Designing and refining algorithms

OCR J277 Paper 2 always includes algorithm-design questions. You need to be fluent in both pseudocode and flowcharts, and able to use a trace table to follow what an algorithm does step-by-step.

Pseudocode (OCR Reference Language)

Pseudocode is a structured English-like notation. OCR provides a Reference Language guide; the key conventions are:

• Assignment uses ← (or = in the exam where ← is unavailable). Example: total ← 0
• Selection uses IF … THEN … ELSE … END IF.
• Iteration uses FOR i ← 1 TO n … NEXT i, or WHILE … END WHILE, or DO … UNTIL.
• Input/output: INPUT and OUTPUT (or PRINT).
• Subroutines: FUNCTION name(parameters) … RETURN value … END FUNCTION; PROCEDURE name(parameters) … END PROCEDURE.

Flowcharts

Symbol	Meaning
Oval (terminator)	START / END
Parallelogram	INPUT / OUTPUT
Rectangle	Process (assignment / calculation)
Diamond	Decision (yes / no, true / false)
Arrow	Flow of control

A flowchart must have exactly one START and at least one END. Decision diamonds always have two outgoing arrows labelled with the conditions.

Trace tables

A trace table records the value of each variable after each step of an algorithm. Columns = variables (and any output); rows = steps.

Example — pseudocode (single-line form): total ← 0; FOR i ← 1 TO 3 do total ← total + i; NEXT i; OUTPUT total

Step	i	total	OUTPUT
Start	—	0
Loop i = 1	1	1
Loop i = 2	2	3
Loop i = 3	3	6
OUTPUT total			6

Refining algorithms

After a first version, look for:

• Correctness — does it produce the right output for normal, boundary and invalid inputs?
• Efficiency — fewer steps, fewer variables, better data structure.
• Readability — meaningful identifiers, comments, broken into subroutines.
• Reusability — can a block be lifted into a function called from elsewhere?

Common OCR exam mistakes

• Using the wrong flowchart shape (rectangle for a decision, etc.).
• Forgetting to fill the trace table row when a variable changes mid-loop.
• Using "IF" without a matching "END IF", or "WHILE" without "END WHILE".
• Designing an algorithm with no terminating condition — the loop never ends.