Refinement & Logic (Cambridge (CIE) A Level Computer Science) : Revision Note

Stepwise refinement

What is stepwise refinement?

• Stepwise refinement is the process of breaking down a complex problem into smaller, more manageable sub-problems in a logical order

• Each sub-problem is refined step by step until it is simple enough to be solved with a single subroutine or module

• This method ensures that the overall problem can be solved by addressing each part individually, in a structured and efficient way

Relationship to decomposition and top-down design

• Decomposition is the general concept of breaking a problem down into smaller parts

• Top-down design is the strategy used to perform decomposition

• Stepwise refinement is the process used in top-down design to gradually refine each major task into simpler sub-tasks

• In other words, stepwise refinement is how top-down design is implemented

Benefits of stepwise refinement

• Helps developers understand and organise the structure of a program

• Makes testing and debugging easier through unit testing of individual subroutines

• Encourages code reuse by breaking tasks into reusable components

• Supports collaborative development, as tasks can be divided between team members

• Each subroutine should:

  • Be clear and focused on a single task

  • Be simple enough to implement directly

  • Not need further breakdown

Example: Calculating student grades

• Here’s how stepwise refinement could be applied to a program designed to calculate student grades for a teacher’s classes:

Top-level task:

• Calculate grades for all students in all classes

Stepwise refinement:

• Step 1 – Calculate the grade for each assessment

  • For each question:

    • Mark the question

    • Store the mark

  • Sum the marks for all questions in the assessment

• Step 2 – Calculate the average grade for each student

  • Add together grades from all assessments

  • Divide by the number of assessments

  • Store the average

• Step 3 – Repeat for each class

  • For every student in the class:

    • Perform Steps 1 and 2

• This structured breakdown allows each task to be turned into a subroutine, simplifying the design, implementation, and testing of the overall program