# Luhn Algorithm in Python

The Luhn Algorithm, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, and more. It's often used to check whether a given number is potentially valid based on its checksum digit. Here's a Python function to perform the Luhn check:

```
def luhn_check(num):
# Convert the number to a list of digits in reverse order
arr = [int(x) for x in str(num)][::-1]
# Remove the last digit (checksum digit)
last_digit = arr.pop(0)
# Calculate the Luhn sum
total = sum(val if i % 2 != 0 else ((val * 2) % 9) or 9 for i, val in enumerate(arr))
# Add back the last digit
total += last_digit
# Check if the total is divisible by 10
return total % 10 == 0
```

## Explantion of Luhncheck Algorithm

`def luhn_check(num):`

: This line defines a function called`luhn_check`

that takes an input`num`

, which is the number you want to validate using the Luhn algorithm.`arr = [int(x) for x in str(num)][::-1]`

: This line converts the input`num`

into a list of digits in reverse order. It does the following:`str(num)`

: Converts the number to a string so that we can iterate through its digits.`[int(x) for x in str(num)]`

: Uses a list comprehension to convert each character (digit) in the string back to an integer, creating a list of digits.`[::-1]`

: Reverses the list so that we can start processing from the rightmost digit (the last digit).

`last_digit = arr.pop(0)`

: This line removes and stores the rightmost digit (the checksum digit) from the list`arr`

.`total = sum(val if i % 2 != 0 else ((val * 2) % 9) or 9 for i, val in enumerate(arr))`

: This line calculates the Luhn sum. It uses a generator expression and the`sum`

function to iterate through the list of digits and perform the following operations for each digit:`enumerate(arr)`

: Enumerates through the list`arr`

, providing both the index`i`

and the digit`val`

.`(val if i % 2 != 0 else ((val * 2) % 9) or 9)`

: For each digit, it checks if the index`i`

is odd (`i % 2 != 0`

). If it's odd, it uses the original digit`val`

. If it's even, it doubles the digit using`(val * 2)`

, and if the result is greater than 9, it subtracts 9 (`((val * 2) % 9) or 9`

). This step handles the doubling and subtracting 9, if necessary, for every second digit.

`total += last_digit`

: Adds back the rightmost digit (the checksum digit) to the`total`

.`return total % 10 == 0`

: Checks if the`total`

is divisible by 10. If it is, the function returns`True`

, indicating that the input number is valid according to the Luhn algorithm. Otherwise, it returns`False`

.

```
# Example usage:
card_number = "79927398713"
if luhn_check(card_number):
print(f"{card_number} is a valid card number.")
else:
print(f"{card_number} is not a valid card number.")
```

## Summary

In summary, this concise Python implementation converting the input number to a list of digits in reverse order, applying the Luhn algorithm operations, and checking the result for divisibility by 10 to determine its validity.

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