Trace tables and the debugging loop

Systematic debugging — a loop, not a hunt:

1. Reproduce on the smallest failing input. A bug you can't shrink, you can't fix.
2. Classify: compile / runtime / logical (Module 16.1).
3. Trace state: walk the code by hand writing every variable's value on every line — a trace table. The row where reality diverges from intention is the bug.
4. Assert mid-way: print or check intermediate values ("at this point, sum should be 6").
5. Fix the cause, not the symptom: if a loop is off-by-one, change the bound — don't add a special case downstream.

Trace-table example — the divergence is line 4:

| line | i | sum | want | | ----------- | - | --- | ------ | | sum = 0 | – | 0 | 0 | | sum += i | 1 | 1 | 1 | | sum += i | 2 | 3 | 3 | | sum += i | 3 | 6 | 9? (goal: sum of 1..3 = 6) |

When your hand-trace of the intended algorithm disagrees with what the code computes, you've found the exact line to change.