Iteration — Three Types of Loop

🎯 Syllabus & Goals 3 min

Cambridge 8.1.4 · Iteration Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

1. Write a count-controlled FOR … TO … NEXT loop (with and without STEP) and its Python for … in range() version.
2. Write a pre-condition WHILE … ENDWHILE loop and a post-condition REPEAT … UNTIL loop, and the Python equivalents.
3. Choose the right loop for a task, and trace a loop with a trace table.

Textbook: Chapter 8, §8.1.4(c) (pp. 312–314)

Recap / Warm-Up 5 min

Last lesson: selection chooses between paths using a condition. Loops use conditions too — to decide whether to go round again.

Quick starter

You need to print a class register of exactly 30 names. Do you know in advance how many times the printing step repeats?

🧠 Key Concept 14 min

There are three loop structures. Each suits a different situation:

1 · Count-controlled: FOR … NEXT

FOR Counter ← 1 TO 10 STEP 2
  OUTPUT Counter
NEXT Counter

for counter in range(1, 11, 2):   # start 1, stop before 11, step 2
    print(counter)

1
3
5
7
9

2 · Pre-condition: WHILE … ENDWHILE

Use this when you do not know how many repetitions are needed, and it is possible that none are needed at all.

WHILE TotalWeight < 100 DO
  INPUT Weight
  TotalWeight ← TotalWeight + Weight
ENDWHILE

while total_weight < 100:
    weight = float(input("Weight: "))
    total_weight = total_weight + weight

3 · Post-condition: REPEAT … UNTIL

Use this when the body must run at least once — for example, asking for input and repeating until it is valid.

REPEAT
  OUTPUT "Enter a PIN: "
  INPUT Pin
UNTIL Pin = CorrectPin

# Python only has pre-condition loops,
# so a post-condition loop is built like this:
while True:
    pin = input("Enter a PIN: ")
    if pin == correct_pin:
        break

Worked Example 12 min

Example 1 · FOR loop — a times table

Output the first five rows of the 7 times table.

1. The number of rows (5) is known in advance.so a count-controlled loop is the right choice.
2. The loop counter is also used in the calculation.it changes by 1 each time, giving 1×7, 2×7, …
3. In Python, the stop value is 6.range stops one before its second argument.

DECLARE Counter, Answer : INTEGER
FOR Counter ← 1 TO 5
  Answer ← Counter * 7
  OUTPUT Counter, " x 7 = ", Answer
NEXT Counter

# The 7 times table, rows 1 to 5
for counter in range(1, 6):      # 1, 2, 3, 4, 5 - stops BEFORE 6
    answer = counter * 7
    print(counter, "x 7 =", answer)

1 x 7 = 7
2 x 7 = 14
3 x 7 = 21
4 x 7 = 28
5 x 7 = 35

Example 2 · WHILE and REPEAT — savings goal and a valid rating

(a) Sam saves $15 each week. How many weeks until the savings reach at least $60?

CONSTANT Goal ← 60
CONSTANT WeeklySaving ← 15
DECLARE Savings, Weeks : INTEGER
Savings ← 0
Weeks ← 0
WHILE Savings < Goal DO
  Savings ← Savings + WeeklySaving
  Weeks ← Weeks + 1
ENDWHILE
OUTPUT "Goal reached after ", Weeks, " weeks with $", Savings

# Pre-condition loop: save $15 a week until the goal is reached
GOAL = 60
WEEKLY_SAVING = 15
savings = 0
weeks = 0
while savings < GOAL:
    savings = savings + WEEKLY_SAVING
    weeks = weeks + 1
print("Goal reached after", weeks, "weeks with $", savings)

Goal reached after 4 weeks with $ 60

Why WHILE? If Sam already had $80, the test 80 < 60 is FALSE at the start and the body is skipped: 0 weeks. A pre-condition loop handles "nothing to do" correctly.

(b) Ask for a film rating from 1 to 5, and keep asking until the rating is valid.

DECLARE Rating : INTEGER
REPEAT
  OUTPUT "Rate the film from 1 to 5: "
  INPUT Rating
UNTIL Rating >= 1 AND Rating <= 5
OUTPUT "Thank you for rating it ", Rating

# Post-condition loop in Python: always ask at least once
while True:
    rating = int(input("Rate the film from 1 to 5: "))
    if rating >= 1 and rating <= 5:
        break                      # the UNTIL condition is met
print("Thank you for rating it", rating)

Rate the film from 1 to 5: 7
Rate the film from 1 to 5: 0
Rate the film from 1 to 5: 4
Thank you for rating it 4

1. The question must be asked at least once.there is nothing to test until the user has typed something — so REPEAT.
2. 7 fails Rating <= 5, 0 fails Rating >= 1: the loop repeats both times.the UNTIL condition is FALSE, so go round again.
3. 4 makes the condition TRUE, so the loop ends.this is a range check (Unit 7 validation) built from a loop.

Try It Yourself 12 min

REPEAT
  INPUT Password
UNTIL LENGTH(Password) >= 8

📝 Exam Practice 10 min

FOR Index ← 1 TO 200
  INPUT Score[Index]
NEXT Index

🗝️ Recap & Key Terms 3 min

Known number of repeats → FOR … NEXT. Unknown, and maybe none → WHILE … ENDWHILE. Unknown, but at least one → REPEAT … UNTIL. Python has for and while; it builds a post-condition loop with while True and break.

Iteration

A section of programming code that can be repeated under certain conditions.

Count-controlled loop

A loop that repeats a set number of times, e.g. FOR … NEXT.

Pre-condition loop

A condition-controlled loop that tests before each iteration, so it may not run at all, e.g. WHILE … ENDWHILE.

Post-condition loop

A condition-controlled loop that tests after each iteration, so it always runs at least once, e.g. REPEAT … UNTIL.

Homework 1 min

Task (≤ 15 min): Complete a trace table for this algorithm and state the final output. [4]

X ← 1
Y ← 0
WHILE X < 20 DO
  Y ← Y + 1
  X ← X * 3
ENDWHILE
OUTPUT Y, " ", X