.     	.  			 .   .  	 	 .  	  .     	.   .    .   			 .  		  			 .   .  	.  .    	 .   .  .  	.   	.  .  .  .  

It was hard to get it to show here properly, but now I tried copying it from the preview and it works. You need to input the number and press enter.


I find the following implementations just hilarious:

The Evolution of a Haskell Programmer

Evolution of a Python programmer



C# Lookup:

Nothing to calculate really, just look it up. To extend it,add another 8 numbers to the table and 64 bit integers are at at their limit. Beyond that, a BigNum class is called for.

public static int Factorial(int f)  {       if (f<0 || f>12)      {          throw new ArgumentException("Out of range for integer factorial");      }      int [] fact={1,1,2,6,24,120,720,5040,40320,362880,3628800,                   39916800,479001600};      return fact[f];  }  


Lazy K

Your pure functional programming nightmares come true!

The only Esoteric Turing-complete Programming Language that has:

Here's the Factorial code in all its parenthetical glory:

K(SII(S(K(S(S(KS)(S(K(S(KS)))(S(K(S(KK)))(S(K(S(K(S(K(S(K(S(SI(K(S(K(S(S(KS)K)I))   (S(S(KS)K)(SII(S(S(KS)K)I))))))))K))))))(S(K(S(K(S(SI(K(S(K(S(SI(K(S(K(S(S(KS)K)I))   (S(S(KS)K)(SII(S(S(KS)K)I))(S(S(KS)K))(S(SII)I(S(S(KS)K)I))))))))K)))))))   (S(S(KS)K)(K(S(S(KS)K)))))))))(K(S(K(S(S(KS)K)))K))))(SII))II)  


  • No subtraction or conditionals
  • Prints all factorials (if you wait long enough)
  • Uses a second layer of Church numerals to convert the Nth factorial to N! asterisks followed by a newline
  • Uses the Y combinator for recursion

In case you are interested in trying to understand it, here is the Scheme source code to run through the Lazier compiler:

(lazy-def '(fac input)     '((Y (lambda (f n a) ((lambda (b) ((cons 10) ((b (cons 42)) (f (1+ n) b))))         (* a n)))) 1 1))  

(for suitable definitions of Y, cons, 1, 10, 42, 1+, and *).


Lazy K Factorial in Decimal

(10KB of gibberish or else I would paste it). For example, at the Unix prompt:

      $ echo "4" | ./lazy facdec.lazy      24      $ echo "5" | ./lazy facdec.lazy      120  

Rather slow for numbers above, say, 5.

The code is sort of bloated because we have to include library code for all of our own primitives (code written in Hazy, a lambda calculus interpreter and LC-to-Lazy K compiler written in Haskell).


XSLT 1.0

The input file, factorial.xml:

<?xml version="1.0"?>  <?xml-stylesheet href="factorial.xsl" type="text/xsl" ?>  <n>    20  </n>  

The XSLT file, factorial.xsl:

<?xml version="1.0"?>  <xsl:stylesheet version="1.0"                                       xmlns:xsl="http://www.w3.org/1999/XSL/Transform"                  xmlns:msxsl="urn:schemas-microsoft-com:xslt" >    <xsl:output method="text"/>    <!-- 0! = 1 -->    <xsl:template match="text()[. = 0]">      1    </xsl:template>    <!-- n! = (n-1)! * n-->    <xsl:template match="text()[. > 0]">      <xsl:variable name="x">        <xsl:apply-templates select="msxsl:node-set( . - 1 )/text()"/>      </xsl:variable>      <xsl:value-of select="$x * ."/>    </xsl:template>    <!-- Calculate n! -->    <xsl:template match="/n">      <xsl:apply-templates select="text()"/>    </xsl:template>  </xsl:stylesheet>  

Save both files in the same directory and open factorial.xml in IE.


