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davearonson's solution

to Luhn in the Elixir Track

Published at Jul 13 2018 · 0 comments
Test suite


This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

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.

Validating a Number

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.

Example 1: valid credit card number

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!

Example 2: invalid credit card number

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.

Running tests

Execute the tests with:

$ elixir luhn_test.exs

Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant @tag :pending with a # symbol.

For example:

# @tag :pending
test "shouting" do
  assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"

Or, you can enable all the tests by commenting out the ExUnit.configure line in the test suite.

# ExUnit.configure exclude: :pending, trace: true

For more detailed information about the Elixir track, please see the help page.


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

Submitting Incomplete Solutions

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


if !System.get_env("EXERCISM_TEST_EXAMPLES") do
  Code.load_file("luhn.exs", __DIR__)

ExUnit.configure(exclude: :pending, trace: true)

defmodule LuhnTest do
  use ExUnit.Case

  test "single digit strings can not be valid" do
    refute Luhn.valid?("1")

  @tag :pending
  test "A single zero is invalid" do
    refute Luhn.valid?("0")

  @tag :pending
  test "a simple valid SIN that remains valid if reversed" do
    assert Luhn.valid?("059")

  @tag :pending
  test "a simple valid SIN that becomes invalid if reversed" do
    assert Luhn.valid?("59")

  @tag :pending
  test "a valid Canadian SIN" do
    assert Luhn.valid?("055 444 285")

  @tag :pending
  test "invalid Canadian SIN" do
    refute Luhn.valid?("055 444 286")

  @tag :pending
  test "invalid credit card" do
    refute Luhn.valid?("8273 1232 7352 0569")

  @tag :pending
  test "valid strings with a non-digit included become invalid" do
    refute Luhn.valid?("055a 444 285")

  @tag :pending
  test "valid strings with punctuation included become invalid" do
    refute Luhn.valid?("055-444-285")

  @tag :pending
  test "valid strings with symbols included become invalid" do
    refute Luhn.valid?("055£ 444$ 285")

  @tag :pending
  test "single zero with space is invalid" do
    refute Luhn.valid?(" 0")

  @tag :pending
  test "more than a single zero is valid" do
    assert Luhn.valid?("0000 0")

  @tag :pending
  test "input digit 9 is correctly converted to output digit 9" do
    assert Luhn.valid?("091")
defmodule Luhn do
  @doc """
  Calculates the total checksum of a number
  @spec checksum(String.t()) :: integer
  def checksum(number_as_string) do
    |> String.graphemes
    |> Enum.map(&String.to_integer &1)
    |> Enum.reverse
    |> do_checksum(0)

  defp do_checksum([single|[double|more]], acc) do
    do_checksum(more, acc + double_value(double) + single)
  defp do_checksum([single], acc), do: acc + single
  defp do_checksum([],       acc), do: acc

  defp double_value(digit) when digit < 5, do: digit * 2
  defp double_value(digit)               , do: digit * 2 - 9

  @doc """
  Checks if the given number is valid via the luhn formula
  @spec valid?(String.t()) :: boolean
  def valid?(number_as_string) do
    rem(checksum(number_as_string), 10) == 0

  @doc """
  Creates a valid number by adding the correct
  checksum digit to the end of the number
  @spec create(String.t()) :: String.t()
  def create(number_as_string) do

  defp check_digit(number_as_string) do
    make_non_negative(-rem(checksum("#{number_as_string}0"), 10))

  defp make_non_negative(0), do: 0
  defp make_non_negative(n), do: n + 10


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