## 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)

else:

return mystery(n//2)

mystery(6)

### DebUgging

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

else:

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 integers 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)

21

>>> fact_adder(1)

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)

87654321