OCR H446 algorithms / AQA 7517 recursion
Write a recursive factorial function with a base case.
Recursion solves a problem by calling the same function on a smaller input. Every recursive solution needs a base case that stops further calls. Trace each call and the values returned as the call stack unwinds.
Watch out: A missing or unreachable base case leads to repeated calls until Python raises a recursion error.
Study this example, identify inputs and outputs, then trace the key variables. Run and adapt it in Python 3.
def factorial(n):
if n < 0: raise ValueError("n must be non-negative")
if n <= 1: return 1
return n * factorial(n-1)
Write a recursive factorial function with a base case. Download the starter, design your solution, and add tests before revealing the answer.
Download starter + solution ZIP ↓
Stretch task: investigate time/space complexity or data validation, then write an evaluation of your approach.
def factorial(n):
if n < 0: raise ValueError("n must be non-negative")
if n <= 1: return 1
return n * factorial(n-1)
assert factorial(0) == 1
assert factorial(5) == 120
print(factorial(5))
Change one boundary condition in the starter or reference program. Predict which test fails, then repair it and document why.
Concept check: What happens if a recursive function has no reachable base case?
It eventually raises RecursionError because calls continue until the call-stack limit.
Describe the algorithm or design in your own words; include a normal test, a boundary test and an invalid input. Compare your answers with the reference solution and record one improvement.
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