Trace Tables for Loop Problems - Easy Starter Questions V2

Trace Tables for Loop Problems - Easy Starter Questions V2

trace2() - Basic Loop

for (int i = 2; i <= 8; i = i + 2) {
    sum = sum + i;
}

Step	i	i <= 8?	sum (before)	sum = sum + i	sum (after)
Init	–	–	0	–	0
1	2	true	0	0 + 2 =	2
2	4	true	2	2 + 4 =	6
3	6	true	6	6 + 6 =	12
4	8	true	12	12 + 8 =	20
5	10	false	20	–	20

Output: 20

trace4() - Loop with Counter

while (n > 1) {
    n = n / 2;
    count++;
}

Step	n	n > 1?	count (before)	n = n / 2	count (after)
Init	15	–	0	–	0
1	15	true	0	15/2 = 7	1
2	7	true	1	7/2 = 3	2
3	3	true	2	3/2 = 1	3
4	1	false	3	–	3

Output: 3 1

trace5() - Loop with Conditional

for (int i = 1; i <= n; i++) {
    if (i % 3 == 0) {
        result = result + i;
    }
}

(with n = 10)

Step	i	i <= 10?	i % 3 == 0?	result (before)	result + i	result (after)
Init	–	–	–	0	–	0
1	1	true	false	0	–	0
2	2	true	false	0	–	0
3	3	true	true	0	0 + 3 =	3
4	4	true	false	3	–	3
5	5	true	false	3	–	3
6	6	true	true	3	3 + 6 =	9
7	7	true	false	9	–	9
8	8	true	false	9	–	9
9	9	true	true	9	9 + 9 =	18
10	10	true	false	18	–	18
11	11	false	–	18	–	18

Output: 18

trace6() - While Loop with Update

while (x * 3 <= n) {
    x = x * 3;
    count++;
}

(with n = 30)

Step	x	x * 3	x * 3 <= 30?	count (before)	x = x * 3	count (after)
Init	1	–	–	0	–	0
1	1	3	true	0	3	1
2	3	9	true	1	9	2
3	9	27	true	2	27	3
4	27	81	false	3	–	3

Output: 27 3

trace8() - Loop with Multiple Updates

while (x < y) {
    x = x * 2;
    y = y - 3;
}

Step	x	y	x < y?	x = x * 2	y = y - 3
Init	2	20	–	–	–
1	2	20	true	4	17
2	4	17	true	8	14
3	8	14	true	16	11
4	16	11	false	–	–

Output: 16 11

trace9() - Accumulator Pattern

while (product < n) {
    product = product * 2;
    count++;
}

(with n = 100)

Step	product	product < 100?	count (before)	product = product * 2	count (after)
Init	1	–	0	–	0
1	1	true	0	2	1
2	2	true	1	4	2
3	4	true	2	8	3
4	8	true	3	16	4
5	16	true	4	32	5
6	32	true	5	64	6
7	64	true	6	128	7
8	128	false	7	–	7

Output: 7 128

trace10() - Complex Loop Logic

for (int i = 0; i < n; i++) {
    int next = x + 2 * y;
    x = y;
    y = next;
}

(with n = 4)

Step	i	i < 4?	x (before)	y (before)	next = x + 2*y	x (after)	y (after)
Init	–	–	1	1	–	1	1
1	0	true	1	1	1 + 2*1 = 3	1	3
2	1	true	1	3	1 + 2*3 = 7	3	7
3	2	true	3	7	3 + 2*7 = 17	7	17
4	3	true	7	17	7 + 2*17 = 41	17	41
5	4	false	17	41	–	17	41

Output: 17