Implementation of Luhn Formula

Question

I was trying to implement the Luhn Formula in Python. Here is my code:

import sys


def luhn_check(number):
    if number.isdigit():
        last_digit = int(         


        

Answer 1

The main problem with your logic is that you are applying some computations that are only for the odd digits to the even digits too.

I have some suggestions for you:

1. Instead of receiving an int as input, receive a string so you can handle numbers with trailing zeros.
2. Try to apply list comprehensions or use map when processing a list
3. You could define some helper functions to improve your code redability.

Considering what I have suggested, this is how I would solve this problem. Notice that I am using Python's type annotations. I will also highlight the steps of Luhn's algorithm with comments.

def compute_sum_of_remainig_digits(remaining_digits: List[int]) -> int:
    # use a list comprehension to extract digits in even positions
    even_positions = remaining_digits[-2::-2]
    # use a list comprehension to extract digits in odd positions
    odd_positions = remaining_digits[-1::-2]
    # 2. Multiply the digits in odd positions (1, 3, 5, etc.) by 2
    # and subtract 9 to all any result higher than 9
    computed_odd = [2 * d - 9 if 2 * d > 9 else 2 * d for d in odd_positions]
    # 3. Add all the numbers together
    return sum(even_positions + computed_odd)


def compute_checksum(number: str) -> int:
    # the following line convert a string of digits into list of digits using map
    # this way you do not need to explicitly declare a for loop
    digits = list(map(int, number))
    # 1. Drop the last digit from the number...
    last_digit = digits[-1]
    total = compute_sum_of_remainig_digits(digits[:-1 ])

    # 4. The check digit (the last number of the card) is
    # the amount that you would need to add...
    return (total + last_digit)


def check_valid_number(number: str) -> bool:
    # 4. ...to get a multiple of 10 (Modulo 10)
    return (compute_checksum(number) * 9) % 10 == 0

Now let's validate the previous code:

>>> valid_number = "4929355681587216"
>>> invalid_number = "5183814022326227"
>>> check_valid_number(valid_number)
True
>>> check_valid_number(invalid_number)
False

I hope this answer helps you or helps other people in trouble to understand how to compute a Luhn's checker.

Answer 2

I think the algorithm is not correct.

The second step you need to sum the digits of the products instead of substract 9. Reference: Wikipedia.

In the Wikipedia you have this example:

def luhn_checksum(card_number):
    def digits_of(n):
        return [int(d) for d in str(n)]
    digits = digits_of(card_number)
    odd_digits = digits[-1::-2]
    even_digits = digits[-2::-2]
    checksum = 0
    checksum += sum(odd_digits)
    for d in even_digits:
        checksum += sum(digits_of(d*2))
    return checksum % 10

def is_luhn_valid(card_number):
    return luhn_checksum(card_number) == 0


result = is_luhn_valid(4532015112830366)
print 'Correct:' + str(result)
result = is_luhn_valid(6011514433546201)
print 'Correct:' + str(result)
result = is_luhn_valid(6771549495586802)
print 'Correct:' + str(result)

Result:

>>>Correct:True
>>>Correct:True
>>>Correct:True