8.2 Iteration: for, while, do … while, and repeat … until Loops

What this competency asks

Within the sequence, selection, and iteration competency, ETS lists tracing, identifying inputs for given outputs, describing purpose, supplying missing code, and identifying equivalent code. For loops specifically, you should be able to:

• Convert code that does not use iteration to equivalent code that uses iteration.
• Trace code with for, while, do … while, and similar loops, and convert from one type of loop to another (a discussion question).

Anatomy of a loop

Every loop has three parts. A missing or wrong part causes most loop bugs.

1. Initialization: set the loop variable, as in int i ← 0.
2. Condition: decide whether to run the body again, as in i < n.
3. Update: move toward ending, as in i ← i + 1.

for ( int i ← 0; i < 5; i ← i + 1 )     // all three parts in the header
    print i                             // print a space after the value
end for

int k ← 1                               // initialization
while ( k ≤ 100 )                       // condition
    k ← k * 2                           // update
end while

The for loop prints 0 1 2 3 4. The while loop doubles k through 2, 4, 8, 16, 32, 64, and 128, and stops with k = 128 after 7 passes.

Counting iterations

After a for loop ends, the loop variable holds the first value that failed the test. For example, i is n after the first header in the table, although in ETS pseudocode a variable declared in the header is not normally used after the loop.

Nested loops

int count ← 0
for ( int i ← 1; i ≤ 4; i ← i + 1 )
    for ( int j ← 1; j ≤ i; j ← j + 1 )
        count ← count + 1
    end for
end for

The inner loop runs 1, 2, 3, and then 4 times, so count = 1 + 2 + 3 + 4 = 10, or n(n + 1)/2 with n = 4. If the inner loop always ran 5 times, the body would run 4 × 5 = 20 times.

Pre-test and post-test loops

int k ← 5
repeat
    k ← k * 2
until ( k ≥ 20 )

Pass 1: k = 10, and 10 ≥ 20 is false, so the loop repeats. Pass 2: k = 20, and 20 ≥ 20 is true, so it stops. The body runs twice and k ends at 20.

Post-test loops suit tasks that must happen at least once, such as showing a menu or prompting for input until it is valid.

Converting code into a loop

Repeated statements that differ only in a number can be replaced by a loop:

// Without iteration
print 3
print 6
print 9
print 12
print 15

// With iteration
for ( int i ← 1; i ≤ 5; i ← i + 1 )
    print 3 * i
end for

To convert, find what changes from line to line (here 3, 6, 9, …, which is 3 × 1, 3 × 2, and so on), make the loop variable produce it, and set the bounds so the loop runs the same number of times. Verify both the first and the last output.

Converting between loop types

for to while. Move the initialization before the loop and the update to the end of the body:

int i ← 0
while ( i < n )
    total ← total + list[i]
    i ← i + 1
end while

while to do … while. These are equivalent only if the condition is true the first time. Otherwise the do … while runs once too often. A guarding if makes them equivalent.

do … while to repeat … until. Negate the condition: do … while ( x < 10 ) is equivalent to repeat … until ( x ≥ 10 ).

Leaving a loop early

Many languages provide break (exit the loop immediately) and continue (skip to the next iteration). They are not part of the ETS notation table. ETS-style code usually exits early by return-ing from a procedure, or by making the condition false with a flag such as while ( ( i < n ) and ( not found ) ).

Common loop bugs