Recursion vs. Iteration in GCSE Computer Science

In GCSE Computer Science (AQA, OCR, Edexcel), you are expected to master standard iterative algorithms—loops like for and while. But what happens when a function calls itself? 

Welcome to Recursion: an advanced algorithmic technique that elegant code relies on.

1. What is Recursion?

A recursive function is simply a function that calls itself from within its own code block. While an iterative loop repeats an action using a counter or condition, recursion breaks a problem down into smaller sub-problems until it reaches the simplest possible version.

2. Case Study: Calculating Factorials (n!)

The factorial of a positive integer n (written as n!) is the product of all positive integers less than or equal to n. 

E.g. 

5! = 5 x 4 x 3  x 2 x 1 = 120.

6! = 6 x 5 x 4 x 3  x 2 x 1 = 720.

0! = 1

1! = 1

Approach A: The Iterative Solution (Standard Loop)

This is the standard approach taught in most GCSE programming lessons:

def factorial_iterative(n):
    result = 1
    # Loop from 1 up to n
    for i in range(1, n + 1):
        result *= i
    return result

print(factorial_iterative(5))  # Output: 120

Approach B: The Recursive Solution (Advanced)

Notice how mathematical definition n! = n  x (n-1)! directly maps into recursive Python code:

def factorial_recursive(n):
    # 1. BASE CASE: Stop when n reaches 1 or 0
    if n <= 1:
        return 1
    # 2. RECURSIVE CASE: Function calls itself with (n - 1)
    else:
        return n * factorial_recursive(n - 1)

print(factorial_recursive(5))  # Output: 120

3. How the Call Stack Works Under the Hood

When factorial_recursive(5) runs, Python pushes each function call onto a Call Stack in memory until the base case is satisfied:

factorial_recursive(5) ──> 5 * factorial_recursive(4)
factorial_recursive(4) ──> 4 * factorial_recursive(3)
factorial_recursive(3) ──> 3 * factorial_recursive(2)
factorial_recursive(2) ──> 2 * factorial_recursive(1)
factorial_recursive(1) ──> RETURNS 1 (BASE CASE REACHED)

Unwinding the stack back up:
Return 1  --> 2 * 1 = 2  --> 3 * 2 = 6  --> 4 * 6 = 24  --> 5 * 24 = 120!

4. Iteration vs Recursion Comparison

5. Practice Challenge for Students

Try copying the recursive code and heading over to our interactive Python Console on the Computer Science page to test your solution! Build a Recursive Countdown Function that counts down from n to 0 and prints "Blast off!".