Decomposition and Composition

Overview

Recall questions on what procedural decomposition is, how a problem is broken down, its benefits and what distinguishes a good decomposition.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is procedural decomposition?

   Model answer

   In procedural decomposition a problem is split into sub-problems, each of which accomplishes some identifiable task, and any sub-problem still too large can be split again in the same way. A payroll system, for example, separates into reading employee records, calculating gross pay, deducting tax and printing payslips — and 'deducting tax' may itself break down further into separate bands and allowances.

2. 2

   Decompose the problem 'produce end-of-year reports for a school' and show the further subdivision.

   Model answer

   At the top level: read the marks from file; calculate each student's results; sort the students into class order; produce the report documents. Each accomplishes an identifiable task. 'Calculate each student's results' subdivides further into: calculate the mean mark per subject; convert each mark into a grade; work out the overall average. 'Produce the report documents' subdivides into: fill in the heading with the student's details; add one line per subject; add the tutor's comment. The subdivision stops when each remaining task is small enough to write as a single procedure.

3. 3

   State three benefits of decomposing a problem before writing any code.

   Model answer

   Each sub-problem is small enough to be understood, written and tested on its own, so mistakes are found in one small piece rather than in a large tangle. Different people can work on different sub-problems at the same time, because each has a defined task. Sub-problems that occur more than once — such as 'convert a mark into a grade' — need only be solved once and can be reused wherever they are needed, and can be improved later in one place.

4. 4

   How do you tell a good decomposition from a poor one?

   Model answer

   In a good decomposition each sub-problem accomplishes a single identifiable task that can be named in a few words, and the sub-problems interact through a small, clearly stated set of values passed between them. In a poor one the pieces are named vaguely, several pieces have to be changed together whenever the requirement changes, and each piece needs to know a great deal about the internal workings of the others — which means the problem has been cut in the wrong place.

5. 5

   What is composition, and how does it relate to decomposition?

   Model answer

   Composition is building something larger by combining existing parts: combining procedures to form compound procedures, and combining data objects to form compound data. It is the opposite direction of travel from decomposition, which starts with a whole problem and splits it into sub-problems. In practice a solution is decomposed on paper and then composed in code, the small procedures being written first and combined into larger ones.

6. 6

   Give a worked example of building a compound procedure by composition.

   Model answer

   Suppose validateMark, convertToGrade and writeToReport already exist. A compound procedure is built by combining them: PROCEDURE processStudent(student) FOR EACH mark IN student.marks IF validateMark(mark) THEN grade ← convertToGrade(mark) writeToReport(student, grade) ENDIF ENDFOR ENDPROCEDURE processStudent is a new procedure made entirely out of existing ones, and it can in turn be combined into processWholeClass. Each level can be used without knowing how the level below works.

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