Trace Tables (Cambridge International A-Level Computer Science)

What a trace table question tests

What is a trace table question in 9618?

• A trace table records the value of each variable, and any output, as an algorithm is dry run one statement at a time

• In 9618, trace tables for pseudocode appear in Paper 2, usually worth 5 or 6 marks

  • Paper 1 also asks you to trace an assembly language program, and Paper 3 has asked for a trace of a recursive function

• The question gives the pseudocode, the starting data and a table with the column headings already filled in

• The command word is almost always Complete, for example:

  • "Complete the trace table by dry running the procedure when it is called as follows: CALL Process("X3Y2W4")"
  • "Complete the trace table below by dry running the procedure Encode() when the following values are input: 12, 24, 57, 43, 56, 22, 31, 32, 47, 99, 0"

• The question tests whether you can follow the exact logic of the code, including loops, selection, array indexes and string functions

How are trace tables marked?

• Mark schemes split the table into zones or groups of rows and award one mark per zone

  • For example, one 6-mark trace table was marked as: one mark for the initialisation row, one mark for each of the first four iterations and one mark for the final iteration

• A mistake in one zone does not lose every mark, but an error that is carried forward into later rows can make those zones wrong too

• Marks are only given when every value in the zone is correct, so accuracy matters more than speed

Step-by-step method

How do you complete a trace table?

• Follow these steps for every trace table question:

  1. Read the whole algorithm first and find the loop, what ends it and which variables change inside it
  2. Fill in the initial values on the first row, exactly as the code assigns them, before the loop starts
  3. Work through one statement at a time, in the order the code runs, not the order of the columns
  4. Only write a value when it changes; leave a cell empty if the variable keeps its value
  5. Start a new row when a variable that already has a value on the current row changes again
  6. Check the loop condition every time the loop is about to repeat, using the current values
  7. Record output exactly as it would be displayed

• Leave the left-over blank rows empty; the number of rows printed is not a clue to the number of iterations

Example: a simple FOR loop

• The pseudocode below adds the numbers 1 to 3

• The first row holds the initial value of Total; Count has no value yet
• Never add a row for a FOR loop counter going past its end value: the loop stops after Count reaches 3, so Count is never shown as 4

Exam Hint

• Before you write anything in the table, find the statement that ends the loop and predict how many times it will run, then check your table matches

Tracing loops, arrays and functions

What changes when the loop is a WHILE or REPEAT loop?

• A WHILE loop checks its condition before each iteration, so the loop body may never run at all
• A REPEAT ... UNTIL loop checks its condition after each iteration, so the body always runs at least once
• When the condition ends the loop, nothing changes, so no new row is needed just for the check
• With input values (for example "12, 24, 57, ... 0"), use each value once, in order, and stop when the loop ends, even if values are left over

Tracing nested loops

• The inner loop runs completely for every single iteration of the outer loop
• Write both counters as columns and update the inner counter on every row
• The outer counter only changes when the inner loop has finished

Tracing arrays

• Each array element in the table gets its own column, such as Mix[1] to Mix[4]

• When the index is a variable, work out the index first, then find the element

  • If Index is 3, Mix[Index] ← Mix[Index] - 1 changes Mix[3] only

• An element keeps its value until the code changes it, so look back up the column for its latest value

Tracing functions and string handling

• Use the Insert to check exactly what each built-in function returns; the Paper 2 guide explains how to use it

  • MID("X3Y2W4", 3, 1) returns "Y", the 1 character starting at position 3
  • LEFT(Result, 3) returns the first 3 characters of Result
  • STR_TO_NUM("3") returns the number 3, not the string "3"

• Keep data types consistent with the question: strings in quotation marks, characters in single quotes, numbers without quotes

  • The OUTPUT column is different: write output exactly as it is displayed, without quotation marks

• When a function is called, trace its parameters as the values passed in, and write the returned value in the column of the variable that receives it

Common mistakes in trace tables

• Examiner reports for 9618 identify these mistakes:

  • Missing the initial values: one series' report noted that otherwise good answers "missed the initial values", which is a full mark lost
  • Merging iterations: the same report stressed that students must "keep the values of variables distinct for each iteration of the loop"
  • Quotation marks around output: in assembly language traces in Paper 1, otherwise correct tables lost marks for putting quotation marks around the output
  • Missing the final value: examiners noted answers that left out the final value of a loop counter (Index = 11) after a conditional loop ended

• Other mistakes that cost marks:

  • Running a loop one time too many or one time too few (an off-by-one error), often by checking the loop condition with old values
  • Using / and DIV interchangeably: DIV gives the whole-number part only, so 583 DIV 10 is 58

Worked Example The procedure Process() is written in pseudocode:

Complete the trace table by dry running the procedure when it is called as follows:

CALL Process(5837)

[5]

Answer:

Num	Digit	Total	Count	OUTPUT
5837		0	0
583	7		1
58	3		2
5	8	8
0	5		3
				Even total: 8, odd digits: 3

One mark for each of:

• the initialisation row [1 mark]
• the first two iterations [1 mark]
• the third iteration [1 mark]
• the fourth iteration, with Num reaching 0 [1 mark]
• the output [1 mark]

MOD 10 takes the last digit and DIV 10 removes it, so the digits are processed from right to left: 7, 3, 8, 5. The loop ends when Num is 0, so there is no fifth iteration. See Writing Pseudocode in the Exam for how MOD and DIV work.

Exam Hint

• When you finish, run your eye down each column: a variable should only change on rows where the code actually assigns it a new value