Loop Statements – Programming Algorithms (Senior 4 ICT) | Ganzaa

Programming Algorithms

Lessons

Senior 4 · ICT

Programming Algorithms

5 lessons

Lesson 5 of 5

Loop Statements

25 min

Doing it again, and again

Uwase belongs to an ikimina, a savings group, and puts aside 2 500 Frw every week. She wants 30 000 Frw for a solar lamp. How many weeks will it take? One way is to write "add 2 500" twelve times. But if the target changes to 47 500, the algorithm has to be rewritten. A loop says it once: keep adding 2 500 while the total is below the target. Repetition is where computers beat people: a loop that runs 12 times can just as easily run 12 million times. (The amounts in this lesson are illustrative.)

Definition

Iteration (loop): a control structure that repeats a block of steps, the loop body.

Count-controlled loop (FOR): repeats a set number of times. Condition-controlled loop (WHILE, REPEAT…UNTIL): repeats until a condition changes.

Counter: a variable that counts the passes (count ← count + 1). Accumulator: a variable that builds up a total (total ← total + value). Both must be given a starting value first.

Sentinel: a special input value, such as −1, that is not real data and signals "stop".

Infinite loop: a loop whose stopping condition is never met.

FOR: a known number of times

FOR i ← 1 TO n … ENDFOR sets the counter $i$ to 1, runs the body, adds 1 to $i$ , and repeats until it has run with $i = n$ .

plaintext

total ← 0
FOR i ← 1 TO 5
    total ← total + i
ENDFOR
OUTPUT total

Code Explanation

An accumulator inside a FOR loop: it adds the numbers 1 to 5.

Worked example 1: trace the FOR loop

Pass	i	total after the pass
before		0
1	1	1
2	2	3
3	3	6
4	4	10
5	5	15

Output: 15. Check with the formula for the sum of the first $n$ whole numbers: $\frac{n(n+1)}{2} = \frac{5 \times 6}{2} = 15$ . The loop body ran exactly 5 times.

WHILE: test first, then repeat

WHILE condition DO … ENDWHILE checks the condition before each pass. If it is TRUE the body runs and the condition is checked again; when it is FALSE the loop ends. If the condition is FALSE at the start, the body never runs at all.

plaintext

target ← 30000
saved ← 0
weeks ← 0
WHILE saved < target DO
    saved ← saved + 2500
    weeks ← weeks + 1
ENDWHILE
OUTPUT "Weeks needed: ", weeks

Code Explanation

Each pass adds a week's savings and counts the week. The loop stops as soon as saved reaches the target.

Worked example 2: trace the savings loop

Check	saved < 30000?	saved after the pass	weeks
1	0: Yes	2 500	1
2	2 500: Yes	5 000	2
…	…	…	…
12	27 500: Yes	30 000	12
13	30 000: No, exit

Output: 12 weeks. Check: $\frac{30\,000}{2\,500} = 12$ . The condition was checked 13 times but the body ran 12 times; the last check is the one that stops the loop.

REPEAT…UNTIL: do first, then test

REPEAT … UNTIL condition runs the body, then checks the condition, and stops when it becomes TRUE. The body always runs at least once, which suits anything that must happen before it can be checked, such as asking for input.

plaintext

attempts ← 0
REPEAT
    OUTPUT "Enter PIN:"
    INPUT pin
    attempts ← attempts + 1
UNTIL pin = correctPIN OR attempts = 3
IF pin = correctPIN THEN
    OUTPUT "Welcome"
ELSE
    OUTPUT "Card blocked"
ENDIF

Code Explanation

A PIN check: the user always gets at least one try, and at most three. The loop stops on a correct PIN or on the third attempt, whichever comes first; the IF after the loop works out which one it was.

Sentinel loops and choosing a loop

When the amount of data is not known in advance, a sentinel ends it: "enter marks, and −1 when you have finished".

plaintext

total ← 0
count ← 0
INPUT mark
WHILE mark ≠ -1 DO
    total ← total + mark
    count ← count + 1
    INPUT mark
ENDWHILE
IF count > 0 THEN
    OUTPUT "Average: ", total / count
ELSE
    OUTPUT "No marks entered"
ENDIF

Code Explanation

The first mark is read before the loop and each next one at the end of the body, so the sentinel −1 is never added to the total. The IF avoids dividing by zero when no marks are entered.

