Algorithm 不同语言中的阶乘算法
我想看看你能想出的所有不同的方法，对于阶乘子程序，或程序。希望是任何人都能来这里，看看他们是否想学习一门新的语言 思想：Algorithm 不同语言中的阶乘算法,algorithm,language-agnostic,Algorithm,Language Agnostic,我想看看你能想出的所有不同的方法，对于阶乘子程序，或程序。希望是任何人都能来这里，看看他们是否想学习一门新的语言 思想： 程序性 功能性 面向对象 一行 模糊的 古怪的 错误代码 基本上我想看一个例子，不同的算法编写方法，以及它们在不同语言中的表现 请将每个条目限制为一个示例。 如果你想强调一种特定的风格、语言，或者仅仅是一个经过深思熟虑的想法，并且适合在一篇文章中发表，我允许你在每个答案中有不止一个例子 唯一真正的要求是它必须找到给定参数的阶乘，用所有语言表示 要有创意！ 建议准则： #
- 程序性
- 功能性
- 面向对象
- 一行
- 模糊的
- 古怪的
- 错误代码
ones = 1 : ones
integers = head ones : zipWith (+) integers (tail ones)
factorials = head integers : zipWith (*) factorials (tail integers)
方案 下面是一个简单的递归定义：
(define (factorial x)
(if (= x 0) 1
(* x (factorial (- x 1)))))
(define factorial
(letrec ((fact (lambda (x accum)
(if (= x 0) accum
(fact (- x 1) (* accum x))))))
(lambda (x)
(fact x 1))))
HAI
CAN HAS STDIO?
I HAS A VAR
I HAS A INT
I HAS A CHEEZBURGER
I HAS A FACTORIALNUM
IM IN YR LOOP
UP VAR!!1
TIEMZD INT!![CHEEZBURGER]
UP FACTORIALNUM!!1
IZ VAR BIGGER THAN FACTORIALNUM? GTFO
IM OUTTA YR LOOP
U SEEZ INT
KTHXBYE
factorial!(5)
template<unsigned int n>
struct factorial {
enum { result = n * factorial<n - 1>::result };
};
template<>
struct factorial<0> {
enum { result = 1 };
};
模板
结构阶乘{
枚举{result=n*阶乘：：result}；
};
模板
结构阶乘{
枚举{result=1}；
};
const unsigned int x = factorial<4>::result;
const unsigned int x=factorial:：result；
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
function factorial( [int] $n )
{
$result = 1;
if ( $n -gt 1 )
{
$result = $n * ( factorial ( $n - 1 ) )
}
$result
}
$n..1 | % {$result = 1}{$result *= $_}{$result}
奇怪的例子？使用gamma函数怎么样！因为，
gamman=（n-1）
OCaml：使用Gamma
让rec gamma z=
设pi=4.0*。atan 1.0英寸
如果z<0.5，则
pi/。（（sin（pi*.z））*（gamma（1.0-.z）））
其他的
设常数=0.99999999980993；676.520368218851；-1259.139216722428；
771.32342877765313; -176.61502916214059; 12.507343278686905;
-0.13857109526572012；9.984369578019516E-6；1.5056327351493116e-7；
|]
在里面
设z=z-。1.0英寸
让结果=Array.fold\u right
（乐趣x y->x+.y）
（Array.mapi）
（乐趣i x->如果i=0那么x其他x/（z+（浮点i）））
常数
)
0
在里面
设x=z+。（float（Array.length consts））-。1.5英寸
设final=（sqrt（2.0*.pi））*。
（x**（z+.0.5））*。
（exp（-.x））*。结果
在里面
最终的
设阶乘_gamma n=_float的int_（gamma（float（n+1）））
BASIC：老派
Java 1.6：递归、记忆化（用于后续调用）
private static Map\u results=new HashMap（）
公共静态BigInteger阶乘（BigInteger n）{
如果（0>=n.compareTo（BigInteger.ONE））
返回BigInteger.ONE.max（n）；
如果（_results.containsKey（n））
返回_results.get（n）；
BigInteger结果=阶乘（n.减法（BigInteger.1））。乘（n）；
_结果：put（n，result）；
返回结果；
}
批次（NT）：
用法：
C:>factorial.bat15C#查找：
没有什么要计算的，只是查一下。要扩展它，请在表中再添加8个数字，64位整数已达到极限。除此之外，还需要一个BigNum类
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];
}
公共静态整数阶乘（intf）
{
如果（f12）
{
抛出新ArgumentException（“超出整数阶乘的范围”）；
}
int[]事实={1,1,2,6,24120720504040320328803628862800，
39916800,479001600};
返回事实[f]；
}
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很难让它正确地显示在这里，但现在我尝试从预览中复制它，它工作了。您需要输入号码并按enter键。
你的纯函数式编程噩梦成真了
唯一具有以下特性的：
一个纯粹的功能基础、核心和库---事实上，这里有完整的API：
- 甚至没有
- 不需要或不允许使用列表
- 没有显式递归，但是
- 一种简单的I/O机制
这是一个带括号的阶乘代码：
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)
特点：
- 没有减法或条件
- 打印所有阶乘（如果等待时间足够长）
- 使用第二层Church数字将第N个阶乘转换为N！星号后跟换行符
- 使用用于递归的
如果您有兴趣尝试理解它，下面是通过Lazier编译器运行的Scheme源代码：
(lazy-def '(fac input)
'((Y (lambda (f n a) ((lambda (b) ((cons 10) ((b (cons 42)) (f (1+ n) b))))
(* a n)))) 1 1))
（有关Y、cons、1、10、42、1+和*）的适当定义）
编辑：
十进制K阶乘
（否则我会粘贴它）。例如，在Unix提示符下：
$ echo "4" | ./lazy facdec.lazy
24
$ echo "5" | ./lazy facdec.lazy
120
$echo“4”|/lazy facdec.lazy
24
$echo“5”|/lazy facdec.lazy
120
对于上面的数字，比如说5，速度相当慢
代码有点臃肿，因为我们必须包括（用lambda演算解释器编写的代码和用Haskell编写的LC-to-Lazy K编译器）。C#：LINQ
Python：函数式，一行程序
注:
- 它支持大整数。例如：
- 当n<0时，它不起作用
$n..1 | % {$result = 1}{$result *= $_}{$result}
fac(0,1).
