Instructions

Test suite

Solution

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:

```
$ elm-test
```

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 `skip <|`

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.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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