Trace or reason?

When to trace, when to reason. Full tracing is expensive; the advanced move is selective execution:

• State-heavy code (objects mutated across many calls): trace it — build a table, one row per call.
• Loop-plus-accumulator code: name the invariant instead. What is true after k iterations? If you can state it, you can answer without simulating every index.
• Reference-heavy code: draw the boxes and arrows once. Aliasing questions are cheap if you draw, expensive if you re-derive.

And the two cheap wins on every exam:

• Eliminate impossible answers before computing: negative lengths, indexes that cannot exist, a String result from an int method.
• Sanity-check extremes: does your reading still hold when the list is empty or has one element? If not, your reading is wrong.