Use pseudocode to write: a 'count-controlled' loop

Topic 11.2 – Constructs

Objective

Use pseudocode to write a count‑controlled loop.

What is a Count‑Controlled Loop?

A count‑controlled loop repeats a block of statements a known number of times. The loop variable is initialised, tested against a limit, and updated each iteration.

General Pseudocode Syntax

Standard Form (FOR‑style)

The most common representation in Cambridge A‑Level pseudocode is the FOR construct:

FOR i ← start TO end STEP step DO
// loop body
END FOR

Where:

• \$i\$ is the loop counter.
• \$\text{start}\$ is the initial value of \$i\$.
• \$\text{end}\$ is the final value at which the loop stops (inclusive).
• \$\text{step}\$ is the amount added to \$i\$ each iteration (default is 1).

Example: Sum of the First 10 Natural Numbers

This example demonstrates a count‑controlled loop that adds the numbers \$1\$ through \$10\$.

DECLARE sum, i : INTEGER
sum ← 0
FOR i ← 1 TO 10 DO
sum ← sum + i
END FOR
OUTPUT "The sum is ", sum

Step‑by‑Step Explanation

1. Initialise sum to \$0\$.
2. Set the loop counter i to \$1\$ (the start value).
3. Check the condition \$i \le 10\$; if true, execute the body.
4. Inside the body, add the current value of i to sum.
5. Increment i by \$1\$ (the default step).
6. Repeat steps 3‑5 until \$i\$ becomes \$11\$, at which point the condition fails and the loop ends.
7. Output the final value of sum.

Common \cdot ariations

• Decrementing loops: FOR i ← 10 DOWNTO 1 DO … END FOR
• Non‑unit steps: FOR i ← 0 TO 20 STEP 5 DO … END FOR
• Using a WHILE loop as count‑controlled: initialise a counter, test a condition, and update inside the loop.

Potential Pitfalls

• Forgetting to update the counter leads to an infinite loop.
• Using the wrong relational operator in the test (e.g., < instead of ≤) can cause the loop to execute one fewer time than intended.
• Off‑by‑one errors are common when the start or end values are mis‑interpreted.

Practice Exercise

Write pseudocode to display the multiplication table for \$7\$ (i.e., \$7 \times 1\$ up to \$7 \times 12\$) using a count‑controlled loop.

Solution Sketch

DECLARE i, product : INTEGER
FOR i ← 1 TO 12 DO
product ← 7 * i
OUTPUT 7, " × ", i, " = ", product
END FOR

Key Take‑aways

• A count‑controlled loop repeats a known number of times.
• The FOR … TO … STEP … DO structure is the standard pseudocode format.
• Always ensure the loop counter is correctly initialised, tested, and updated.
• Check boundary conditions to avoid off‑by‑one errors.