Decomposition: Breaking Problems into Sub-Problems

This lesson covers decomposition in detail, as required by OCR J277 Section 2.1. Decomposition is one of the four key components of computational thinking and is often the first step in solving any complex problem.

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What Is Decomposition?

Decomposition is the process of breaking a complex problem down into smaller, more manageable sub-problems. Each sub-problem can then be understood, solved, and tested individually before being combined into a complete solution.

Think of decomposition like building a house:

• You do not try to build an entire house in one step.
• You break it into sub-tasks: foundations, walls, roof, plumbing, electrics, decoration.
• Each sub-task can be assigned to specialists and completed independently.
• When all sub-tasks are complete, the house is finished.

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Why Is Decomposition Important?

Reason	Explanation
Makes problems manageable	Smaller sub-problems are easier to understand and solve than one large, complex problem
Enables teamwork	Different people or teams can work on different sub-problems simultaneously
Facilitates testing	Each sub-problem can be tested independently, making it easier to find and fix errors
Promotes code reuse	Solutions to common sub-problems can be reused in other projects
Improves clarity	A decomposed problem is easier to communicate to others

OCR Exam Tip: When asked why decomposition is important, always mention that it makes complex problems easier to solve by breaking them into smaller parts. Also mention that it allows different sub-problems to be worked on independently and tested separately.

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Decomposition in Practice

Example 1: Creating a Computer Game

A student wants to create a simple quiz game. Without decomposition, this is one big, overwhelming task. With decomposition:

Sub-Problem	Detail
User interface	Design the screen layout, buttons, and text display
Question storage	Decide how to store questions and answers (list, file, database)
Displaying questions	Write code to show questions one at a time
Getting user input	Write code to accept the user's answer
Checking answers	Compare the user's answer to the correct answer
Scoring	Keep track of the score and display it
Feedback	Tell the user if they are right or wrong
End of game	Display the final score and offer to play again

Each of these sub-problems can be solved independently and then combined to create the complete game.

Example 2: Online Shopping System

Main Problem	Sub-Problems
Build an online shop	Browse products, search products, add to basket, manage basket, create account, log in, enter delivery address, process payment, confirm order, send email confirmation, update stock levels

Example 3: School Registration System

Main Problem	Sub-Problems
Build a registration system	Take the register (present/absent/late), store attendance data, calculate attendance percentages, generate reports for form tutors, send alerts for persistent absence, display attendance on student profiles

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Levels of Decomposition

The following tree diagram illustrates how a complex problem is decomposed into sub-problems: