Cambridge Syllabus Notes

Algorithm Design & Problem‑Solving 📐

In IGCSE Computer Science, you’ll learn how to turn a problem into a clear step‑by‑step plan (an algorithm) and then test it with trace tables and real data. Think of an algorithm like a recipe for a cake – it tells you exactly what ingredients to use and in what order.

What is a Trace Table? 🔍

A trace table records the values of variables at each step of the algorithm. It’s like a diary that shows how the algorithm changes the data.

Example: Find the Largest of Three Numbers

Algorithm (pseudo‑code):

Input three numbers: a, b, c.
Set max = a.
If $b > \text{max}$, set max = b.
If $c > \text{max}$, set max = c.
Output max.

Let’s trace the algorithm with the test data a = 7, b = 12, c = 5:

Step	a	b	c	max
1	7	12	5	—
2	7	12	5	7
3	7	12	5	12
4	7	12	5	12
5	7	12	5	12

Result: max = 12.

Exam Tip Box 📝

Tip: When creating a trace table, label each column clearly and update the table after every line of the algorithm. This shows the examiner that you understand how data changes over time. Also, test with at least two different sets of data – one where the first number is the largest and one where the last number is the largest – to prove your algorithm works for all cases.

Analogy: The Algorithm as a Road Map 🚗

Imagine you’re planning a road trip. The algorithm is the map that tells you which roads to take, when to stop for gas, and how to avoid traffic. A trace table is like a GPS that records every turn you make, so you can see if you followed the map correctly.

Practice Question

Write a simple algorithm that checks whether a number n is even or odd. Then create a trace table for n = 7 and n = 10.

Exam Hint: Remember to use the modulo operator ($n \bmod 2$) to test for evenness. Show the intermediate value of $n \bmod 2$ in your trace table.

Key Takeaways 🎯

Algorithms are step‑by‑step instructions that solve a problem.
Trace tables help you verify that each step behaves as expected.
Always test your algorithm with multiple data sets.
Use clear, descriptive variable names.
In exams, show your trace table neatly and label every column.

Good luck, and remember: practice makes perfect! 🚀

Test algorithms using trace tables and test data