Trace tables and finding errors

What a trace table is

A dry run means working through an algorithm by hand, line by line, without a computer.

A trace table records the dry run. It has one column for each variable, and one for the output.

Write a new value in a column only when that variable changes. Move to a new row when the loop goes round again.

Worked dry run

This algorithm reads numbers until the user types -1. A value that only means 'stop' is called a rogue value.

Input data: 12, 7, 20, 9, -1. Follow each row of the table below and check you agree.

Then use the toy. Pick Counting (WHILE), a similar rogue-value loop, and press Step to run it one line at a time.

DECLARE Value : INTEGER
DECLARE Total : INTEGER
DECLARE Count : INTEGER
DECLARE Highest : INTEGER
Total ← 0
Count ← 0
Highest ← 0
INPUT Value
WHILE Value <> -1 DO
  Total ← Total + Value
  Count ← Count + 1
  IF Value > Highest
    THEN
      Highest ← Value
  ENDIF
  INPUT Value
ENDWHILE
OUTPUT Total / Count, " ", Highest

total = 0
count = 0
highest = 0
value = int(input())
while value != -1:
    total = total + value
    count = count + 1
    if value > highest:
        highest = value
    value = int(input())
print(total / count, highest)

There is something to try for this step in the IGCSE library.

Two kinds of error

A syntax error breaks the rules of the language, like a spelling mistake in a keyword. The program will not run.

A logic error means the program runs but gives the wrong answer. Examples: `<` instead of `>`, or a total that starts at 1.

Exam questions mostly test logic errors. Trace tables and test data are how you find them.

Worked example: find four errors

This algorithm should input 10 numbers, output their average, and count how many are over 50. It has four errors.

Work through it line by line. For each line ask: does this do what the purpose says?

01 DECLARE Total : INTEGER
02 DECLARE Count : INTEGER
03 DECLARE Number : INTEGER
04 DECLARE Index : INTEGER
05 Total ← 0
06 Count ← 1
07 FOR Index ← 1 TO 10
08   INPUT Number
09   Total ← Number
10   IF Number < 50
11     THEN
12       Count ← Count + 1
13   ENDIF
14 NEXT Index
15 OUTPUT "Average: ", Total / Index
16 OUTPUT "Numbers over 50: ", Count

The corrected algorithm

Here is the fixed version in pseudocode and in Python. Run the Python with the test data above to check it.

After a fix, test again. A fix in one place can cause a new error somewhere else.

DECLARE Total : INTEGER
DECLARE Count : INTEGER
DECLARE Number : INTEGER
DECLARE Index : INTEGER
Total ← 0
Count ← 0
FOR Index ← 1 TO 10
  INPUT Number
  Total ← Total + Number
  IF Number > 50
    THEN
      Count ← Count + 1
  ENDIF
NEXT Index
OUTPUT "Average: ", Total / 10
OUTPUT "Numbers over 50: ", Count

total = 0
count = 0
for index in range(10):
    number = int(input())
    total = total + number
    if number > 50:
        count = count + 1
print("Average:", total / 10)
print("Numbers over 50:", count)