Haskell中的Luhn算法

Question

我想我已经在Haskell中正确地计算了Luhn algorithm：

f1 :: Integer -> [Integer]
f1 x = if x < 10 then [x] else (f1 (div x 10))++[mod x 10]

f2 :: [Integer] -> [Integer]
f2 xs = [(!!) xs (x - 1) | x <- [1..(length xs)] , even x]

f3 :: [Integer] -> [Integer]
f3 xs = if mod (length xs) 2 /= 0 then (f2 xs) else (f2 (0:xs))

f4 :: [Integer] -> [Integer]
f4 xs = map (*2) (f3 xs)

f5 :: [Integer] -> [[Integer]]
f5 xs = map f1 xs

f6 :: [[Integer]] -> [Integer]
f6 [] = []
f6 (xs : xss) = xs++(f6 xss)

f7 :: [Integer] -> [Integer]
f7 xs = [(!!) xs (x - 1) | x <- [1..(length xs)] , odd x]

f8 :: [Integer] -> [Integer]
f8 xs = if mod (length xs) 2 /= 0 then (f7 xs) else (f7 (0:xs))

f9 :: [Integer] -> [Integer]
f9 xs = (f8 xs) ++ (f4 xs)

f :: Integer -> Integer
f x = sum (f6 (f5 (f9 xs)))
   where xs = f1 x

luhn :: Integer -> Bool
luhn x = if mod (f x) 10 == 0 then True else False

例如,

luhn 49927398716 ==> True
luhn 49927398717 ==> False

现在我必须创建一个新的函数sigLuhn，在给定一个整数n的情况下，使用luhn n == True，然后sigLuhn n给出数字，这样如果我们将数字加到最后的数字到n，那么新的数字也会验证Luhn算法；如果是luhn n == False，函数会给出一个错误。例如,

sigLuhn 49927398716 ==> [8]

因为如果我们调用n = 49927398716

luhn (10*n + 8) ==> True

8是0中的最小整数。我的想法是下一个：

g1 :: Integer -> Integer
g1 x = div 10 x + 1

g2 :: Integer -> Integer -> Integer
g2 x y = x*(floor (10)^(g1 y)) + y

g3 :: Integer -> [Bool]
g3 x = [luhn (g2 x y) | y <- [1..]]

g4 :: [Bool] -> Int
g4 xs = minimum (elemIndices True xs)

g :: Integer -> Int
g x = g4 (g3 x)

sigLuhn :: Integer -> [Int]
sigLuhn x = if (luhn x) then [g x] else error "The conditions of Luhn's algorithm are not valid"

代码不会给出错误，但是sigLuhn不能正确使用此代码。简而言之，如果我们假设函数luhn是好的，您能帮助我正确地编写sigLuhn吗？非常感谢。

Answer 1

我是去年秋天在班上布置的。这是最好的解决方案之一。

doubleAndSum :: [Int] -> Int
doubleAndSum = fst . foldr (\i (acc, even) -> (acc + nextStep even i, not even)) (0,False)
  where 
    nextStep even i
        | even      = (uncurry (+) . (`divMod` 10) . (*2)) i
        | otherwise = i 

myLuhn :: Int -> Bool
myLuhn = (0 ==) . (`mod` 10) . doubleAndSum . (map (read . (: ""))) . show

testCC :: [Bool]
testCC = map myLuhn [49927398716, 49927398717, 1234567812345678, 1234567812345670]
-- => [True,False,False,True]