Python: Functional, One-liner

factorial = lambda n: reduce(lambda x,y: x*y, range(1, n+1), 1)  


  • It supports big integers. Example:

print factorial(100)  93326215443944152681699238856266700490715968264381621468592963895217599993229915\  608941463976156518286253697920827223758251185210916864000000000000000000000000  

  • It does not work for n < 0.


APL (oddball/one-liner):

  1. ⍳X expands X into an array of the integers 1..X
  2. ×/ multiplies every element in the array

Or with the built-in operator:


Source: http://www.webber-labs.com/mpl/lectures/ppt-slides/01.ppt



sub factorial ($n) { [*] 1..$n }  

I hardly know about Perl6. But I guess this [*] operator is same as Haskell's product.

This code runs on Pugs, and maybe Parrot (I didn't check it.)


This code also works.

sub postfix:<!> ($n) { [*] 1..$n }    # This function(?) call like below ... It looks like mathematical notation.  say 10!;  


x86-64 Assembly: Procedural

You can call this from C (only tested with GCC on linux amd64). Assembly was assembled with nasm.

section .text      global factorial  ; factorial in x86-64 - n is passed in via RDI register  ; takes a 64-bit unsigned integer  ; returns a 64-bit unsigned integer in RAX register  ; C declaration in GCC:  ;   extern unsigned long long factorial(unsigned long long n);  factorial:      enter 0,0      ; n is placed in rdi by caller      mov rax, 1 ; factorial = 1      mov rcx, 2 ; i = 2  loopstart:      cmp rcx, rdi      ja loopend      mul rcx ; factorial *= i      inc rcx      jmp loopstart  loopend:      leave      ret  


Recursively in Inform 7

(it reminds you of COBOL because it's for writing text adventures; proportional font is deliberate):

To decide what number is the factorial of (n - a number):
    if n is zero, decide on one;
    otherwise decide on the factorial of (n minus one) times n.

If you want to actually call this function ("phrase") from a game you need to define an action and grammar rule:

"The factorial game" [this must be the first line of the source]

There is a room. [there has to be at least one!]

Factorialing is an action applying to a number.

Understand "factorial [a number]" as factorialing.

Carry out factorialing:
    Let n be the factorial of the number understood;
    Say "It's [n]".



    public static int factorial(int n)      {          return (Enumerable.Range(1, n).Aggregate(1, (previous, value) => previous * value));      }  


Erlang: tail recursive

fac(0) -> 1;  fac(N) when N > 0 -> fac(N, 1).    fac(1, R) -> R;  fac(N, R) -> fac(N - 1, R * N).  



ones = 1 : ones  integers   = head ones     : zipWith (+) integers   (tail ones)  factorials = head integers : zipWith (*) factorials (tail integers)  



+++++  >+<[[->>>>+<<<<]>>>>[-<<<<+>>+>>]<<<<>[->>+<<]<>>>[-<[->>+<<]>>[-<<+<+>>>]<]<[-]><<<-]  

Written by Michael Reitzenstein.


BASIC: old school

10 HOME  20 INPUT N  30 LET ANS = 1  40 FOR I = 1 TO N  50   ANS = ANS * I  60 NEXT I  70 PRINT ANS  


Batch (NT):

@echo off    set n=%1  set result=1    for /l %%i in (%n%, -1, 1) do (      set /a result=result * %%i  )    echo %result%  

Usage: C:>factorial.bat 15


F#: Functional

Straight forward:

let rec fact x =       if   x < 0 then failwith "Invalid value."      elif x = 0 then 1      else x * fact (x - 1)  

Getting fancy:

let fact x = [1 .. x] |> List.fold_left ( * ) 1  


Recursive Prolog

fac(0,1).  fac(N,X) :- N1 is N -1, fac(N1, T), X is N * T.  

