Practice Quiz3.md

Practice Quiz: Recursion

1.What is recursion used for?

Recursion lets us tackle complex problems by reducing the problem to a simpler one.

2.Which of these activities are good use cases for recursive programs? Check all that apply.

Going through a file system collecting information related to directories and files.
Managing permissions assigned to groups inside a company, when each group can contain both subgroups and users.

3.Fill in the blanks to make the is_power_of function return whether the number is a power of the given base. Note: base is assumed to be a positive number. Tip: for functions that return a boolean value, you can return the result of a comparison.

def is_power_of(number, base):

if number == base:
    return True
# If number is equal to 1, it's a power (base**0).
if number == 1 and base == 0:
    return True

# Base case: when number is smaller than base.
if number < base:
    return False

# Recursive case: keep dividing number by base.
return is_power_of(number/base, base)

print(is_power_of(1,0)) # Should be True
print(is_power_of(8,2)) # Should be True
print(is_power_of(64,4)) # Should be True
print(is_power_of(70,10)) # Should be False

4.The count_users function recursively counts the amount of users that belong to a group in the company system, by going through each of the members of a group and if one of them is a group, recursively calling the function and counting the members. But it has a bug! Can you spot the problem and fix it?

def count_users(group):
count = 0
for member in get_members(group):   
    if is_group(member):
    count += count_users(member)
    else:
    count += 1
return count

print(count_users("sales")) # Should be 3
print(count_users("engineering")) # Should be 8
print(count_users("everyone")) # Should be 18

5.Implement the sum_positive_numbers function, as a recursive function that returns the sum of all positive numbers between the number n received and 1. For example, when n is 3 it should return 1+2+3=6, and when n is 5 it should return 1+2+3+4+5=15.

def sum_positive_numbers(n):
if n == 0:
    return 0
return n + sum_positive_numbers(n - 1)

print(sum_positive_numbers(3)) # Should be 6
print(sum_positive_numbers(5)) # Should be 15