Algorithms

Computer Science AS · Algorithm design and problem-solving. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

An algorithm is a solution to a problem written as a sequence of defined steps. It can be documented in structured English, as a flowchart or in pseudocode, and you must be able to convert between these forms.

Every algorithm is built from three constructs. Sequence is steps carried out one after another. Selection chooses a path with a condition (IF or CASE). Iteration repeats steps (FOR, WHILE or REPEAT).

Stepwise refinement starts with the main steps and breaks each one into smaller steps, again and again, until every step is detailed enough to be coded. Conditions are written as logic statements using AND, OR and NOT.

Rules to remember

Identifier table: lists each identifier with its data type and a description of its purpose.
Identifiers should be meaningful, for example TotalMark, not T.
FOR ... NEXT: count-controlled loop, the number of repeats is known.
WHILE ... ENDWHILE: condition tested at the start, so the loop may run zero times.
REPEAT ... UNTIL: condition tested at the end, so the loop runs at least once.
Flowchart symbols: parallelogram for input or output, rectangle for a process, diamond for a decision.
A range needs both tests joined with AND, e.g. Mark >= 40 AND Mark <= 59. Use brackets when AND and OR are mixed: (A OR B) AND C.

Common mistake

In a range test students write OR in place of AND. Mark >= 40 OR Mark <= 59 is true for every mark. Test the condition with a value outside the range to check it.

Worked example

What is output by this algorithm?
Total ← 0
FOR Count ← 1 TO 4
Total ← Total + Count * Count
NEXT Count
OUTPUT Total

The loop runs four times, with Count = 1, 2, 3 and 4.
Count * Count gives 1, 4, 9 and 16.
Total after each pass: 0 + 1 = 1, 1 + 4 = 5, 5 + 9 = 14, 14 + 16 = 30.

Answer: 30

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