Tail Recursive Prolog

fac(0,N,N).  fac(X,N,T) :- A is N * X, X1 is X - 1, fac(X1,A,T).  fac(N,T) :- fac(N,1,T).  


ruby recursive



factorial[5]   => 120  



Here is a simple recursive definition:

(define (factorial x)    (if (= x 0) 1        (* x (factorial (- x 1)))))  

In Scheme tail-recursive functions use constant stack space. Here is a version of factorial that is tail-recursive:

(define factorial    (letrec ((fact (lambda (x accum)                     (if (= x 0) accum                         (fact (- x 1) (* accum x))))))      (lambda (x)        (fact x 1))))  


Oddball examples? What about using the gamma function! Since, Gamma n = (n-1)!.

OCaml: Using Gamma

let rec gamma z =      let pi = 4.0 *. atan 1.0 in      if z < 0.5 then          pi /. ((sin (pi*.z)) *. (gamma (1.0 -. z)))      else          let consts = [| 0.99999999999980993; 676.5203681218851; -1259.1392167224028;                          771.32342877765313; -176.61502916214059; 12.507343278686905;                   -0.13857109526572012; 9.9843695780195716e-6; 1.5056327351493116e-7;                       |]           in          let z = z -. 1.0 in          let results = Array.fold_right                             (fun x y -> x +. y)                            (Array.mapi                                 (fun i x -> if i = 0 then x else x /. (z+.(float i)))                                consts                            )                            0.0          in          let x = z +. (float (Array.length consts)) -. 1.5 in          let final = (sqrt (2.0*.pi)) *.                       (x ** (z+.0.5)) *.                      (exp (-.x)) *. result          in          final    let factorial_gamma n = int_of_float (gamma (float (n+1)))  


Freshman Haskell programmer

fac n = if n == 0              then 1             else n * fac (n-1)  

Sophomore Haskell programmer, at MIT (studied Scheme as a freshman)

fac = (\(n) ->          (if ((==) n 0)              then 1              else ((*) n (fac ((-) n 1)))))  

Junior Haskell programmer (beginning Peano player)

fac  0    =  1  fac (n+1) = (n+1) * fac n  

Another junior Haskell programmer (read that n+k patterns are “a disgusting part of Haskell” [1] and joined the “Ban n+k patterns”-movement [2])

fac 0 = 1  fac n = n * fac (n-1)  

Senior Haskell programmer (voted for Nixon Buchanan Bush â€" “leans right”)

fac n = foldr (*) 1 [1..n]  

Another senior Haskell programmer (voted for McGovern Biafra Nader â€" “leans left”)

fac n = foldl (*) 1 [1..n]  

Yet another senior Haskell programmer (leaned so far right he came back left again!)

-- using foldr to simulate foldl    fac n = foldr (\x g n -> g (x*n)) id [1..n] 1  

Memoizing Haskell programmer (takes Ginkgo Biloba daily)

facs = scanl (*) 1 [1..]    fac n = facs !! n  

Pointless (ahem) “Points-free” Haskell programmer (studied at Oxford)

fac = foldr (*) 1 . enumFromTo 1  

Iterative Haskell programmer (former Pascal programmer)

fac n = result (for init next done)          where init = (0,1)                next   (i,m) = (i+1, m * (i+1))                done   (i,_) = i==n                result (_,m) = m    for i n d = until d n i  

Iterative one-liner Haskell programmer (former APL and C programmer)

fac n = snd (until ((>n) . fst) (\(i,m) -> (i+1, i*m)) (1,1))  

Accumulating Haskell programmer (building up to a quick climax)

facAcc a 0 = a  facAcc a n = facAcc (n*a) (n-1)    fac = facAcc 1  

Continuation-passing Haskell programmer (raised RABBITS in early years, then moved to New Jersey)

facCps k 0 = k 1  facCps k n = facCps (k . (n *)) (n-1)    fac = facCps id  

Boy Scout Haskell programmer (likes tying knots; always “reverent,” he belongs to the Church of the Least Fixed-Point [8])

y f = f (y f)    fac = y (\f n -> if (n==0) then 1 else n * f (n-1))  

