9.1 Computational Thinking Skills: Decomposition

Decomposition is a fundamental computational thinking skill that involves breaking down a complex problem into smaller, more manageable parts. This makes the problem easier to understand, solve, and test. By dividing a problem, we can tackle each component individually, leading to a more structured and efficient solution.

Why is Decomposition Important?

Decomposition offers several advantages:

• Simplifies Complexity: Large, intricate problems can be overwhelming. Decomposition breaks them down into smaller, less daunting tasks.
• Improved Understanding: Examining each part individually enhances understanding of the overall problem.
• Modular Design: Decomposition naturally leads to modular designs, where each part can be developed, tested, and reused independently.
• Easier Debugging: When errors occur, it's easier to isolate and fix them within smaller, well-defined components.
• Parallel Processing: Sub-problems can often be solved concurrently, improving efficiency.

How to Perform Decomposition

1. Identify the Main Goal: Clearly define the overall objective of the problem.
2. Break Down into Sub-problems: Identify the major components or tasks required to achieve the main goal. These sub-problems should be as independent as possible.
3. Further Decomposition (if necessary): If a sub-problem is still too complex, break it down into even smaller sub-sub-problems. This process can be repeated until the components are manageable.
4. Define Interfaces: Determine how the different components will interact with each other. This involves defining the inputs and outputs of each sub-problem.

Example: Making a Cup of Tea

Let's decompose the problem of making a cup of tea:

Step	Description
Boil Water	Heat water to boiling point.
Get Teabag	Obtain a teabag of the desired flavor.
Place Teabag in Cup	Put the teabag into a cup.
Pour Water into Cup	Pour the boiling water over the teabag.
Steep	Allow the tea to steep for the recommended time.
Remove Teabag	Take the teabag out of the cup.
Add Milk/Sugar (Optional)	Add milk and/or sugar to taste.

Each of these steps can be considered a sub-problem. We could even further decompose "Boil Water" into steps like "Fill Kettle", "Plug in Kettle", and "Wait for Boiling".

Decomposition in Programming

In programming, decomposition is often achieved through functions or procedures. Each function encapsulates a specific sub-problem, making the code more organized and reusable.

For example, a program to process a list of numbers might be decomposed into functions like:

• calculate_sum(numbers): Calculates the sum of a list of numbers.
• find_maximum(numbers): Finds the maximum value in a list of numbers.
• filter_even(numbers): Filters a list to return only even numbers.

These functions can then be combined to solve the overall problem.