Trace tables and finding errors in algorithms

Filling in a trace table

• Give each variable its own column, plus one column for output.
• Work through the algorithm one line at a time, exactly as written, not as you think it was meant to work.
• Write a variable’s new value in its column whenever it changes, moving down a row as the algorithm moves on, usually each time round a loop.
• Only write in a column when that value changes. Leave the other cells empty.
• Write down every OUTPUT, in the order it happens.

Working out what an algorithm does

After a trace, describe the purpose in terms of the problem, not the code. “It outputs the largest of the numbers entered” earns more than “it compares Number with Max”. Look for the standard patterns: a total, a count, a maximum, a search.

Finding and fixing errors

Questions often give an algorithm with a few errors and ask you to find and correct them. Trace it with simple data and compare what happens with what should happen. The usual errors are:

• a variable not set to its starting value, or set inside the loop instead of before it;
• the wrong comparison, such as > instead of >=, or < instead of >;
• a loop that runs one time too many or too few;
• the wrong variable being updated or output;
• something done inside the loop that belongs after it.