Given a number determine whether or not it is valid per the Luhn formula.
The Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers.
The task is to check if a given string is valid.
Strings of length 1 or less are not valid. Spaces are allowed in the input, but they should be stripped before checking. All other non-digit characters are disallowed.
4539 1488 0343 6467
The first step of the Luhn algorithm is to double every second digit, starting from the right. We will be doubling
4_3_ 1_8_ 0_4_ 6_6_
If doubling the number results in a number greater than 9 then subtract 9 from the product. The results of our doubling:
8569 2478 0383 3437
Then sum all of the digits:
8+5+6+9+2+4+7+8+0+3+8+3+3+4+3+7 = 80
If the sum is evenly divisible by 10, then the number is valid. This number is valid!
8273 1232 7352 0569
Double the second digits, starting from the right
7253 2262 5312 0539
Sum the digits
7+2+5+3+2+2+6+2+5+3+1+2+0+5+3+9 = 57
57 is not evenly divisible by 10, so this number is not valid.
Refer to the Installing Elm page for information about installing elm.
The first time you start an exercise, you'll need to ensure you have the appropriate dependencies installed. Thankfully, Elm makes that easy for you and will install dependencies when you try to run tests or build the code.
Execute the tests with:
Automatically run tests again when you save changes:
$ elm-test --watch
As you work your way through the test suite, be sure to remove the
calls from each test until you get them all passing!
The Luhn Algorithm on Wikipedia http://en.wikipedia.org/wiki/Luhn_algorithm
It is possible to submit an incomplete solution so you can see how others have completed the exercise.
module Tests exposing (tests) import Expect import Luhn exposing (valid) import Test exposing (Test, describe, skip, test) tests : Test tests = describe "Luhn" [ test "single digit strings can not be valid" <| \_ -> Expect.equal False (valid "1") , skip <| test "a single zero is invalid" <| \_ -> Expect.equal False (valid "0") , skip <| test "a simple valid SIN that remains valid if reversed" <| \_ -> Expect.equal True (valid "059") , skip <| test "a simple valid SIN that becomes invalid if reversed" <| \_ -> Expect.equal True (valid "59") , skip <| test "a valid Canadian SIN" <| \_ -> Expect.equal True (valid "055 444 285") , skip <| test "invalid Canadian SIN" <| \_ -> Expect.equal False (valid "055 444 286") , skip <| test "invalid credit card" <| \_ -> Expect.equal False (valid "8273 1232 7352 0569") , skip <| test "valid strings with a non-digit included become invalid" <| \_ -> Expect.equal False (valid "055a 444 285") , skip <| test "valid strings with punctuation included become invalid" <| \_ -> Expect.equal False (valid "055-444-285") , skip <| test "valid strings with symbols included become invalid" <| \_ -> Expect.equal False (valid "055£ 444$ 285") , skip <| test "single zero with space is invalid" <| \_ -> Expect.equal False (valid " 0") , skip <| test "more than a single zero is valid" <| \_ -> Expect.equal True (valid "0000 0") , skip <| test "input digit 9 is correctly converted to output digit 9" <| \_ -> Expect.equal True (valid "091") ]
module Luhn exposing (valid) valid : String -> Bool valid input = let number = input |> String.replace " " "" in isValidFormat number && isValidValue number -- PRIVATE isValidFormat : String -> Bool isValidFormat number = String.length number > 1 && String.all Char.isDigit number isValidValue : String -> Bool isValidValue number = let isEvenlyDivisibleBy10 : Int -> Bool isEvenlyDivisibleBy10 num = remainderBy 10 num == 0 in number |> toReversedNumbers |> chunkEvery 2 |> List.foldl addLuhnValue 0 |> isEvenlyDivisibleBy10 toReversedNumbers : String -> List Int toReversedNumbers number = number |> String.reverse |> String.split "" |> List.filterMap String.toInt chunkEvery : Int -> List Int -> List (List Int) chunkEvery size list = if size >= List.length list then [ list ] else let chunk = List.take size list tail = List.drop size list in chunk :: chunkEvery size tail addLuhnValue : List Int -> Int -> Int addLuhnValue chunk acc = case chunk of [ leftValue ] -> acc + leftValue [ leftValue, rightValue ] -> let double : Int -> Int double number = number * 2 subtract9IfGreaterThan9 : Int -> Int subtract9IfGreaterThan9 number = if number > 9 then number - 9 else number rightLuhnValue = rightValue |> double |> subtract9IfGreaterThan9 in acc + leftValue + rightLuhnValue _ -> acc
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.