Published at Mar 20 2019
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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.

For installation and learning resources, refer to the exercism help page.

To work on the exercises, you will need `Opam`

and `Base`

. Consult opam website for instructions on how to install `opam`

for your OS. Once `opam`

is installed open a terminal window and run the following command to install base:

```
opam install base
```

To run the tests you will need `OUnit`

. Install it using `opam`

:

```
opam install ounit
```

A Makefile is provided with a default target to compile your solution and run the tests. At the command line, type:

```
make
```

`utop`

is a command line program which allows you to run Ocaml code interactively. The easiest way to install it is via opam:

```
opam install utop
```

Consult utop for more detail.

The exercism/ocaml repository on GitHub is the home for all of the Ocaml exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!

The Luhn Algorithm on Wikipedia http://en.wikipedia.org/wiki/Luhn_algorithm

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
open Base
open OUnit2
open Luhn
let assert_valid expected input _test_ctxt =
assert_equal ~printer:Bool.to_string expected (valid input)
let tests = [
"single digit strings can not be valid" >::
assert_valid false "1";
"a single zero is invalid" >::
assert_valid false "0";
"a simple valid SIN that remains valid if reversed" >::
assert_valid true "059";
"a simple valid SIN that becomes invalid if reversed" >::
assert_valid true "59";
"a valid Canadian SIN" >::
assert_valid true "055 444 285";
"invalid Canadian SIN" >::
assert_valid false "055 444 286";
"invalid credit card" >::
assert_valid false "8273 1232 7352 0569";
"valid strings with a non-digit included become invalid" >::
assert_valid false "055a 444 285";
"valid strings with punctuation included become invalid" >::
assert_valid false "055-444-285";
"valid strings with symbols included become invalid" >::
assert_valid false "055\194\163 444$ 285";
"single zero with space is invalid" >::
assert_valid false " 0";
"more than a single zero is valid" >::
assert_valid true "0000 0";
"input digit 9 is correctly converted to output digit 9" >::
assert_valid true "091";
"strings with non-digits is invalid" >::
assert_valid false ":9";
]
let () =
run_test_tt_main ("luhn tests" >::: tests)
```

```
open! Base
let to_luhn_digits (digits: int list): int list =
let clamp n = if n > 9 then n - 9 else n in
let f index digit =
if (index + 1) % 2 = 0
then clamp (digit * 2)
else digit in
List.rev digits |> List.mapi ~f
let to_digits = List.map ~f:Char.get_digit_exn
let is_valid_luhn digits =
let sum = to_luhn_digits digits |> List.sum (module Int) ~f:Fn.id in
sum % 10 = 0
let valid string =
let char_list =
String.to_list string
|> List.filter ~f:(fun c -> not (Char.equal ' ' c)) in
let is_long_enough =
List.length char_list > 1 in
let is_digits_only =
not (List.exists char_list ~f:(fun c -> not (Char.is_digit c))) in
is_long_enough && is_digits_only && is_valid_luhn (to_digits char_list)
```

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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