Pseudocode: Iteration & the Purpose of an Algorithm — Cambridge IGCSE CS (0478)

🎯 Syllabus & Goals 3 min

Cambridge 7.2 · Design methods — pseudocode Cambridge 7.3 · Explain the purpose of an algorithm Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

Write the three loops — FOR…TO…NEXT, REPEAT…UNTIL and WHILE…DO…ENDWHILE — and choose the right one.
Use INPUT and OUTPUT correctly, including lists of values.
Explain the purpose of a given algorithm and list the processes in it.

Textbook: Chapter 7, §7.2.3 Pseudocode — iteration, input and output (pp. 268–270) and §7.3 (p. 271)

Recap / Warm-Up 5 min

Last lesson covered assignment and selection. The third building block of every algorithm is iteration — repeating steps.

Quick starter

After A ← 5, B ← A + 2, A ← B * 2, what are A and B?

Reveal the answer

B = 7, then A = 14. A's old value (5) is replaced.

🧠 Key Concept 14 min

1 · Iteration: three kinds of loop

Repeating actions is called iteration. Pseudocode has three loop structures. All three can do the same job, but each suits a different situation.

Loop	When to use it	Condition tested	Runs at least once?
`FOR … TO … NEXT`	the number of repeats is known	counter managed automatically	yes, if start ≤ end
`REPEAT … UNTIL`	number of repeats not known	at the end (post-condition)	always
`WHILE … DO … ENDWHILE`	number of repeats not known	at the start (pre-condition)	not necessarily — may run zero times

Where the test sits is the whole difference. REPEAT tests after the body, so the body always runs once. WHILE tests before, so the body may never run.

FOR — five repeats, known in advance

FOR Counter ← 1 TO 5
  OUTPUT "Lap ", Counter
NEXT Counter

REPEAT — ask until valid

REPEAT
  OUTPUT "PIN? "
  INPUT Pin
UNTIL Pin = 4096

WHILE — keep adding until the rogue value −1

Total ← 0
INPUT Mark
WHILE Mark <> -1 DO
  Total ← Total + Mark
  INPUT Mark
ENDWHILE

Key point: inside a FOR loop you may use the counter, but never change it. NEXT Counter adds 1 automatically. Cambridge always closes a count-controlled loop with NEXT.

2 · Input and output

INPUT Name — data is entered and stored in the variable Name.
OUTPUT "Your name is ", Name — a list of values separated by commas is displayed.
READ may replace INPUT when reading a file; PRINT may replace OUTPUT for a hard copy.

3 · Explaining the purpose of an algorithm

An exam may give you an algorithm with no explanation — often with single-letter names — and ask for its purpose. Answer in two parts: what it achieves, and the processes it uses to get there.

Real worldA phone alarm repeats: wait 10 seconds, read the clock, compare with the alarm time — until they match, then play a sound. Purpose: sound the alarm at the right time. Processes: waiting, reading the time, comparing, outputting the sound.

Worked Example 12 min

Worked example 1 · Summing with a rogue value (WHILE)

Trace the WHILE loop above with the inputs 12, 8, 5, −1.

Total ← 0
INPUT Mark
WHILE Mark <> -1 DO
  Total ← Total + Mark
  INPUT Mark
ENDWHILE
OUTPUT "Total: ", Total

total = 0
mark = int(input())
while mark != -1:
    total = total + mark
    mark = int(input())
print("Total:", total)

A blank cell means that variable did not change on that step.
Mark	Total	Mark <> -1 ?	OUTPUT
	0
12		TRUE
	12
8		TRUE
	20
5		TRUE
	25
-1		FALSE	Total: 25

The first INPUT is before the loop. So the condition has a value to test.WHILE tests at the start; without a first input, Mark would have no value.
Each pass adds then inputs again. 0 + 12 = 12; 12 + 8 = 20; 20 + 5 = 25.
−1 is read, the test is FALSE, the loop ends. −1 is never added.that is why the second INPUT is the last line inside the loop.
If −1 were the very first input, the loop body would run zero times and output Total: 0.

Key point: Python's != means "not equal", the same as pseudocode's <>. Python has for and while, but no REPEAT…UNTIL.

