IGCSE Computer Science 0478: Tracing a FOR Loop with STEP

A firework display uses a digital countdown board. This pseudocode counts down from 15 to 3 in steps of 3, displaying each number and totalling how many numbers are displayed.

01 DECLARE Count : INTEGER
02 DECLARE Displays : INTEGER
03 Displays ← 0
04 FOR Count ← 15 TO 3 STEP -3
05     OUTPUT Count
06     Displays ← Displays + 1
07 NEXT Count
08 OUTPUT Displays

(a) State the value of Count on the first pass of this loop, and the value of Count on the final pass of this loop. [2]

(b) Complete a trace table showing the value of Count and Displays after each pass of the loop. [4]

(c) A technician changes line 04 to FOR Count ← 15 TO 3 STEP -4. State the sequence of values output for Count, and the final value of Displays, for this modified loop, showing your working. [2]

Part (a): First and final values of Count

For a FOR loop with a negative STEP, Count starts at the given start value and decreases by the step size on each pass, continuing only while Count is still greater than or equal to the end value.

First pass: Count is assigned its starting value directly from line 04, so Count = 15.
Final pass: Count decreases by 3 each time (15, 12, 9, 6, 3,…). The next value after 3 would be 3 - 3 = 0, and since 0 is less than the end value 3, the loop does not run again. So the final pass this loop actually executes is Count = 3.

[2 marks]: [1] for Count = 15 on the first pass, [1] for Count = 3 on the final pass.

Part (b): Tracing the FOR loop

Displays starts at 0 (line 03). Each pass outputs the current value of Count, then adds 1 to Displays.

Pass	Count	OUTPUT	Displays
1	15	15	1
2	12	12	2
3	9	9	3
4	6	6	4
5	3	3	5

After pass 5, the next value of Count would be 3 - 3 = 0, which is less than the end value 3, so the loop stops. Line 08 then outputs the final value of Displays.

[4 marks]: [1] for the correct decreasing sequence of Count values (15, 12, 9, 6, 3), [1] for correctly stopping the loop after Count = 3 rather than continuing to 0 or below, [1] for a correctly incrementing Displays column, [1] for the correct final value Displays = 5.

Part (c): Changing STEP to -4

With FOR Count ← 15 TO 3 STEP -4, Count now decreases by 4 each pass instead of 3:

Pass 1: Count = 15 (15 >= 3, runs)
Pass 2: Count = 15 - 4 = 11 (11 >= 3, runs)
Pass 3: Count = 11 - 4 = 7 (7 >= 3, runs)
Pass 4: Count = 7 - 4 = 3 (3 >= 3, runs)
Next value: Count = 3 - 4 = -1 (-1 < 3, loop stops)

So Count takes the values 15, 11, 7, 3, in that order, 4 passes in total, so:

Displays = 4

[2 marks]: [1] for the correct sequence 15, 11, 7, 3, [1] for the correct final value Displays = 4.

Final answers

(a) Count = 15 on the first pass; Count = 3 on the final pass.
(b) Trace as shown above. Count takes 15, 12, 9, 6, 3; Displays ends at 5.
(c) Count takes 15, 11, 7, 3; Displays = 4.