Nested Iteration: Practice Questions (Computer Science A 2.11)

These are original Marlbridge practice questions, not past exam questions. All scenarios are fictional. Mark points are a suggested Marlbridge rubric, not an official scoring guideline. Assume every code segment compiles unless a question says otherwise, and that no calculator is allowed.

Question 1 (multiple choice · foundation)

How many times does System.out.print("#") execute?

for (int i = 0; i < 3; i++) {
    for (int j = 0; j < 5; j++) {
        System.out.print("#");
    }
}

(A) 8
(B) 15
(C) 5
(D) 3

Answer and explanation

Answer: (B). The inner loop runs 5 times for each of the 3 outer passes: 3 x 5 = 15.

(A) adds the bounds (3 + 5).
(C) counts only one outer pass.
(D) counts only the outer loop.

Question 2 (multiple choice · core)

What is printed?

for (int r = 1; r <= 3; r++) {
    for (int c = 1; c <= r; c++) {
        System.out.print(c);
    }
    System.out.println();
}

(A) 1, then 12, then 123, each on its own line
(B) 123, then 123, then 123, each on its own line
(C) 1, then 2, then 3, each on its own line
(D) 111, then 22, then 3, each on its own line

Answer and explanation

Answer: (A). For each r, the inner loop prints c from 1 up to r, then println ends the line: row 1 prints “1”, row 2 prints “12”, row 3 prints “123”.

(B) assumes the inner loop always runs to 3.
(C) prints the row number rather than the column counter.
(D) mixes up the two counters and reverses the row lengths; it does not match any pass of the loops.

Question 3 (multiple choice · core)

What is the value of count after the code runs?

int count = 0;
for (int i = 0; i < 4; i++) {
    for (int j = i; j < 4; j++) {
        count++;
    }
}

(A) 6
(B) 10
(C) 12
(D) 16

Answer and explanation

Answer: (B). For i = 0, 1, 2, 3 the inner loop runs 4, 3, 2, 1 times: 4 + 3 + 2 + 1 = 10.

(A) is 3 + 2 + 1 + 0, which comes from starting the inner loop at i + 1.
(C) is 4 x 3, which treats the inner loop as running 3 times.
(D) is 4 x 4, which ignores the dependence on i.

Question 4 (multiple choice · core)

What is printed?

int i = 1;
int j = 1;
while (i <= 2) {
    while (j <= 3) {
        System.out.print(j);
        j++;
    }
    System.out.print("|");
    i++;
}

(A) 123|123|
(B) 123||
(C) 123|
(D) 112233|

Answer and explanation

Answer: (B). In the first outer pass j runs 1, 2, 3 and ends at 4, then | is printed. In the second outer pass j is still 4, so the inner loop does not run, and only | is printed. The output is 123||.

(A) assumes j restarts at 1, which only happens if it is reset.
(C) forgets the second outer pass.
(D) is not produced by any pass.

Question 5 (multiple choice · core)

What is printed?

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

(A) 6
(B) 10
(C) 3
(D) 18

Answer and explanation

Answer: (B). The inner sums are 1, then 1 + 2 = 3, then 1 + 2 + 3 = 6, giving 1 + 3 + 6 = 10.

(A) is only the last row’s sum.
(C) is the number of outer passes, not the total.
(D) is 3 x 6: it treats the inner loop as always running j from 1 to 3, ignoring that the inner bound is i.

Question 6 (multiple choice · stretch)

Which statement about the code is true?

for (int a = 0; a < 3; a++) {
    for (int b = 0; b < 3; b++) {
        if (a == b) {
            System.out.print("X");
        } else {
            System.out.print(".");
        }
    }
    System.out.println();
}

(A) It prints a 3 by 3 pattern with X on the diagonal.
(B) It prints a single row of X characters.
(C) It prints X in every cell.
(D) It prints a 9 by 9 pattern.

Answer and explanation

Answer: (A). The output has three rows; the X appears where the row number equals the column number, which forms the diagonal: X.., .X., ..X.

(B) ignores the selection, which prints . when a != b.
(C) ignores that the if is only true when a == b.
(D) confuses the 9 executions with a 9 by 9 grid.

Question 7 (constructed response · core)

Write nested loops that print a rectangle of # characters with 4 rows and 6 columns, and then a second block that prints a staircase of 5 rows in which row r has r characters. (6 marks)

Answer and explanation

Model answer.

for (int row = 1; row <= 4; row++) {
    for (int col = 1; col <= 6; col++) {
        System.out.print("#");
    }
    System.out.println();
}
for (int row = 1; row <= 5; row++) {
    for (int col = 1; col <= row; col++) {
        System.out.print("#");
    }
    System.out.println();
}

Suggested Marlbridge rubric (6 marks).