Combinatory Haskell programmer (eschews variables, if not obfuscation; all this currying’s just a phase, though it seldom hinders)

s f g x = f x (g x)    k x y   = x    b f g x = f (g x)    c f g x = f x g    y f     = f (y f)    cond p f g x = if p x then f x else g x    fac  = y (b (cond ((==) 0) (k 1)) (b (s (*)) (c b pred)))  

List-encoding Haskell programmer (prefers to count in unary)

arb = ()    -- "undefined" is also a good RHS, as is "arb" :)    listenc n = replicate n arb  listprj f = length . f . listenc    listprod xs ys = [ i (x,y) | x<-xs, y<-ys ]                   where i _ = arb    facl []         = listenc  1  facl n@(_:pred) = listprod n (facl pred)    fac = listprj facl  

Interpretive Haskell programmer (never “met a language” he didn't like)

-- a dynamically-typed term language    data Term = Occ Var            | Use Prim            | Lit Integer            | App Term Term            | Abs Var  Term            | Rec Var  Term    type Var  = String  type Prim = String      -- a domain of values, including functions    data Value = Num  Integer             | Bool Bool             | Fun (Value -> Value)    instance Show Value where    show (Num  n) = show n    show (Bool b) = show b    show (Fun  _) = ""    prjFun (Fun f) = f  prjFun  _      = error "bad function value"    prjNum (Num n) = n  prjNum  _      = error "bad numeric value"    prjBool (Bool b) = b  prjBool  _       = error "bad boolean value"    binOp inj f = Fun (\i -> (Fun (\j -> inj (f (prjNum i) (prjNum j)))))      -- environments mapping variables to values    type Env = [(Var, Value)]    getval x env =  case lookup x env of                    Just v  -> v                    Nothing -> error ("no value for " ++ x)      -- an environment-based evaluation function    eval env (Occ x) = getval x env  eval env (Use c) = getval c prims  eval env (Lit k) = Num k  eval env (App m n) = prjFun (eval env m) (eval env n)  eval env (Abs x m) = Fun  (\v -> eval ((x,v) : env) m)  eval env (Rec x m) = f where f = eval ((x,f) : env) m      -- a (fixed) "environment" of language primitives    times = binOp Num  (*)    minus = binOp Num  (-)  equal = binOp Bool (==)  cond  = Fun (\b -> Fun (\x -> Fun (\y -> if (prjBool b) then x else y)))    prims = [ ("*", times), ("-", minus), ("==", equal), ("if", cond) ]      -- a term representing factorial and a "wrapper" for evaluation    facTerm = Rec "f" (Abs "n"                 (App (App (App (Use "if")                     (App (App (Use "==") (Occ "n")) (Lit 0))) (Lit 1))                     (App (App (Use "*")  (Occ "n"))                          (App (Occ "f")                                 (App (App (Use "-") (Occ "n")) (Lit 1))))))    fac n = prjNum (eval [] (App facTerm (Lit n)))  

Static Haskell programmer (he does it with class, he’s got that fundep Jones! After Thomas Hallgren’s “Fun with Functional Dependencies” [7])

-- static Peano constructors and numerals    data Zero  data Succ n    type One   = Succ Zero  type Two   = Succ One  type Three = Succ Two  type Four  = Succ Three      -- dynamic representatives for static Peanos    zero  = undefined :: Zero  one   = undefined :: One  two   = undefined :: Two  three = undefined :: Three  four  = undefined :: Four      -- addition, a la Prolog    class Add a b c | a b -> c where    add :: a -> b -> c    instance              Add  Zero    b  b  instance Add a b c => Add (Succ a) b (Succ c)      -- multiplication, a la Prolog    class Mul a b c | a b -> c where    mul :: a -> b -> c    instance                           Mul  Zero    b Zero  instance (Mul a b c, Add b c d) => Mul (Succ a) b d      -- factorial, a la Prolog    class Fac a b | a -> b where    fac :: a -> b    instance                                Fac  Zero    One  instance (Fac n k, Mul (Succ n) k m) => Fac (Succ n) m    -- try, for "instance" (sorry):  --   --     :t fac four  

