Tracing a 1D array program with a trace table

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Quick Questions

Shade in the A or B circle for each question.

1. Which columns should a trace table for a FOR loop over a 1D array include?

A Only one column showing the final OUTPUT

B A column for Index and a column for each variable and array element being changed

2. When do you add a new row to a trace table?

A After each pass of the loop, to record the new values

B Only once, after the loop has finished

3. FOR Index ← 1 TO 3 then Scores[Index] ← Index * 2 then NEXT Index. After the loop, what is Scores[3]?

A 6

B 3

4. Nums holds 4, 5, 6. Total ← 0, then FOR i ← 1 TO 3: Total ← Total + Nums[i]. What is Total after the loop?

A 9

B 15

5. An array is declared ARRAY[1:5], but the loop is FOR Index ← 1 TO 6. What does the trace table show on the last row?

A Index = 6, which is outside the bounds 1 to 5 (off-by-one error)

B Index = 6, which is fine because the loop says TO 6

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1Index \| Total \| Scores[Index]		ADECLARE Nums : ARRAY[1:5] OF INTEGER FOR Index ← 1 TO 6 OUTPUT Nums[Index] NEXT Index
2Scores[3] ← 7 (row 3 of the table)		BFOR Index ← 1 TO 3 Total ← Total + Nums[Index] NEXT Index OUTPUT Total
3Use a trace table to find the final OUTPUT by following the loop one pass at a time		CThe trace table starts at the wrong index. The loop begins at 0, which is below the lower bound of 1, so the first row should show Index = 0 and an error
4A trace table shows an off-by-one error when Index goes past the upper bound of the array		DColumn headings of a trace table: the loop variable, a running variable and the array element being used
5Trace table has only an Index column, with no column for Total or the array contents		EThe table is missing columns for the variables that change, so you cannot see the array contents or the running total after each pass
6FOR Index ← 0 TO 4 on ARRAY[1:5], trace starts with Index = 1		FRecord the new array contents after the pass where Index is 3

Definitions

trace table

Fill in the Blanks

Complete each line of code by filling in the missing parts.

DECLARE Score : ARRAY[1:3] OF INTEGER FOR Index ← 1 __ 3 OUTPUT Score[Index]

FOR Index ← 1 TO 3 Total ← Total + Score[_____] NEXT Index

DECLARE Mark : ARRAY[1:5] OF INTEGER FOR Index ← 1 TO _ OUTPUT Mark[Index]

DECLARE Mark : ARRAY[0:2] OF INTEGER FOR Index ← _ TO 2 Mark[Index] ← Index * 2

Total ← _ Total ← Total + Score[1] OUTPUT Total

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A Total ← 0

B FOR Index ← 1 TO 3

C Total ← Total + Score[Total]

D NEXT Index

E OUTPUT Total

Question 2

A FOR i ← 1 TO 4

B Num[i] ← i * 2

C NEXT i

D OUTPUT Num[5]

Question 3

A // Temp has indexes 1 to 5

B FOR Day ← 0 TO 5

C Temp[Day] ← Day * 10

D NEXT Day

E OUTPUT Temp[5]

Question 4

A Total ← 1

B FOR i ← 1 TO 3

C Total ← Total + Data[i]

D NEXT i

E OUTPUT Total

Question 5

A Big ← Data[1] // Data[1:4]

B FOR i ← 2 TO 3

C IF Data[i] > Big THEN

D Big ← Data[i]

E ENDIF

F NEXT i

Answer Key

Tracing a 1D array program with a trace table

Section A: Quick Questions

B — A column for Index and a column for each variable and array element being changed

A — After each pass of the loop, to record the new values

A — 6

B — 15

A — Index = 6, which is outside the bounds 1 to 5 (off-by-one error)

Section B: Match the Pairs

Index | Total | Scores[Index] → Column headings of a trace table: the loop variable, a running variable and the array element being used

Scores[3] ← 7 (row 3 of the table) → Record the new array contents after the pass where Index is 3

Use a trace table to find the final OUTPUT by following the loop one pass at a time → FOR Index ← 1 TO 3 Total ← Total + Nums[Index] NEXT Index OUTPUT Total

A trace table shows an off-by-one error when Index goes past the upper bound of the array → DECLARE Nums : ARRAY[1:5] OF INTEGER FOR Index ← 1 TO 6 OUTPUT Nums[Index] NEXT Index

Trace table has only an Index column, with no column for Total or the array contents → The table is missing columns for the variables that change, so you cannot see the array contents or the running total after each pass

FOR Index ← 0 TO 4 on ARRAY[1:5], trace starts with Index = 1 → The trace table starts at the wrong index. The loop begins at 0, which is below the lower bound of 1, so the first row should show Index = 0 and an error

Section C: Definitions

trace table — A table that records the loop variable, index and array contents after each pass of a loop, so you can predict the final OUTPUT and spot errors such as off-by-one.

Section D: Fill in the Blanks

DECLARE Score : ARRAY[1:3] OF INTEGER
FOR Index ← 1 TO 3
  OUTPUT Score[Index]

FOR Index ← 1 TO 3
  Total ← Total + Score[Index]
NEXT Index

DECLARE Mark : ARRAY[1:5] OF INTEGER
FOR Index ← 1 TO 5
  OUTPUT Mark[Index]

DECLARE Mark : ARRAY[0:2] OF INTEGER
FOR Index ← 0 TO 2
  Mark[Index] ← Index * 2

Total ← 0
Total ← Total + Score[1]
OUTPUT Total

Section E: Spot the Error

C — The index must be the loop variable Index. Using Total as the index means the trace table shows the wrong elements being read. It should be Score[Index].

D — The trace table only fills Num[1] to Num[4]. Num[5] is outside the array (or never set). It should be OUTPUT Num[4], which gives 8.

B — This is an off-by-one error. The first row of the trace table would use Day = 0, but Temp[0] does not exist. The loop should start at 1.

A — The Total column in the trace table must start at 0. Starting at 1 makes every row, and the final OUTPUT, too big by 1. It should be Total ← 0.

B — This is an off-by-one error. The loop stops at 3, so the trace table never checks Data[4]. The upper limit should be 4.