while Loops: Revision Notes (Computer Science A 2.7)

Recap

A while loop repeats its body zero or more times while its Boolean expression is true.

initialise the loop variable
while (condition) {
    body
    update the loop variable
}

The condition is tested before every iteration, including the first, so if it is false at the start the body never runs. When the loop ends, the condition has just been tested and found false.

Key relationships

Idea	Rule
Tests versus iterations	The condition is tested one more time than the body runs
Zero iterations	Condition false before the first test
Infinite loop	Condition always true: no update, or update in the wrong direction
Off-by-one	`<` versus `<=`, or the wrong start value: one pass too many or too few
Variable after the loop	Holds the first value that failed the test
Accumulator	Set before the loop, changed inside, used after

Assumptions

The Boolean expression uses variables that have been assigned before the loop.
The loop variable is updated inside the body.
The initial values must make the loop do what the question intends (for example, starting above the limit gives zero iterations).

Mistakes to avoid

Forgetting to update the variable the condition depends on.
Updating it in the wrong direction.
Using < when the last value must be included, or <= when it must not.
Reading the final value of the loop variable as the last value processed.
Printing inside the loop when the question asks for a single result after it.
Starting the accumulator at the wrong value (0 for a sum, 1 for a product).

Worked mini-example

int x = 3;
int product = 1;
while (x > 0) {
    product = product * x;
    x--;
}

Test	`x`	`x > 0`?	`product` after the body	`x` after the body
1	3	true	3	2
2	2	true	6	1
3	1	true	6	0
4	0	false	loop ends

The loop computes 3 x 2 x 1 = 6, so product is 6 and x is 0 afterwards. The condition was tested four times and the body ran three times.

Quick self-check

How many times does the body of int i = 0; while (i < 4) { i++; } run? Answer: 4.
What is i afterwards? Answer: 4.
int j = 9; while (j < 3) { j--; } runs how many times? Answer: zero.
Why does int m = 1; while (m > 0) { m = m + 1; } never end? Answer: m grows, so m > 0 stays true.

Full explanations and diagrams are in the Topic 2.7 study guide.