Beginning graduate Haskell programmer (graduate education tends to liberate one from petty concerns about, e.g., the efficiency of hardware-based integers)

-- the natural numbers, a la Peano    data Nat = Zero | Succ Nat      -- iteration and some applications    iter z s  Zero    = z  iter z s (Succ n) = s (iter z s n)    plus n = iter n     Succ  mult n = iter Zero (plus n)      -- primitive recursion    primrec z s  Zero    = z  primrec z s (Succ n) = s n (primrec z s n)      -- two versions of factorial    fac  = snd . iter (one, one) (\(a,b) -> (Succ a, mult a b))  fac' = primrec one (mult . Succ)      -- for convenience and testing (try e.g. "fac five")    int = iter 0 (1+)    instance Show Nat where    show = show . int    (zero : one : two : three : four : five : _) = iterate Succ Zero  

Origamist Haskell programmer (always starts out with the “basic Bird fold”)

-- (curried, list) fold and an application    fold c n []     = n  fold c n (x:xs) = c x (fold c n xs)    prod = fold (*) 1      -- (curried, boolean-based, list) unfold and an application    unfold p f g x =     if p x        then []        else f x : unfold p f g (g x)    downfrom = unfold (==0) id pred      -- hylomorphisms, as-is or "unfolded" (ouch! sorry ...)    refold  c n p f g   = fold c n . unfold p f g    refold' c n p f g x =     if p x        then n        else c (f x) (refold' c n p f g (g x))      -- several versions of factorial, all (extensionally) equivalent    fac   = prod . downfrom  fac'  = refold  (*) 1 (==0) id pred  fac'' = refold' (*) 1 (==0) id pred  

Cartesianally-inclined Haskell programmer (prefers Greek food, avoids the spicy Indian stuff; inspired by Lex Augusteijn’s “Sorting Morphisms” [3])

-- (product-based, list) catamorphisms and an application    cata (n,c) []     = n  cata (n,c) (x:xs) = c (x, cata (n,c) xs)    mult = uncurry (*)  prod = cata (1, mult)      -- (co-product-based, list) anamorphisms and an application    ana f = either (const []) (cons . pair (id, ana f)) . f    cons = uncurry (:)    downfrom = ana uncount    uncount 0 = Left  ()  uncount n = Right (n, n-1)      -- two variations on list hylomorphisms    hylo  f  g    = cata g . ana f    hylo' f (n,c) = either (const n) (c . pair (id, hylo' f (c,n))) . f    pair (f,g) (x,y) = (f x, g y)      -- several versions of factorial, all (extensionally) equivalent    fac   = prod . downfrom  fac'  = hylo  uncount (1, mult)  fac'' = hylo' uncount (1, mult)  

Ph.D. Haskell programmer (ate so many bananas that his eyes bugged out, now he needs new lenses!)

-- explicit type recursion based on functors    newtype Mu f = Mu (f (Mu f))  deriving Show    in      x  = Mu x  out (Mu x) = x      -- cata- and ana-morphisms, now for *arbitrary* (regular) base functors    cata phi = phi . fmap (cata phi) . out  ana  psi = in  . fmap (ana  psi) . psi      -- base functor and data type for natural numbers,  -- using a curried elimination operator    data N b = Zero | Succ b  deriving Show    instance Functor N where    fmap f = nelim Zero (Succ . f)    nelim z s  Zero    = z  nelim z s (Succ n) = s n    type Nat = Mu N      -- conversion to internal numbers, conveniences and applications    int = cata (nelim 0 (1+))    instance Show Nat where    show = show . int    zero = in   Zero  suck = in . Succ       -- pardon my "French" (Prelude conflict)    plus n = cata (nelim n     suck   )  mult n = cata (nelim zero (plus n))      -- base functor and data type for lists    data L a b = Nil | Cons a b  deriving Show    instance Functor (L a) where    fmap f = lelim Nil (\a b -> Cons a (f b))    lelim n c  Nil       = n  lelim n c (Cons a b) = c a b    type List a = Mu (L a)      -- conversion to internal lists, conveniences and applications    list = cata (lelim [] (:))    instance Show a => Show (List a) where    show = show . list    prod = cata (lelim (suck zero) mult)    upto = ana (nelim Nil (diag (Cons . suck)) . out)    diag f x = f x x    fac = prod . upto  

