Problems Without Labels

Problems Without Labels

Real contest problems do not announce their topics. This module's sets are built that way on purpose: the statement gives what is asked, the constraints give how fast, and the samples give shape. Naming the tool is your job, and it is worth doing before coding — a wrong family costs the whole implementation.

The classification protocol

For each problem, in order:

1. Constraints first. n ≤ 20 screams enumeration; n ≤ 2·10⁵ demands O(n log n); values ≤ 1000 hint at counting tricks.
2. Query shape second. Point updates with range queries = tree structure. Offline-able queries = sort by something. All queries known up front = think offline.
3. Sample arithmetic third. Trace the sample; the trace usually exposes the invariant.

The sets

• Set A (advanced) — five problems, one per family you already own.
• Set B (hard) — five problems, each needing one non-obvious observation.
• Set C (very hard) — five problems, each fusing two ideas.
• Checkpoint set — five problems in contest order (easy → hard), the HSG-challenge tier.

After each set, grade yourself honestly: which problems did you name within two minutes? Those are the ones the two-minute rule from the clock lesson protects. The others go on your weakness list with the topic you should have seen.