Worked example 2 · What is the purpose of this algorithm?

INPUT A
B ← 1
FOR C ← 1 TO A
  B ← B * 2
NEXT C
OUTPUT B

Trace it with easy data, A = 4.
A B C OUTPUT
4 1
2 1
4 2
8 3
16 4 16
Spot the pattern. B doubles A times: 1 → 2 → 4 → 8 → 16 = 2⁴.one easy trace usually shows the pattern; a second (A = 3 → 8) confirms it.
State the purpose. It inputs a whole number and outputs 2 raised to the power of that number.
List the processes. Input a number; set B to 1; multiply B by 2 once per loop, A times; output the result.

A	B	C	OUTPUT
4	1
	2	1
	4	2
	8	3
	16	4	16

a = int(input())
b = 1
for c in range(1, a + 1):
    b = b * 2
print(b)

4
16

Key point: range(1, a + 1) stops before its second value, so it gives 1 to a — the same as FOR C ← 1 TO A.

Try It Yourself 12 min

🟢 Easy

Goal: Write a FOR loop that outputs the 7 times table from 7 × 1 to 7 × 12.

🟡 Medium

Goal: Rewrite the WHILE rogue-value algorithm as a REPEAT … UNTIL loop that gives the same total. Trace it with 12, 8, 5, −1 to prove it.

🔴 Stretch

Goal: State the purpose of this algorithm and list its processes.

INPUT N
F ← 1
WHILE N > 1 DO
  F ← F * N
  N ← N - 1
ENDWHILE
OUTPUT F

Hint

Trace it with N = 4: F becomes 4, then 12, then 24. What is 4 × 3 × 2 × 1?

📝 Exam Practice 10 min

Describe[2]

Describe the difference between a REPEAT … UNTIL loop and a WHILE … DO … ENDWHILE loop.

Mark scheme

REPEAT tests its condition at the end / is post-condition, so it always runs at least once (1).
WHILE tests its condition at the start / is pre-condition, so it may not run at all (1).

Write[4]

Rewrite this algorithm using a WHILE … DO … ENDWHILE loop instead of FOR. It must give the same output.

FOR Count ← 1 TO 10
  OUTPUT Count * 3
NEXT Count

Mark scheme

Count ← 1 before the loop (1)
WHILE Count <= 10 DO (or < 11) (1)
OUTPUT Count * 3 inside the loop (1)
Count ← Count + 1 inside the loop, then ENDWHILE (1)

Explain[3]

Explain the purpose of this algorithm and state its output when the inputs are 3, 9, 4, 0.

X ← 0
REPEAT
  INPUT Y
  IF Y > X
    THEN
      X ← Y
  ENDIF
UNTIL Y = 0
OUTPUT X

Mark scheme

Inputs numbers until 0 is entered (1).
Finds / outputs the largest number entered (1).
Output: 9 (1).

Explain[2]

A program asks a user to enter a password until it is correct. Explain which loop structure is most suitable.

Mark scheme

REPEAT … UNTIL (1)…
…because the number of attempts is not known and the password must be entered at least once (1).

🗝️ Recap & Key Terms 3 min

Use FOR when the number of repeats is known, REPEAT when the body must run at least once, and WHILE when it might not run at all. To explain an algorithm, trace it, spot the pattern, then state its purpose and processes.

Iteration: Repeating a set of actions using a loop structure.
Count-controlled loop: FOR … TO … NEXT: repeats a set number of times; the counter is managed automatically.
Post-condition loop: REPEAT … UNTIL: the condition is tested at the end, so it runs at least once.
Pre-condition loop: WHILE … DO … ENDWHILE: the condition is tested at the start, so it may never run.
Rogue value: A value that is not real data, used to end a loop (e.g. −1).
Purpose of an algorithm: What the algorithm achieves, together with the processes it uses to achieve it.

