← IGCSE Computer Science Paper 2

How many times a FOR loop runs

The number of times a FOR loop runs. FOR i ← 1 TO 5 runs 5 times, 3 TO 3 runs once, and 5 TO 1 runs zero times because the start value is bigger than the end value.

Part of: IGCSE Computer Science 0478 — 7c Pseudocode and Flowcharts — Module 31

Understanding How many times a FOR loop runs in IGCSE Computer Science Paper 2

What it does: 3 - 3 + 1 = 1, so the body runs one time with i equal to 3 and then the loop finishes. The loop runs 5 - 1 + 1 = 5 times. i takes the values 1, 2, 3, 4 and 5. You must add 1 because both the start value and the end value are used. Forgetting the + 1 is a classic off-by-one mistake. 1 TO 10 runs 10 - 1 + 1 = 10 times. 1 TO 9 would run only 9 times, which is an off-by-one error. 7 - 2 + 1 = 6. The values of i are 2, 3, 4, 5, 6 and 7. Subtracting without adding 1 gives the wrong answer of 5.

Common mistakes: Assignment uses the arrow ←, not =. The line should be Count ← Count + 1, so Count goes up by 1 on each of the 5 runs of the loop. The loop should run exactly once, which happens when the start and end values are equal. It should be FOR i ← 3 TO 3. With 3 TO 2 the start is bigger than the end, so the loop runs zero times.

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Learning

Duo

How many times does FOR i ← 1 TO 5 run its loop body?

5 times4 times

Matches

FOR i ← 1 TO 10 // meant to run 9 times

↓

Off-by-one error: 1 TO 10 runs 10 times, not 9. The count was worked out as end - start and the + 1 was forgotten.

Applying

Meanings

Term

end - start + 1

Meaning

The number of times a FOR loop runs. FOR i ← 1 TO 5 runs 5 times, 3 TO 3 runs once, and 5 TO 1 runs zero times because the start value is bigger than the end value.

Practice

DECLARE Count : INTEGER

Testing

Gaps

FOR i ← 1 TO

Check Answer

Spots

2FOR i ← 1 TO 5

3 Count = Count + 1

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Quick Questions

1. How many times does FOR i ← 1 TO 5 run its loop body?

A. 5 times ✓

B. 4 times

The loop runs 5 - 1 + 1 = 5 times. i takes the values 1, 2, 3, 4 and 5.

2. Which formula gives the number of times a FOR loop runs?

A. end - start

B. end - start + 1 ✓

You must add 1 because both the start value and the end value are used. Forgetting the + 1 is a classic off-by-one mistake.

3. FOR i ← 3 TO 3 ... NEXT i. What happens?

A. The loop body never runs

B. The loop body runs exactly once ✓

3 - 3 + 1 = 1. When the start and end values are equal the loop runs once, with i equal to 3.

4. FOR i ← 5 TO 1 ... NEXT i. What happens?

A. The loop body runs zero times ✓

B. The loop body runs 5 times, counting down

A FOR loop without STEP counts up. Because the start value 5 is bigger than the end value 1, the loop is skipped completely.

5. A student wants a loop to run 10 times. Which loop header is correct?

A. FOR i ← 1 TO 10 ✓

B. FOR i ← 1 TO 9

1 TO 10 runs 10 - 1 + 1 = 10 times. 1 TO 9 would run only 9 times, which is an off-by-one error.

Match the Pairs

FOR i ← 1 TO 5 → The loop body runs 5 times, because 5 - 1 + 1 = 5

FOR i ← 5 TO 1 → The loop body runs zero times, because the start value is bigger than the end value

When the start and end values are equal, the loop runs exactly once → FOR i ← 3 TO 3

The number of repetitions is end - start + 1, so this loop runs 8 times → FOR Count ← 4 TO 11

FOR i ← 1 TO 10 // meant to run 9 times → Off-by-one error: 1 TO 10 runs 10 times, not 9. The count was worked out as end - start and the + 1 was forgotten.

FOR i ← 10 TO 1 // meant to run 10 times → The start value is bigger than the end value, so the loop runs zero times instead of 10.

Key Term

end - start + 1

The number of times a FOR loop runs. FOR i ← 1 TO 5 runs 5 times, 3 TO 3 runs once, and 5 TO 1 runs zero times because the start value is bigger than the end value.

Fill in the Blanks

1. FOR i ← 1 TO 5 OUTPUT i NEXT i

Hint: Type the end value that makes this loop run exactly five times.

2. FOR i ← 3 TO 3 OUTPUT i NEXT i

Hint: Type the end value that makes the loop run only once, because it equals the start value.

3. FOR i ← 5 TO 1 // runs 0 times OUTPUT i NEXT i

Hint: Type how many times this loop runs when the start value is bigger than the end value.

4. FOR i ← 3 TO 8 // runs 8 - 3 + 1 times OUTPUT i NEXT i

Hint: Type the number added in the formula end - start + something to count the runs.

5. FOR i ← 0 TO 9 // runs 10 times OUTPUT i NEXT i

Hint: Type the end value; starting at zero, it is one less than the number of runs (avoid the off-by-one mistake).

Spot the Error

Question 1

A Count ← 0

B FOR i ← 1 TO 5

C Count = Count + 1

D NEXT i

E OUTPUT Count

Line C — Assignment uses the arrow ←, not =. The line should be Count ← Count + 1, so Count goes up by 1 on each of the 5 runs of the loop.

Question 2

A // Runs once

B FOR i ← 3 TO 2

C OUTPUT i

D NEXT i

Line B — The loop should run exactly once, which happens when the start and end values are equal. It should be FOR i ← 3 TO 3. With 3 TO 2 the start is bigger than the end, so the loop runs zero times.

Question 3

A FOR i ← 1 TO 4

B OUTPUT "Hello"

C NEXT i

D // Hello is shown 5 times

Line A — This is an off-by-one mistake. 1 TO 4 runs 4 - 1 + 1 = 4 times. To run 5 times the line must be FOR i ← 1 TO 5.

Question 4

A FOR i ← 3 TO 1

B OUTPUT i * 2

C NEXT i

D // Output: 2 4 6

Line A — The start value 3 is bigger than the end value 1, so the loop would run zero times and print nothing. It should be FOR i ← 1 TO 3, which runs 3 times.

Question 5

A Runs ← 0

B FOR i ← 2 TO 6

C Runs ← Runs + 1

D NEXT Runs

E OUTPUT Runs

Line D — NEXT must name the loop variable used in the FOR line. It should be NEXT i. The loop runs 6 - 2 + 1 = 5 times, so Runs ends as 5.

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