Post-doc Haskell programmer (from Uustalu, Vene and Pardo’s “Recursion Schemes from Comonads” [4])

-- explicit type recursion with functors and catamorphisms    newtype Mu f = In (f (Mu f))    unIn (In x) = x    cata phi = phi . fmap (cata phi) . unIn      -- base functor and data type for natural numbers,  -- using locally-defined "eliminators"    data N c = Z | S c    instance Functor N where    fmap g  Z    = Z    fmap g (S x) = S (g x)    type Nat = Mu N    zero   = In  Z  suck n = In (S n)    add m = cata phi where    phi  Z    = m    phi (S f) = suck f    mult m = cata phi where    phi  Z    = zero    phi (S f) = add m f      -- explicit products and their functorial action    data Prod e c = Pair c e    outl (Pair x y) = x  outr (Pair x y) = y    fork f g x = Pair (f x) (g x)    instance Functor (Prod e) where    fmap g = fork (g . outl) outr      -- comonads, the categorical "opposite" of monads    class Functor n => Comonad n where    extr :: n a -> a    dupl :: n a -> n (n a)    instance Comonad (Prod e) where    extr = outl    dupl = fork id outr      -- generalized catamorphisms, zygomorphisms and paramorphisms    gcata :: (Functor f, Comonad n) =>             (forall a. f (n a) -> n (f a))               -> (f (n c) -> c) -> Mu f -> c    gcata dist phi = extr . cata (fmap phi . dist . fmap dupl)    zygo chi = gcata (fork (fmap outl) (chi . fmap outr))    para :: Functor f => (f (Prod (Mu f) c) -> c) -> Mu f -> c  para = zygo In      -- factorial, the *hard* way!    fac = para phi where    phi  Z             = suck zero    phi (S (Pair f n)) = mult f (suck n)      -- for convenience and testing    int = cata phi where    phi  Z    = 0    phi (S f) = 1 + f    instance Show (Mu N) where    show = show . int  

Tenured professor (teaching Haskell to freshmen)

fac n = product [1..n]  


D Templates: Functional

template factorial(int n : 1)  {    const factorial = 1;  }    template factorial(int n)  {    const factorial =       n * factorial!(n-1);  }  


template factorial(int n)  {    static if(n == 1)      const factorial = 1;    else       const factorial =         n * factorial!(n-1);  }  

Used like this:



Java 1.6: recursive, memoized (for subsequent calls)

private static Map<BigInteger, BigInteger> _results = new HashMap()    public static BigInteger factorial(BigInteger n){      if (0 >= n.compareTo(BigInteger.ONE))         return BigInteger.ONE.max(n);      if (_results.containsKey(n))         return _results.get(n);      BigInteger result = factorial(n.subtract(BigInteger.ONE)).multiply(n);      _results.put(n, result);      return result;  }  



function factorial( [int] $n )   {       $result = 1;         if ( $n -gt 1 )       {           $result = $n * ( factorial ( $n - 1 ) )       }         $result   }  

Here's a one-liner:

$n..1 | % {$result = 1}{$result *= $_}{$result}  


Bash: Recursive

In bash and recursive, but with the added advantage that it deals with each iteration in a new process. The max it can calculate is !20 before overflowing, but you can still run it for big numbers if you don't care about the answer and want your system to fall over ;)

#!/bin/bash  echo $(($1 * `( [[ $1 -gt 1 ]] && ./$0 $(($1 - 1)) ) || echo 1`));  

Note:If u also have question or solution just comment us below or mail us on toontricks1994@gmail.com
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