Published at Jul 28 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.

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
`raise Exception`

, you should write:

```
raise Exception("Meaningful message indicating the source of the error")
```

To run the tests, run the appropriate command below (why they are different):

- Python 2.7:
`py.test luhn_test.py`

- Python 3.4+:
`pytest luhn_test.py`

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
`python -m pytest luhn_test.py`

`pytest`

options-
`-v`

: enable verbose output -
`-x`

: stop running tests on first failure -
`--ff`

: run failures from previous test before running other test cases

For other options, see `python -m pytest -h`

Note that, when trying to submit an exercise, make sure the solution is in the `$EXERCISM_WORKSPACE/python/luhn`

directory.

You can find your Exercism workspace by running `exercism debug`

and looking for the line that starts with `Workspace`

.

For more detailed information about running tests, code style and linting, please see Running the Tests.

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.

```
# -*- coding: utf-8 -*-
import unittest
from luhn import Luhn
# Tests adapted from `problem-specifications//canonical-data.json` @ v1.6.1
class LuhnTest(unittest.TestCase):
def test_single_digit_strings_can_not_be_valid(self):
self.assertIs(Luhn("1").valid(), False)
def test_a_single_zero_is_invalid(self):
self.assertIs(Luhn("0").valid(), False)
def test_a_simple_valid_SIN_that_remains_valid_if_reversed(self):
self.assertIs(Luhn("059").valid(), True)
def test_a_simple_valid_SIN_that_becomes_invalid_if_reversed(self):
self.assertIs(Luhn("59").valid(), True)
def test_a_valid_Canadian_SIN(self):
self.assertIs(Luhn("055 444 285").valid(), True)
def test_invalid_Canadian_SIN(self):
self.assertIs(Luhn("055 444 286").valid(), False)
def test_invalid_credit_card(self):
self.assertIs(Luhn("8273 1232 7352 0569").valid(), False)
def test_valid_number_with_an_even_number_of_digits(self):
self.assertIs(Luhn("095 245 88").valid(), True)
def test_valid_number_with_an_odd_number_of_spaces(self):
self.assertIs(Luhn("234 567 891 234").valid(), True)
def test_valid_strings_with_non_digit_added_at_end_become_invalid(self):
self.assertIs(Luhn("059a").valid(), False)
def test_valid_strings_with_punctuation_included_become_invalid(self):
self.assertIs(Luhn("055-444-285").valid(), False)
def test_valid_strings_with_symbols_included_become_invalid(self):
self.assertIs(Luhn("055# 444$ 285").valid(), False)
def test_single_zero_with_space_is_invalid(self):
self.assertIs(Luhn(" 0").valid(), False)
def test_more_than_a_single_zero_is_valid(self):
self.assertIs(Luhn("0000 0").valid(), True)
def test_input_digit_9_is_correctly_converted_to_output_digit_9(self):
self.assertIs(Luhn("091").valid(), True)
def test_using_ascii_value_for_non_doubled_non_digit_isnot_allowed(self):
self.assertIs(Luhn("055b 444 285").valid(), False)
def test_using_ascii_value_for_doubled_non_digit_isnot_allowed(self):
self.assertIs(Luhn(":9").valid(), False)
def test_is_valid_can_be_called_repeatedly(self):
# Additional track specific test case
# This test was added, because we saw many implementations
# in which the first call to valid() worked, but the
# second call failed().
number = Luhn("055 444 285")
self.assertIs(number.valid(), True)
self.assertIs(number.valid(), True)
if __name__ == '__main__':
unittest.main()
```

```
class Luhn:
def __init__(self, card_num):
self.card_num = card_num # we may need to retrieve original
def valid(self):
digits = self.card_num.replace(" ", "")
if len(digits) <= 1 or not digits.isdigit(): return False
return self.__class__._calc(digits) % 10 == 0
@staticmethod
def _calc(digits, even_spot=False, accumulator=0):
if not digits: return accumulator
value = int(digits[-1])
if even_spot:
value = value * 2
if value >= 10: value = value - 9
return Luhn._calc(digits[:-1], not even_spot, accumulator + value)
```

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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