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 library documentation, follow Useful OCaml resources.
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The Luhn Algorithm on Wikipedia http://en.wikipedia.org/wiki/Luhn_algorithm
(* luhn - 1.6.1 *)
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 number with an even number of digits" >::
assert_valid true "095 245 88";
"valid number with an odd number of spaces" >::
assert_valid true "234 567 891 234";
"valid strings with a non-digit added at the end become invalid" >::
assert_valid false "059a";
"valid strings with punctuation included become invalid" >::
assert_valid false "055-444-285";
"valid strings with symbols included become invalid" >::
assert_valid false "055# 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";
"using ascii value for non-doubled non-digit isn't allowed" >::
assert_valid false "055b 444 285";
"using ascii value for doubled non-digit isn't allowed" >::
assert_valid false ":9";
]
let () =
run_test_tt_main ("luhn tests" >::: tests)
let valid sn = match String.trim sn with
| s when String.length s < 2 -> false
| s ->
let cint c = Char.code c - 0x30 in
let luhn n = if n > 4 then n * 2 - 9 else n * 2 in
let even n = n land 1 = 0 in
let rec check ?(i=String.length s) ?(n=1) ?(a=0) () =
match i with
| 0 -> Some a
| _ ->
begin match s.[i-1] with
| ' ' -> check ~i:(i-1) ~n:n ~a:a ()
| '0'..'9' as c -> if even n
then check ~i:(i-1) ~n:(n+1) ~a:(a + luhn (cint c)) ()
else check ~i:(i-1) ~n:(n+1) ~a:(a + cint c) ()
| _ -> None
end
in match check() with
| Some a -> a mod 10 = 0
| None -> false
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