for Loops: Revision Notes (Computer Science A 2.8)

Recap

A for loop gathers the three parts of a counting loop into one header.

for (initialization; Boolean expression; update) {
    body
}

Part	Runs	Example
Initialization	once, before the first test	int i = 0
Boolean expression	before every iteration	i < 5
Update	after the whole body, before the next test	i++

Order: initialization once, then (test, body, update) repeated, then a final test that is false.

Key relationships

Idea	Rule
Iterations of for (int i = 0; i < n; i++)	exactly n (values 0 to n - 1)
Iterations of for (int i = 1; i <= n; i++)	exactly n (values 1 to n)
Step by s from a while i <= b	the number of values a, a + s, ... that do not exceed b
Zero iterations	test false on the first evaluation
Equivalent while	initialization before; test in brackets; update last in body
Scope	variable declared in the header is out of scope after the loop

Assumptions

• The loop control variable is an int and the update moves it toward making the test false.
• Nothing in the body changes the loop control variable unless the question says so.
• The body is in braces.

Mistakes to avoid

• A semicolon after the header.
• Using the header variable after the loop.
• Writing <= when < is needed (or the reverse): an off-by-one error.
• Assuming the update runs before the first iteration.
• Counting down with i++, or counting up with i--.
• Forgetting to change the accumulator inside the loop.

Worked mini-example

int result = 0;
for (int k = 5; k > 0; k -= 2) {
    result = result * 10 + k;
}

Iteration	k	k > 0?	result after the body
1	5	true	0 * 10 + 5 = 5
2	3	true	5 * 10 + 3 = 53
3	1	true	53 * 10 + 1 = 531
(test)	-1	false	loop ends

result is 531. The loop control variable k is out of scope afterwards, so the code after the loop cannot refer to it. As a while loop: int k = 5; while (k > 0) { result = result * 10 + k; k -= 2; }.

Quick self-check

1. How many times does for (int i = 3; i < 12; i += 3) run? Answer: 3 times (i = 3, 6, 9).
2. What does for (int i = 0; i < 4; i++) print if the body is System.out.print(i)? Answer: 0123.
3. Why does for (int i = 0; i < 3; i++); followed by a block print the block’s message only once? Answer: the semicolon is an empty body; the block runs once after the loop.
4. Write for (int j = 1; j <= 5; j++) as a while loop. Answer: int j = 1; while (j <= 5) { ... j++; }.

Full explanations and diagrams are in the Topic 2.8 study guide.