Trace Tables & Correcting Errors

🎯 Syllabus & Goals 3 min

Cambridge 7.7 · Trace tables Cambridge 7.8 · Identify and correct errors Paper 2 · Algorithms, Programming and Logic

By the end of this lesson you can:

1. Complete a trace table to document a dry run of a flowchart or pseudocode.
2. Use a trace table and test data to find the error in an algorithm.
3. Identify errors in given pseudocode and write the corrected version.

Textbook: Chapter 7, §7.7–7.8 (pp. 282–288)

Recap / Warm-Up 5 min

Last lesson you chose test data and expected results. A trace table is where you run that data through an algorithm, by hand, one step at a time.

Quick starter

A range check should accept 1 to 10 but is written UNTIL N > 1 AND N < 10. Which boundary value exposes the error?

🧠 Key Concept 14 min

1 · Dry runs and trace tables

Set up one column per variable and one for OUTPUT. Then, during the dry run:

• each time a variable changes, write its new value in its column;
• each time something is output, write it in the OUTPUT column — without quotation marks;
• move down a row as the algorithm moves on (a new pass of a loop usually starts a new row).

Here is a flowchart that exam papers love — single-letter names, and you must work out what it does:

2 · Using a trace table to find errors

Trace tables and test data are how errors are found. If the actual output differs from the expected output, the trace shows where the values first go wrong. Look for these six common faults:

Worked Example 12 min

Worked example 1 · Dry run and purpose

The flowchart as pseudocode, dry run with test data 14, 3, 27, 9, 30, 6, 18, 1, 22, 11.

A ← 0
B ← 0
C ← 100
OUTPUT "Enter ten numbers"
REPEAT
  INPUT X
  IF X > B
    THEN
      B ← X
  ENDIF
  IF X < C
    THEN
      C ← X
  ENDIF
  A ← A + 1
UNTIL A = 10
OUTPUT B, " ", C

1. Row 1 = initial values and the prompt.examiners award a mark for the starting values.
2. X = 14: 14 > 0 so B ← 14; 14 < 100 so C ← 14; A ← 1.
3. Only changes are written. X = 9 changes neither B nor C, so those cells stay blank.
4. Purpose: it inputs ten numbers and outputs the largest (B) and smallest (C). Output: 30 1.

Worked example 2 · Finding and fixing the error

Now dry run the same algorithm with 250, 180, 320, 140, 210, 400, 190, 160, 300, 170. Expected output: 400 140.

1. Compare actual with expected. Largest is right (400); smallest is wrong (100).
2. Find where it went wrong. C starts at 100 and no input is below 100, so C never changes.the error is in initialisation: the starting values only suit numbers from 0 to 100. Negative numbers would break B the same way.
3. Correct it. Set B and C to the first number input, then loop for the other nine:

   OUTPUT "Enter ten numbers"
   INPUT X
   B ← X
   C ← X
   A ← 0
   REPEAT
     INPUT X
     IF X > B
       THEN
         B ← X
     ENDIF
     IF X < C
       THEN
         C ← X
     ENDIF
     A ← A + 1
   UNTIL A = 9
   OUTPUT B, " ", C

   print("Enter ten numbers")
   x = int(input())
   b = x
   c = x
   for a in range(9):
       x = int(input())
       if x > b:
           b = x
       if x < c:
           c = x
   print(b, c)

4. Re-test with the same data to prove the fix:

   A	B	C	X	OUTPUT
   				Enter ten numbers
   0	250	250	250
   1		180	180
   2	320		320
   3		140	140
   4			210
   5	400		400
   6			190
   7			160
   8			300
   9			170	400 140

   the loop now runs 9 times, because the first number was input before it.

Worked example 3 · Identify and correct four errors

This algorithm should input 8 positive numbers and output their average. It contains four errors.

01 Total ← 1
02 FOR Count ← 1 TO 8
03   REPEAT
04     INPUT Number
05   UNTIL Number < 0
06   Total ← Total + Count
07 NEXT Count
08 Average ← Total / 7
09 OUTPUT Average

Total ← 0
FOR Count ← 1 TO 8
  REPEAT
    OUTPUT "Enter a positive number "
    INPUT Number
  UNTIL Number > 0
  Total ← Total + Number
NEXT Count
Average ← Total / 8
OUTPUT Average

total = 0
for count in range(1, 9):
    number = 0
    while number <= 0:
        number = int(input("Enter a positive number "))
    total = total + number
average = total / 8
print(average)

Test the corrected version with 4, 6, −3, 10, 2, 8, 5, 7, 6 (−3 should be rejected):

6.0

Try It Yourself 12 min

Even ← 0
Count ← 0
REPEAT
  INPUT N
  IF N MOD 2 = 1
    THEN
      Even ← Even + 1
  ENDIF
UNTIL Count = 5
OUTPUT Even

📝 Exam Practice 10 min

Count ← 0
Total ← 0
REPEAT
  INPUT Value
  IF Value > 0
    THEN
      Total ← Total + Value
      Count ← Count + 1
  ENDIF
UNTIL Value = 0
OUTPUT Total / Count

01 Largest ← 1000
02 FOR Count ← 1 TO 20
03   OUTPUT Number
04   IF Number > Largest
05     THEN
06       Largest ← Count
07   ENDIF
08 NEXT Largest
09 OUTPUT Largest

🗝️ Recap & Key Terms 3 min

A dry run works through an algorithm by hand; a trace table records every change and every output. Comparing actual and expected results shows where an algorithm goes wrong. Check initialisation, conditions, loop bounds, variables, order and missing statements.

Dry run

The manual exercise of working through an algorithm step by step, using test data.

Trace table

A table recording the value of each variable each time it changes, and any output, during a dry run.

Expected result

The output the algorithm should produce for given test data, worked out beforehand.

Error (in an algorithm)

A fault that makes the actual result differ from the expected result, e.g. a wrong condition or start value.

Homework 1 min

Task (≤ 15 min): This should input 12 whole numbers, each from 1 to 50, and output their total. (a) Identify four errors. [4] (b) Rewrite it correctly. [4]

Sum ← 1
FOR Index ← 1 TO 12
  REPEAT
    OUTPUT "Enter a number from 1 to 50 "
    INPUT Value
  UNTIL Value < 1 OR Value > 50
  Sum ← Sum + Index
  Index ← Index + 1
NEXT Value
OUTPUT Sum

Sum ← 0
FOR Index ← 1 TO 12
  REPEAT
    OUTPUT "Enter a number from 1 to 50 "
    INPUT Value
  UNTIL Value >= 1 AND Value <= 50
  Sum ← Sum + Value
NEXT Index
OUTPUT Sum