3. A powerful method in control flow is recursion. A function acts recursively if it calls itself while being
executed. This is often useful when a large computation can be reduced to the same calculation on smaller
parts.
Here's an example:
def count_down(n)
if n 0:
print(n)
count_down(n-1)
elif n ==0:
print('Boom!')
This function counts down from a given integer, and then prints Boom when it gets to zero.
Use recursion to write a function that returns n!, where
2.1.
n!=n.(n-1).(n- . - 2) .

Question

3. A powerful method in control flow is recursion. A function acts recursively if it calls itself while being
executed. This is often useful when a large computation can be reduced to the same calculation on smaller
parts.
Here's an example:
def count_down(n)
if n > 0:
print(n)
count_down(n-1)
elif n ==0:
print('Boom!')
This function counts down from a given integer, and then prints Boom when it gets to zero.
Use recursion to write a function that returns n!, where
2.1.
n!=n.(n-1).(n- . - 2) .

Accepted Answer

∻Explanation∻ ⚹The student is asking for a recursive function to calculate the factorial of a number $n$.⚹ ∻Step-by-step Instruction∻ ‖ ▪ ⋮ **Define the main function required here**: A function that calculates the factorial of a number using recursion. ‖ ‖ ▪ ⋮ The function should call itself with a decremented value of $n$ until it reaches 1. ‖ ‖ ▪ ⋮ **Define concrete use cases and testing cases for the function**: When the function is called with a positive integer, it should return the factorial of that integer. ‖ Here is the code to achieve this: ```python # define a function to calculate factorial using recursion def factorial(n): # if n is 0 or 1, return 1 (base case) if n == 0 or n == 1: return 1 # else, return n multiplied by factorial of n-1 (recursive case) else: return n * factorial(n - 1) ``` ```python # main function that tests factorial function def main_factorial(): # test the factorial function # use case 1: factorial of 5 assert factorial(5) == 120 # use case 2: factorial of 3 assert factorial(3) == 6 ``` ∻Time Complexity∻ ⚹The time complexity of the recursive factorial function is $O(n)$ because it makes $n$ recursive calls.⚹ ∻Space Complexity∻ ⚹The space complexity is also $O(n)$ due to the $n$ recursive calls that add to the call stack.⚹

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