solution.py

# In this Kata, you will implement the Luhn Algorithm, which is used to help validate credit card numbers.
# Given a positive integer of up to 16 digits, return true if it is a valid credit card number, and false if it is not.

# Here is the algorithm:
# Double every other digit, scanning from right to left, starting from the second digit (from the right).

# Another way to think about it is:
# if there are an even number of digits, double every other digit starting with the first;
# if there are an odd number of digits, double every other digit starting with the second:
# 1714 ==> [1*, 7, 1*, 4] ==> [2, 7, 2, 4]
# 12345 ==> [1, 2*, 3, 4*, 5] ==> [1, 4, 3, 8, 5]
# 891 ==> [8, 9*, 1] ==> [8, 18, 1]

# If a resulting number is greater than 9,
# replace it with the sum of its own digits (which is the same as subtracting 9 from it):
# [8, 18*, 1] ==> [8, (1+8), 1] ==> [8, 9, 1]
# or:
# [8, 18*, 1] ==> [8, (18-9), 1] ==> [8, 9, 1]

# Sum all of the final digits:
# [8, 9, 1] ==> 8 + 9 + 1 = 18

# Finally, take that sum and divide it by 10. If the remainder equals zero, the original credit card number is valid.
# 18 (modulus) 10 ==> 8 , which is not equal to 0, so this is not a valid credit card number


def validate(numbers):
    numbers = list(map(int, str(numbers)))

    is_even = len(numbers) % 2
    start_range = 1 if is_even else 0
    indexes = list(range(start_range, len(numbers), 2))

    for i in indexes:
        numbers[i] = numbers[i] * 2
        numbers[i] = numbers[i] - 9 if numbers[i] > 9 else numbers[i]

    return not sum(numbers) % 10