def factorial_iterative(n):
    """
    Returns the factorial of n, iteratively
    :param n: (num) the number to calculate its factorial
    :return: (num) n!
    """
    num = 1

    for i in range(2, n + 1):
        num *= i  # same as num = num * i

    return num


def factorial_iterative2(n):
    """
    Returns the factorial of n, iteratively, in an alternative implementation
    :param n: (num) the number to calculate its factorial
    :return: (num) n!
    """
    num = 1

    for i in range(n):
        num *= (i + 1)  # same as num = num * i

    return num


def factorial(n):
    """
    Returns the factorial of n, recursively
    :param n: (num) the number to calculate its factorial
    :return: (num) n!
    """
    # check the base case
    if n == 1:
        return 1
    else:
        # the recursive case
        return n * factorial(n - 1)


def rec_sum(n):
    """
    Calculates the sum of all numbers from 1 to n
    :param n: (positive int) the num to calculate the sum up to
    :return: (int) the sum from 1 to n
    """
    if n == 0:
        return 0
    else:
        return n + rec_sum(n-1)


def rec_sum_list(some_list):
    """
    Calculates the sum of all numbers in some_list
    :param some_list: (list) a list of numbers
    :return: (int) the sum of all the numbers in the list
    """
    if some_list == []:
        return 0
    else:
        return some_list[0] + rec_sum_list(some_list[1:])


def rec_sum_list_print(some_list):
    """
    Calculates the sum of all numbers in some_list and prints the intermediate steps of the recursion
    :param some_list: (list) a list of numbers
    :return: (int) the sum of all the numbers in the list
    """
    print("Calling rec_sum_list: " + str(some_list))

    if some_list == []:
        print("base case returning 0")
        return 0
    else:
        answer = some_list[0] + rec_sum_list_print(some_list[1:])
        print(str(some_list) + " returning " + str(answer))
        return answer


def reverse(some_string):
    """
    Returns the reverse of some_string
    :param some_string: (str) the string to reverse
    :return: (str) the reversed string
    """
    if some_string == "":
        return ""
    else:
        return reverse(some_string[1:]) + some_string[0]


def reverse_print(some_string):
    """
    Returns the reverse of some_string and prints the intermediate steps of the recursion
    :param some_string: (str) the string to reverse
    :return: (str) the reversed string
    """
    print("calling " + some_string)
    if some_string == "":
        print("return base ")
        return ""
    else:
        answer = reverse_print(some_string[1:]) + some_string[0]
        print("returning " + answer)
        return answer


def power(base, exponent):
    """
    Returns base^exponent
    :param base: (num) the base
    :param exponent: (num) the exponent
    :return: (num) base^exponent
    """
    if exponent == 0:
        return 1
    else:
        return base * power(base, exponent - 1)