Problem Solving and Design

Decomposition is the process of breaking a large, complex problem down into smaller, easier sub-problems.

A small problem is easier to design, code, test and debug than a big one. Once each sub-problem has been solved, the solutions are combined to solve the original problem.

Example — A teacher wants a program that takes attendance, calculates each student's percentage attendance for the term, and reports which students fall below 80 %.

The big problem breaks naturally into smaller sub-problems:

1. Read a list of students from a file.
2. Take today's attendance (a yes/no per student).
3. Save today's data so it is not lost.
4. Run through every saved day to count each student's presents.
5. Calculate the percentage for each student (presents ÷ total days × 100).
6. Display the report, highlighting students below 80 %.

Each numbered step is now a small, well-defined task that one programmer can work on (and test) by itself. When all six work, the whole program works.

Why decomposition helps

• Easier to think about: a small task is easier to plan than a huge one.
• Easier to code: each sub-problem becomes a procedure or function (topic 24).
• Easier to test: small chunks of code can be tested in isolation.
• Easier to share: different programmers can work on different sub-problems in parallel.
• Easier to debug: a bug in one sub-problem can be fixed without disturbing the others.