fac(N,X) :- N1 is N -1, fac(N1, T), X is N * T.
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).
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)))
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
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;
}
@echo off
set n=%1
set result=1
for /l %%i in (%n%, -1, 1) do (
set /a result=result * %%i
)
echo %result%
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];
}
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)
(lazy-def '(fac input)
'((Y (lambda (f n a) ((lambda (b) ((cons 10) ((b (cons 42)) (f (1+ n) b))))
(* a n)))) 1 1))
public static int factorial(int n)
{
return (Enumerable.Range(1, n).Aggregate(1, (previous, value) => previous * value));
}
factorial = lambda n: reduce(lambda x,y: x*y, range(1, n+1), 1)
print factorial(100)
93326215443944152681699238856266700490715968264381621468592963895217599993229915\
608941463976156518286253697920827223758251185210916864000000000000000000000000
curl http://www.google.com/search?q=170!
curl http://www58.wolframalpha.com/input/?i=171!
(factorial=Hash.new{|h,k|k*h[k-1]})[1]=1
factorial[5]
=> 120
+++++
>+<[[->>>>+<<<<]>>>>[-<<<<+>>+>>]<<<<>[->>+<<]<>>>[-<[->>+<<]>>[-<<+<+>>>]<]<[-]><<<-]
×/⍳X
!X
#!/bin/bash
echo $(($1 * `( [[ $1 -gt 1 ]] && ./$0 $(($1 - 1)) ) || echo 1`));
fac(0) -> 1;
fac(N) when N > 0 -> fac(N, 1).
fac(1, R) -> R;
fac(N, R) -> fac(N - 1, R * N).
sub factorial ($n) { [*] 1..$n }
sub postfix:<!> ($n) { [*] 1..$n }
# This function(?) call like below ... It looks like mathematical notation.
say 10!;
<?xml version="1.0"?>
<?xml-stylesheet href="factorial.xsl" type="text/xsl" ?>
<n>
20
</n>
<?xml version="1.0"?>
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:msxsl="urn:schemas-microsoft-com:xslt" >
<xsl:output method="text"/>
<!-- 0! = 1 -->
<xsl:template match="text()[. = 0]">
1
</xsl:template>
<!-- n! = (n-1)! * n-->
<xsl:template match="text()[. > 0]">
<xsl:variable name="x">
<xsl:apply-templates select="msxsl:node-set( . - 1 )/text()"/>
</xsl:variable>
<xsl:value-of select="$x * ."/>
</xsl:template>
<!-- Calculate n! -->
<xsl:template match="/n">
<xsl:apply-templates select="text()"/>
</xsl:template>
</xsl:stylesheet>
fac n = if n == 0
then 1
else n * fac (n-1)
fac = (\(n) ->
(if ((==) n 0)
then 1
else ((*) n (fac ((-) n 1)))))
fac 0 = 1
fac (n+1) = (n+1) * fac n
fac 0 = 1
fac n = n * fac (n-1)
fac n = foldr (*) 1 [1..n]
fac n = foldl (*) 1 [1..n]
-- using foldr to simulate foldl
fac n = foldr (\x g n -> g (x*n)) id [1..n] 1
facs = scanl (*) 1 [1..]
fac n = facs !! n
fac = foldr (*) 1 . enumFromTo 1
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
fac n = snd (until ((>n) . fst) (\(i,m) -> (i+1, i*m)) (1,1))
facAcc a 0 = a
facAcc a n = facAcc (n*a) (n-1)
fac = facAcc 1
facCps k 0 = k 1
facCps k n = facCps (k . (n *)) (n-1)
fac = facCps id
y f = f (y f)
fac = y (\f n -> if (n==0) then 1 else n * f (n-1))
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)))
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
-- 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 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
-- 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
-- (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
-- (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)
-- 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
-- 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
fac n = product [1..n]