Nested Iteration: Revision Notes (Computer Science A 2.11)

Recap

Nested iteration is a loop inside the body of another loop. The inner loop completes all its iterations each time the outer loop runs once.

for (outer) {
    for (inner) {
        innermost statement
    }
    statement that runs once per outer pass (such as println)
}

Key relationships

Idea	Rule
Order	Outer pass 1: inner runs fully; outer pass 2: inner runs fully again; and so on
Independent bounds	innermost body runs (outer count) x (inner count) times
Inner bound uses the outer variable	add the inner count for each outer value
Triangle j <= i for i = 1 to n	1 + 2 + … + n = n(n + 1) / 2
Strict upper triangle j = i + 1	(n - 1) + … + 1 + 0 = n(n - 1) / 2
Row ending	System.out.println() after the inner loop, in the outer body
Inner while variable	set it (declare it) inside the outer loop before the inner loop

Assumptions

• Bounds are integers and the loops terminate.
• The inner loop is entirely inside the outer loop’s body.
• print keeps the cursor on the line; println ends the line.

Mistakes to avoid

• Putting println inside the inner loop (a column of single items) or after the outer loop (one long line).
• Multiplying the bounds when the inner bound depends on the outer variable.
• Forgetting to reset an inner while loop variable.
• Starting the inner loop at the wrong place (j = i versus j = i + 1) and changing the count.
• Counting the inner statement as if it ran once per outer iteration.
• Mixing up which loop variable controls rows and which controls columns.

Worked mini-example

int total = 0;
for (int i = 1; i <= 3; i++) {
    for (int j = 1; j <= i; j++) {
        total = total + j;
    }
}

i	inner values of j	added this pass	total after
1	1	1	1
2	1, 2	3	4
3	1, 2, 3	6	10

total is 10. The innermost statement ran 1 + 2 + 3 = 6 times. The inner loop restarted from j = 1 on every outer pass because j is declared in the inner for header.

Quick self-check

1. How many stars does for (i < 5) { for (j < 6) { print("*"); } } print? Answer: 30.
2. For for (int i = 0; i < 4; i++) { for (int j = 0; j < i; j++) { ... } }, how many times does the inner body run? Answer: 0 + 1 + 2 + 3 = 6.
3. Where must System.out.println(); go to end each row of a rectangle? Answer: after the inner loop, inside the outer loop.
4. Why might an inner while loop run only once? Answer: its variable is not reset for later outer passes.

Full explanations and diagrams are in the Topic 2.11 study guide.