Algorithmic Problem-Solving Guides: Tracing Algorithms Using Trace Tables (Copy)

Tracing Algorithms Using Trace Tables

What Trace Tables Are (Exam Definition)

• A trace table is a structured table used to:
  • Track variable values step by step
  • Show how an algorithm executes line by line
• Used to:
  • Predict output
  • Detect logic errors
  • Verify loop and condition behaviour
• Frequently tested in:
  • Dry-run questions
  • “What is the output?” questions
  • Debugging-style problems

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Core Examiner Rule (Non-Negotiable)

• Marks are awarded for correct intermediate values, not just the final answer
• A correct final output with incorrect steps can still lose marks

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Why Students Lose Easy Marks Here

• Skipping rows
• Updating variables in the wrong order
• Forgetting loop conditions
• Mixing old and new values
• Guessing instead of tracing

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What A Proper Trace Table Must Show

• Variable names as column headings
• A new row every time a variable changes
• Values updated in correct execution order

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Basic Trace Table Structure

Step	Variable 1	Variable 2	Condition / Output
Start	Initial value	Initial value	—
1	Updated	Unchanged	—
2	Updated	Updated	OUTPUT

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Rule Before You Start Tracing

• Always write initial values first
• Even if they are 0, FALSE, or empty

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Example 1: Simple Assignment Tracing

Pseudocode

a ← 5
b ← a + 3
a ← b - 2
OUTPUT a

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Trace Table

Step	a	b	Output
Start	—	—	—
1	5	—	—
2	5	8	—
3	6	8	—
4	6	8	6

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Key Learning

• Updates happen sequentially
• Later lines use latest values

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Example 2: Tracing A FOR Loop

Pseudocode

total ← 0

FOR i ← 1 TO 4
  total ← total + i
NEXT i

OUTPUT total

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Trace Table

i	total
Start	0
1	1
2	3
3	6
4	10

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Final Output

10

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

Example 3: Tracing IF Statements

Pseudocode

x ← 4

IF x > 3 THEN
  x ← x + 2
ELSE
  x ← x - 2
ENDIF

OUTPUT x

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Trace Table

Step	x	Condition
Start	4	—
IF check	4	TRUE
Update	6	—
OUTPUT	6	—

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Key Learning

• Only one branch executes
• ELSE block is skipped entirely

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Example 4: Tracing WHILE Loops

Pseudocode

count ← 1
total ← 0

WHILE count <= 3 DO
  total ← total + count
  count ← count + 1
ENDWHILE

OUTPUT total

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Trace Table

count	total
Start	0
1	1
2	3
3	6

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Loop Stops When

• count = 4
• Condition becomes FALSE

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Example 5: Tracing REPEAT UNTIL Loops

Pseudocode

x ← 2

REPEAT
  x ← x * 2
UNTIL x > 10

OUTPUT x

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Trace Table

Iteration	x
Start	2
1	4
2	8
3	16

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Key Difference

• Condition checked after execution
• Loop runs at least once

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

Example 6: Tracing With Arrays

Pseudocode

DECLARE nums : ARRAY[1..3] OF INTEGER
nums[1] ← 5
nums[2] ← 2
nums[3] ← 7

sum ← 0

FOR i ← 1 TO 3
  sum ← sum + nums[i]
NEXT i

OUTPUT sum

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Trace Table

i	nums[i]	sum
Start	—	0
1	5	5
2	2	7
3	7	14

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Final Output

14

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Example 7: Tracing String Processing

Pseudocode

text ← "CAT"
count ← 0

FOR i ← 1 TO LENGTH(text)
  IF text[i] = "A" THEN
    count ← count + 1
  ENDIF
NEXT i

OUTPUT count

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Trace Table

i	text[i]	count
1	C	0
2	A	1
3	T	1

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Output

1

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

How Examiners Expect Trace Tables To Be Presented

• Clear column headings
• No skipped iterations
• Logical progression
• Correct termination point

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Common Trace Table Mistakes (High-Frequency)

Mistake 1: Updating Variables In Wrong Order

• Especially inside loops

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Mistake 2: Forgetting Initial Values

• Causes entire table to be wrong

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Mistake 3: Continuing After Loop Ends

• Loop stops as soon as condition fails

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Mistake 4: Confusing Loop Variable With Data Variable

• i vs nums[i]

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Mistake 5: Mixing Old And New Values

• Always use latest assigned value

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Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change AS Level Computer Science Full Scale Course

Examiner Trace Table Checklist

• Are all variables included?
• Is each iteration shown?
• Are updates done in correct sequence?
• Does the loop stop correctly?
• Is the final output correct?

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Exam-Ready Trace Table Strategy

1. Write initial values
2. Follow code line by line
3. Update only when a statement executes
4. Stop exactly when condition fails
5. Double-check loop bounds

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One-Line Rules To Memorise

• Trace, don’t guess
• Update in order
• One row per change
• Conditions control flow
• Accuracy beats speed