Haskell作业|检查一个信用卡卡号是否有效
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Have you ever wondered how websites validate your credit card number when you shop online? They don’t check a massive database of numbers, and they don’t use magic. In fact, most credit providers rely on a checksum formula for distinguishing valid numbers from random collection of digits (or typing mistakes).
In this lab, you will implement a validation algorithm for credit cards. The algorithm follows these steps:
- Double the value of every second digit beginning with the rightmost.
- Add the digits of the doubled values and the undoubled digits from the original number.
- Calculate the modulus of the sum divided by 10.
If the result equals 0, then the number is valid. Here is an example of the results of each step on the number 4012888888881881.
- In order to start with the rightmost digit, we produce a reversed list of digits. Then, we double every second digit.
Result: [1,16,8,2,8,16,8,16,8,16,8,16,2,2,0,8].
- We sum all of the digits of the resulting list above. Note that we must again split the elements of the list into their digits (e.g. 16 becomes [1, 6]).
Result: 90.
- Finally, we calculate the modulus of 90 over 10.
Result: 0.
Since the final value is 0, we know that the above number is a valid credit card number. If we make a mistake in typing the credit card number and instead provide 4012888888881891, then the result of the last step is 2, proving that the number is invalid.
isValid :: Integer -> Bool
isValid x = if mod (sum (splitNumGtTen (doubleSecondDigit (formARevList x)))) 10 == 0 then True else False
numValid :: [Integer] -> Integer
numValid xs = sum . map (\_ -> 1) $ filter isValid xs
formARevList :: Integer -> [Integer]
formARevList x
|x <= 9 = [x]
|otherwise = formARevList (mod x 10) ++ formARevList (div x 10)
doubleSecondDigit :: [Integer] -> [Integer]
doubleSecondDigit [x] = [x]
doubleSecondDigit (x:[y]) = [x] ++ [2*y]
doubleSecondDigit (x:y:xs) = [x] ++ [2*y] ++ doubleSecondDigit xs
splitNumGtTen :: [Integer] -> [Integer]
splitNumGtTen [x]
|x <= 9 = [x]
|otherwise = [div x 10] ++ [mod x 10]
splitNumGtTen (x:xs)
|x <= 9 = [x] ++ splitNumGtTen xs
|otherwise = [div x 10] ++ [mod x 10] ++ splitNumGtTen xs
creditcards :: [Integer]
creditcards = [ 4716347184862961,
4532899082537349,
4485429517622493,
4320635998241421,
4929778869082405,
5256283618614517,
5507514403575522,
5191806267524120,
5396452857080331,
5567798501168013,
6011798764103720,
6011970953092861,
6011486447384806,
6011337752144550,
6011442159205994,
4916188093226163,
4916699537435624,
4024607115319476,
4556945538735693,
4532818294886666,
5349308918130507,
5156469512589415,
5210896944802939,
5442782486960998,
5385907818416901,
6011920409800508,
6011978316213975,
6011221666280064,
6011285399268094,
6011111757787451,
4024007106747875,
4916148692391990,
4916918116659358,
4024007109091313,
4716815014741522,
5370975221279675,
5586822747605880,
5446122675080587,
5361718970369004,
5543878863367027,
6011996932510178,
6011475323876084,
6011358905586117,
6011672107152563,
6011660634944997,
4532917110736356,
4485548499291791,
4532098581822262,
4018626753711468,
4454290525773941,
5593710059099297,
5275213041261476,
5244162726358685,
5583726743957726,
5108718020905086,
6011887079002610,
6011119104045333,
6011296087222376,
6011183539053619,
6011067418196187,
4532462702719400,
4420029044272063,
4716494048062261,
4916853817750471,
4327554795485824,
5138477489321723,
5452898762612993,
5246310677063212,
5211257116158320,
5230793016257272,
6011265295282522,
6011034443437754,
6011582769987164,
6011821695998586,
6011420220198992,
4716625186530516,
4485290399115271,
4556449305907296,
4532036228186543,
4916950537496300,
5188481717181072,
5535021441100707,
5331217916806887,
5212754109160056,
5580039541241472,
6011450326200252,
6011141461689343,
6011886911067144,
6011835735645726,
6011063209139742,
379517444387209,
377250784667541,
347171902952673,
379852678889749,
345449316207827,
349968440887576,
347727987370269,
370147776002793,
374465794689268,
340860752032008,
349569393937707,
379610201376008,
346590844560212,
376638943222680,
378753384029375,
348159548355291,
345714137642682,
347556554119626,
370919740116903,
375059255910682,
373129538038460,
346734548488728,
370697814213115,
377968192654740,
379127496780069,
375213257576161,
379055805946370,
345835454524671,
377851536227201,
345763240913232
]