The Climb: Brute → Better → Best

Consider a problem where the ladder is explicit. The professional workflow is not "think about the full solution." It is a climb:

Rung 1 — the brute (minutes 0–15). Implement the most obviously correct thing the subtask-1 constraints allow. Test it on the samples by hand. This is not wasted time: it is your oracle for the rest of the problem. When your clever solution disagrees with it on a random case, you have found a bug before the judge did.

Rung 2 — the improvement (as time allows). Find the bottleneck of the brute — usually a repeated scan — and kill it with the cheapest tool that works: prefix sums, sorting, a set, a sweep. Do not reach for the heavy machinery (segment trees, HLD) while a light tool suffices; every extra moving part is a bug surface.

Rung 3 — the full solution. Only now the intended complexity. And the climb has a safety property: if rung 3 never compiles, rung 1 already banked points.

The failure mode of skipping rungs

The classic HSG disaster: attack the full solution first, get it 90% right, have a subtle bug, and score zero — while a classmate with a 15-minute brute scored the same subtask. The judge does not award style points. The ladder exists precisely so that partial effort converts to partial score.

What the judge sees

Each subtask is typically all-or-nothing per test group: one test in the group fails, the whole group scores zero. That is why this module's verification is brutal on purpose: your brute must pass every small test, your full solution every test, and the greedy shortcut that "seems right" must demonstrably fail its big test — so you learn what all-or-nothing feels like before the contest, not during it.