Lecture_7

Definition:
Recursive function: a function is called recursive if the body of that function calls itself, either directly or indirectly.

A useful algorithm:
def split(n):
   return n // 10, n % 10

def sum_digits(n):
    if n < 10:
        return n
    else:
        all_but_last, last = split(n)
        return sum_digits(all_but_last) + last

>>> sum_digits(123)
6

Another example of factorial:
def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n - 1)

>>> factorial(3)
6

Note: iteration is a special case of recursion.

Now we need to study the Luhn algorithm. This algorithm applies widely in checking credit card numbers. That is, it will double every digits of the credit card number, if the product is greater than 9, then replace it with the sum of its digits. At last find the sum of the transformed digits.

def sum_digits(n):
    if n < 10:
        return n
    else:
        all_but_last, last = split(n)
        return sum_digits(all_but_last) + last
        
def luhn_sum(n):
    if n < 10:
        return n
    else:
        all_but_last, last = split(n)
        return luhn_sum_double(all_but_last) + last

def luhn_sum_double(n):
    all_but_last, last = split(n)
    luhn_digit = sum_digits(2 * last)
    if n < 10:
        return luhn_digit
    else:
        return luhn_sum(all_but_last) + luhn_digit