def factorial_iter(num):
    '''Returns the factorial of num using iteration.'''
    total = 1
    for i in range(2, num + 1):
        total *= i
    return total


def factorial(num):
    '''Returns the factorial of num using recursion.'''
    print("computing {0}!".format(num))
    if num == 0:
        print("computed 0! = 1")
        return 1
    else:
        answer = num * factorial(num - 1)
        print("computed {0}! = {1}".format(num, answer))
        return answer


def strlen_iter(my_str):
    '''Return the length of my_str without using len.'''
    count = 0
    for char in my_str:
        count += 1
    return count


def strlen(my_str):
    '''recursive strlen'''
    if my_str == '':
        return 0    # base case
    else:
        # recursive case
        return 1 + strlen(my_str[1:])
    
    
def num_digits(num):
    '''Return the number of digits in (positive) num'''
    if num < 10:    # base case
        return 1
    else:           # recursive case
        return 1 + num_digits(num / 10)
    

def power(base, n):
    '''Return base raised to the power n.'''
    if n == 0: # base case
        return 1
    else:       # recursive case
        return base * power(base, n - 1)


def fib(n):
    '''Returns the nth fibonacci number.'''
    if n == 0 or n == 1:  # base cases
        return 1
    else:   # recursive case
        return fib(n - 1) + fib(n - 2)