Marks	Awarded for
1	Outer loop with 4 passes (rows)
1	Inner loop with 6 passes, printing one `#` each time
1	`println` after the inner loop and inside the outer loop
1	Second block: outer loop with 5 passes
1	Inner bound depends on the row (`col <= row`)
1	`println` correctly placed in the second block

Question 8 (constructed response · core)

Write a method countEvenProducts(int n) that returns how many pairs of whole numbers a and b with 1 <= a < b <= n have an even product. Then give the value for n = 4. (5 marks)

Answer and explanation

Model answer.

public static int countEvenProducts(int n) {
    int count = 0;
    for (int a = 1; a <= n; a++) {
        for (int b = a + 1; b <= n; b++) {
            if (a * b % 2 == 0) {
                count++;
            }
        }
    }
    return count;
}

For n = 4 the pairs are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4). The products are 2, 3, 4, 6, 8 and 12. Five are even; 3 is odd. The result is 5.

Suggested Marlbridge rubric (5 marks).

Marks	Awarded for
1	Counter initialised before the loops and returned after them
1	Outer loop over `a`
1	Inner loop starting at `a + 1` (so `a < b`)
1	Test for an even product, inside both loops, incrementing the counter
1	Value 5

Question 9 (constructed response · stretch)

This code is intended to print three rows of “ABC”, but it prints something else.

int row = 0;
int col = 0;
while (row < 3) {
    while (col < 3) {
        System.out.print("ABC".substring(col, col + 1));
        col++;
    }
    System.out.println();
    row++;
}

(a) State what is printed. (2 marks)

(b) Explain the fault in terms of the initial condition of the inner loop. (2 marks)

Answer and explanation

(a) The first row prints ABC; the second and third rows print nothing, so the output is ABC followed by two empty lines.

(b) After the first row col is 3. The inner loop condition col < 3 is false for the second and third rows, so the inner loop does not run. The inner loop needs col to be 0 each time it starts, but nothing resets it.

(c)

int row = 0;
while (row < 3) {
    int col = 0;
    while (col < 3) {
        System.out.print("ABC".substring(col, col + 1));
        col++;
    }
    System.out.println();
    row++;
}

Declaring col (or assigning col = 0;) inside the outer loop restores the starting value for every row. A for loop would do this automatically.

Suggested Marlbridge rubric (6 marks). 2 marks for (a) (1 for the first row, 1 for the two empty lines); 1 mark for stating that col stays at 3; 1 mark for relating this to the inner loop’s initial condition; 2 marks for (c) (1 for the reset position, inside the outer loop but before the inner one, and 1 for the rest unchanged).

Question 10 (constructed response · stretch)

Three methods each use nested loops with a counter.

public static int f(int n) {
    int c = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) { c++; }
    }
    return c;
}
public static int g(int n) {
    int c = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < i; j++) { c++; }
    }
    return c;
}
public static int h(int n) {
    int c = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < 3; j++) { c++; }
    }
    return c;
}

(a) Complete the table of return values. (6 marks)

Method	`n = 5`	`n = 10`
`f`
`g`
`h`

(b) When n doubles from 5 to 10, by what factor does the work change for each method? (3 marks)

Answer and explanation

(a)

Method	`n = 5`	`n = 10`
`f`	25	100
`g`	10	45
`h`	15	30

f is n x n. g is 0 + 1 + … + (n - 1) = n(n - 1) / 2: 10 for n = 5 and 45 for n = 10. h is 3 passes for each of n outer passes: 3n, which is 15 and 30.

(b) f: 100 / 25 = 4 times as much. g: 45 / 10 = 4.5 times as much. h: 30 / 15 = 2 times as much. The nested loops whose inner bound grows with n (f and g) grow much faster than h, whose inner loop is a fixed 3.

Suggested Marlbridge rubric (9 marks). 1 mark for each of the six table values; 1 mark for each of the three factors in (b).

How did you do?

Questions 1, 3 and 5 test counting executions. If you missed Question 3, revisit “Counting the inner body” in the study guide. If you missed Question 4 or 9, review “The inner variable must start again”. If you missed Question 2 or 6, review “Rows and columns”. Then use the checklist.