Recursion/Tree Recursion: Conceptual

Environment DIagram

Draw the environment diagram for the code.

def mystery(n):
    if n <= 0:
        return n
    elif n % 2 == 0
        return mystery(2 * n -1)
        return mystery(n//2)


Look at the following versions of the factorial function. Each of them has one bug that is preventing them from working properly. Identify the bug in each example and explain why it’s wrong. DO NOT JUST LOOK AT THE FACTORIAL FROM LECTURE.

def factorial(num):
    return num * factorial(num - 1)

def factorial(num):
    if num == 1:
        return 1
        return num * factorial(num)

def factorial(num):
    if num == 0:
        return 0
    return num * factorial(num - 1)

Code Writing

Write a recursive function that sums up all numbers between the given parameter num and 0 (kind of like factorial, but instead of multiplication, it uses addition to combine the numbers). Assume num will never be less than 1.
def fact_adder(num):
>>> fact_adder(6)
>>> fact_adder(1)

Write a recursive function that takes in a number num and the number of digits in the number length and reverses the digits in num.
def digit_reverse(num, length):
>>> digit_reverse(12345678, 8)