	FOR	WHILE	REPEAT…UNTIL
Controlled by	a counter	a condition	a condition
Condition checked	(counter limit)	before each pass	after each pass
Fewest passes	fixed number	0	1
Stops when the condition is	(counter passes the limit)	FALSE	TRUE
Use when	the number of repeats is known	it may not need to run at all	it must run at least once

python

# Loops in Python: the savings loop, then a sentinel loop.
target = 30000
saved = 0
weeks = 0
while saved < target:
    saved = saved + 2500
    weeks = weeks + 1
print("Weeks needed:", weeks)

total = 0
count = 0
mark = int(input("Mark (-1 to finish): "))
while mark != -1:
    total = total + mark
    count = count + 1
    mark = int(input("Mark (-1 to finish): "))
if count > 0:
    print("Average:", total / count)
else:
    print("No marks entered")

Code Explanation

Press Run. The first loop prints Weeks needed: 12. Then type some marks, for example 60, 75 and 81, and finish with −1; the average is 72.0. Python has while and for but no REPEAT…UNTIL; Unit 4 shows how to get the same effect.

Pseudocode Pro: Iteration, For, While and Repeat Until loops. Watch when each kind of loop is chosen and how a count-controlled loop differs from a condition-controlled one.

Warning

Infinite loops. If nothing inside a WHILE loop changes the condition (for example, forgetting saved ← saved + 2500), the loop never ends. Every loop body must move towards the exit.

Off by one. FOR i ← 0 TO 5 runs 6 times, not 5. Check the first and last values of the counter.

Initialise before the loop. Set counters and totals to 0 before the loop, not inside it, or they restart on every pass.

Tip

Trace the first two passes and the last one. Most loop mistakes happen at the start (wrong initial value) or the end (one pass too many or too few). A trace table with columns for the counter, the condition and each variable shows both.

✦

Practice

Name the three kinds of loop and state the fewest number of times each body can run.
Trace: x ← 1; FOR i ← 1 TO 4: x ← x * 2; ENDFOR; OUTPUT x.
Write a FOR loop that outputs the 7 times table from $7 \times 1$ to $7 \times 10$ .
Uwase raises her weekly saving to 3 000 Frw and her target to 47 500 Frw. Trace the WHILE loop enough to find how many weeks she needs, and the amount saved at the end.
Write pseudocode that keeps asking for a mark until one between 0 and 100 is entered (input validation). Which loop is most suitable, and why?
What is wrong with this loop? n ← 10; WHILE n > 0 DO OUTPUT n ENDWHILE. Correct it so it counts down 10, 9, …, 1.
Write pseudocode using a sentinel to find the largest of a list of positive numbers ending with 0.
A student writes: total ← 0; count ← 0; mark ← 0; WHILE mark ≠ -1 DO INPUT mark; total ← total + mark; count ← count + 1 ENDWHILE; OUTPUT total / count. Trace it with the inputs 60, 80, −1 and evaluate the result.

Show answersHide answers

FOR (a fixed number of times, set by the counter limits), WHILE (0), REPEAT…UNTIL (1).
x: 2, 4, 8, 16. Output 16 (that is, $2^{4}$ ).
FOR i ← 1 TO 10; OUTPUT "7 x ", i, " = ", 7 * i; ENDFOR.
After 15 weeks: $15 \times 3\,000 = 45\,000$ , still below 47 500, so the loop runs again. After 16 weeks: 48 000. So 16 weeks, with 48 000 Frw saved.
REPEAT; INPUT mark; UNTIL mark ≥ 0 AND mark ≤ 100. REPEAT…UNTIL suits it because the mark must be entered at least once before it can be checked.
n never changes, so n > 0 stays TRUE: an infinite loop. Add n ← n - 1 after OUTPUT n.
largest ← 0; INPUT x; WHILE x ≠ 0 DO IF x > largest THEN largest ← x ENDIF; INPUT x; ENDWHILE; OUTPUT largest.
The passes read 60, then 80, then −1, and −1 is added before the loop can check it: total = 60 + 80 − 1 = 139, count = 3, output 46.33 (to 2 d.p.) instead of 70. The sentinel must be checked before it is used, so read once before the loop and again at the end of the body.

Quick check

Which loop always runs its body at least once?

Key points

FOR repeats a known number of times; WHILE tests before each pass (may run 0 times); REPEAT…UNTIL tests after (runs at least once) and stops when its condition is TRUE.
Counters and accumulators must be set before the loop; every loop body must move towards the exit.
A sentinel value ends input of unknown length; read once before the loop and again at the end of the body.
Trace the first passes and the last one to catch off-by-one mistakes and infinite loops.

1Doing it again, and again

2FOR: a known number of times

3WHILE: test first, then repeat

4REPEAT…UNTIL: do first, then test

5Sentinel loops and choosing a loop

Doing it again, and again

FOR: a known number of times

WHILE: test first, then repeat

REPEAT…UNTIL: do first, then test

Sentinel loops and choosing a loop