def factorial_iterative(n):
    '''returns the factorial of n'''
    total = 1
    for i in range(2, n + 1):
        total *= i
    return total

def factorial_recursive(n):
    print("computing {0}!".format(n))
    if n == 0: # base case
        print("computed 0! = 1")
        return 1
    else: # recursive case
        result = n * factorial(n - 1)
        print("computed {0}! = {1}".format(n, result))
        return result
    
def strlen_iterative(s):
    '''returns the length of s without using len'''
    count = 0
    for char in s:
        count += 1
    return count

def strlen_recursive(s):
    if s == '':
        # base case
        return 0
    else:
        # recursive case
        return 1 + strlen(s[1:])
    
def num_digits(n):
    '''return the number of digits in n'''
    if n < 10:
        # base case
        return 1
    else:
        # recursive case
        return 1 + num_digits(n / 10)
    
def power(base, n):
    '''returns base raised to the power n'''
    if n == 0:
        # base case
        return 1
    else:
        # recursive case
        return base * power(base, n - 1)