Homework 1 min

Task (≤ 15 min): Write pseudocode that inputs positive numbers until the user enters 0, then outputs how many numbers were entered and their total. Explain why you chose your loop. [5]

Model answer

Count ← 0
Total ← 0
INPUT Number
WHILE Number <> 0 DO
  Count ← Count + 1
  Total ← Total + Number
  INPUT Number
ENDWHILE
OUTPUT "How many: ", Count
OUTPUT "Total: ", Total

Marks: both variables initialised (1); input before and at the end of the loop (1); correct WHILE condition (1); count and total updated (1). Reason: WHILE, because the number of inputs is unknown and 0 might be the first input, so the body may run zero times (1).

🎯 Syllabus & Goals 3 min

Cambridge 7.2 · Design methods — pseudocode Cambridge 7.3 · Explain the purpose of an algorithm Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

Write the three loops — FOR…TO…NEXT, REPEAT…UNTIL and WHILE…DO…ENDWHILE — and choose the right one.
Use INPUT and OUTPUT correctly, including lists of values.
Explain the purpose of a given algorithm and list the processes in it.

Textbook: Chapter 7, §7.2.3 Pseudocode — iteration, input and output (pp. 268–270) and §7.3 (p. 271)

Recap / Warm-Up 5 min

Last lesson covered assignment and selection. The third building block of every algorithm is iteration — repeating steps.

Quick starter

After A ← 5, B ← A + 2, A ← B * 2, what are A and B?

Reveal the answer

B = 7, then A = 14. A's old value (5) is replaced.

🧠 Key Concept 14 min

1 · Iteration: three kinds of loop

Repeating actions is called iteration. Pseudocode has three loop structures. All three can do the same job, but each suits a different situation.

Loop	When to use it	Condition tested	Runs at least once?
`FOR … TO … NEXT`	the number of repeats is known	counter managed automatically	yes, if start ≤ end
`REPEAT … UNTIL`	number of repeats not known	at the end (post-condition)	always
`WHILE … DO … ENDWHILE`	number of repeats not known	at the start (pre-condition)	not necessarily — may run zero times

Where the test sits is the whole difference. REPEAT tests after the body, so the body always runs once. WHILE tests before, so the body may never run.

FOR — five repeats, known in advance

FOR Counter ← 1 TO 5
  OUTPUT "Lap ", Counter
NEXT Counter

REPEAT — ask until valid

REPEAT
  OUTPUT "PIN? "
  INPUT Pin
UNTIL Pin = 4096

WHILE — keep adding until the rogue value −1

Total ← 0
INPUT Mark
WHILE Mark <> -1 DO
  Total ← Total + Mark
  INPUT Mark
ENDWHILE

Key point: inside a FOR loop you may use the counter, but never change it. NEXT Counter adds 1 automatically. Cambridge always closes a count-controlled loop with NEXT.

2 · Input and output

INPUT Name — data is entered and stored in the variable Name.
OUTPUT "Your name is ", Name — a list of values separated by commas is displayed.
READ may replace INPUT when reading a file; PRINT may replace OUTPUT for a hard copy.

3 · Explaining the purpose of an algorithm

Worked Example 12 min

Worked example 1 · Summing with a rogue value (WHILE)

Trace the WHILE loop above with the inputs 12, 8, 5, −1.

Total ← 0
INPUT Mark
WHILE Mark <> -1 DO
  Total ← Total + Mark
  INPUT Mark
ENDWHILE
OUTPUT "Total: ", Total

total = 0
mark = int(input())
while mark != -1:
    total = total + mark
    mark = int(input())
print("Total:", total)

A blank cell means that variable did not change on that step.
Mark	Total	Mark <> -1 ?	OUTPUT
	0
12		TRUE
	12
8		TRUE
	20
5		TRUE
	25
-1		FALSE	Total: 25

The first INPUT is before the loop. So the condition has a value to test.WHILE tests at the start; without a first input, Mark would have no value.
Each pass adds then inputs again. 0 + 12 = 12; 12 + 8 = 20; 20 + 5 = 25.
−1 is read, the test is FALSE, the loop ends. −1 is never added.that is why the second INPUT is the last line inside the loop.
If −1 were the very first input, the loop body would run zero times and output Total: 0.

Key point: Python's != means "not equal", the same as pseudocode's <>. Python has for and while, but no REPEAT…UNTIL.

