## Practice Quiz: Recursion

#### 11. What is recursion used for?

• Recursion is used to create loops in languages where other loops are not available.
• We use recursion only to implement mathematical formulas in code.
• Recursion is used to iterate through files in a single directory.
• Recursion is used to call a function from inside the same function.

#### 12. 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.
• Creating a user account for a new employee.
• Installing or upgrading software on a computer.
• Managing permissions assigned to groups inside a company, when each group can contain both subgroups and users.
• Checking if a computer is connected to the local network.

#### 13. 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): # Base case: when number is smaller than base. if number < base: # If number is equal to 1, it's a power (base**0). return __ # Recursive case: keep dividing number by base. return is_power_of(__, ___)print(is_power_of(8,2)) # Should be Trueprint(is_power_of(64,4)) # Should be Trueprint(is_power_of(70,10)) # Should be False

def is_power_of(number, base):
# Base case: when number is smaller than base.
if number < base:
# If number is equal to 1, it’s a power (base**0).
return number == 1

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

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

#### 14. 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): count += 1 if is_group(member): count += count_users(member) return countprint(count_users("sales")) # Should be 3print(count_users("engineering")) # Should be 8print(count_users("everyone")) # Should be 18

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

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

#### 15. 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): return 0print(sum_positive_numbers(3)) # Should be 6print(sum_positive_numbers(5)) # Should be 15

• def sum_positive_numbers(n):
if n == 1:
return1
elif n <= 0:
return0
else:
return n + sum_positive_numbers(n-1)

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