Published at Aug 10 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.

Execute the tests with:

```
$ mix test
```

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!"
end
```

Or, you can enable all the tests by commenting out the
`ExUnit.configure`

line in the test suite.

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

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.

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.

```
defmodule LuhnTest do
use ExUnit.Case
test "single digit strings can not be valid" do
refute Luhn.valid?("1")
end
@tag :pending
test "A single zero is invalid" do
refute Luhn.valid?("0")
end
@tag :pending
test "a simple valid SIN that remains valid if reversed" do
assert Luhn.valid?("059")
end
@tag :pending
test "a simple valid SIN that becomes invalid if reversed" do
assert Luhn.valid?("59")
end
@tag :pending
test "a valid Canadian SIN" do
assert Luhn.valid?("055 444 285")
end
@tag :pending
test "invalid Canadian SIN" do
refute Luhn.valid?("055 444 286")
end
@tag :pending
test "invalid credit card" do
refute Luhn.valid?("8273 1232 7352 0569")
end
@tag :pending
test "valid strings with a non-digit included become invalid" do
refute Luhn.valid?("055a 444 285")
end
@tag :pending
test "valid strings with punctuation included become invalid" do
refute Luhn.valid?("055-444-285")
end
@tag :pending
test "valid strings with symbols included become invalid" do
refute Luhn.valid?("055£ 444$ 285")
end
@tag :pending
test "single zero with space is invalid" do
refute Luhn.valid?(" 0")
end
@tag :pending
test "more than a single zero is valid" do
assert Luhn.valid?("0000 0")
end
@tag :pending
test "input digit 9 is correctly converted to output digit 9" do
assert Luhn.valid?("091")
end
end
```

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

```
defmodule Luhn do
@two_or_more_digits_only ~r/\A\d{2,}\z/
@doc """
Checks if the given number is valid via the luhn formula
"""
@spec valid?(String.t()) :: boolean
def valid?(number) do
number = String.replace(number, " ", "")
valid_format?(number) and valid_value?(number)
end
defp valid_format?(number) do
String.match?(number, @two_or_more_digits_only)
end
defp valid_value?(number) do
number
|> to_reversed_numbers()
|> Enum.chunk_every(2)
|> Enum.reduce(0, &add_luhn_value/2)
|> evenly_divisible_by_10?()
end
defp to_reversed_numbers(number) do
number
|> String.reverse()
|> String.codepoints()
|> Enum.map(&String.to_integer/1)
end
defp add_luhn_value([left_value, right_value], acc) do
right_luhn_value =
right_value
|> double()
|> subtract_9_if_greater_than_9()
acc + left_value + right_luhn_value
end
defp add_luhn_value([left_value], acc), do: acc + left_value
defp double(number), do: number * 2
defp subtract_9_if_greater_than_9(number) do
if number > 9, do: number - 9, else: number
end
defp evenly_divisible_by_10?(number), do: rem(number, 10) == 0
end
```

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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