Worked example 2 · What is the purpose of this algorithm?

INPUT A
B ← 1
FOR C ← 1 TO A
  B ← B * 2
NEXT C
OUTPUT B

Trace it with easy data, A = 4.
A B C OUTPUT
4 1
2 1
4 2
8 3
16 4 16
Spot the pattern. B doubles A times: 1 → 2 → 4 → 8 → 16 = 2⁴.one easy trace usually shows the pattern; a second (A = 3 → 8) confirms it.
State the purpose. It inputs a whole number and outputs 2 raised to the power of that number.
List the processes. Input a number; set B to 1; multiply B by 2 once per loop, A times; output the result.

A	B	C	OUTPUT
4	1
	2	1
	4	2
	8	3
	16	4	16

a = int(input())
b = 1
for c in range(1, a + 1):
    b = b * 2
print(b)

4
16

Key point: range(1, a + 1) stops before its second value, so it gives 1 to a — the same as FOR C ← 1 TO A.

Try It Yourself 12 min

🟢 Easy

Goal: Write a FOR loop that outputs the 7 times table from 7 × 1 to 7 × 12.

🟡 Medium

Goal: Rewrite the WHILE rogue-value algorithm as a REPEAT … UNTIL loop that gives the same total. Trace it with 12, 8, 5, −1 to prove it.

🔴 Stretch

Goal: State the purpose of this algorithm and list its processes.

INPUT N
F ← 1
WHILE N > 1 DO
  F ← F * N
  N ← N - 1
ENDWHILE
OUTPUT F

Hint

Trace it with N = 4: F becomes 4, then 12, then 24. What is 4 × 3 × 2 × 1?

📝 Exam Practice 10 min

Describe[2]

Describe the difference between a REPEAT … UNTIL loop and a WHILE … DO … ENDWHILE loop.

Mark scheme

REPEAT tests its condition at the end / is post-condition, so it always runs at least once (1).
WHILE tests its condition at the start / is pre-condition, so it may not run at all (1).

Write[4]

Rewrite this algorithm using a WHILE … DO … ENDWHILE loop instead of FOR. It must give the same output.

FOR Count ← 1 TO 10
  OUTPUT Count * 3
NEXT Count

Mark scheme

Count ← 1 before the loop (1)
WHILE Count <= 10 DO (or < 11) (1)
OUTPUT Count * 3 inside the loop (1)
Count ← Count + 1 inside the loop, then ENDWHILE (1)

Explain[3]

Explain the purpose of this algorithm and state its output when the inputs are 3, 9, 4, 0.

X ← 0
REPEAT
  INPUT Y
  IF Y > X
    THEN
      X ← Y
  ENDIF
UNTIL Y = 0
OUTPUT X

Mark scheme

Inputs numbers until 0 is entered (1).
Finds / outputs the largest number entered (1).
Output: 9 (1).

Explain[2]

A program asks a user to enter a password until it is correct. Explain which loop structure is most suitable.

Mark scheme

REPEAT … UNTIL (1)…
…because the number of attempts is not known and the password must be entered at least once (1).

🗝️ Recap & Key Terms 3 min

Iteration: Repeating a set of actions using a loop structure.
Count-controlled loop: FOR … TO … NEXT: repeats a set number of times; the counter is managed automatically.
Post-condition loop: REPEAT … UNTIL: the condition is tested at the end, so it runs at least once.
Pre-condition loop: WHILE … DO … ENDWHILE: the condition is tested at the start, so it may never run.
Rogue value: A value that is not real data, used to end a loop (e.g. −1).
Purpose of an algorithm: What the algorithm achieves, together with the processes it uses to achieve it.

Homework 1 min

Task (≤ 15 min): Write pseudocode that inputs positive numbers until the user enters 0, then outputs how many numbers were entered and their total. Explain why you chose your loop. [5]

Model answer

Count ← 0
Total ← 0
INPUT Number
WHILE Number <> 0 DO
  Count ← Count + 1
  Total ← Total + Number
  INPUT Number
ENDWHILE
OUTPUT "How many: ", Count
OUTPUT "Total: ", Total