usaco.org/index.php?page=viewproblem2&cpid=…, cpids 591–602).
Round metadata
| Contest | USACO 2016 January |
|---|---|
| Window | Roughly Jan 22–25, 2016 (4-day window, single 4-hour personal timer) |
| Length per division | 4 hours (Dec/Jan/Feb format; US Open is the 5-hour round) |
| Problems per division | 3 |
| Total problems | 12 (Bronze 1–3, Silver 1–3, Gold 1–3, Platinum 1–3) |
| Scoring | IOI-style partial credit, 1000 points per problem, 3000 max per division |
| Allowed languages | C, C++11, Java, Pascal, Python 2.7, Python 3 (C++ is the default for serious climbers) |
| Promotion cutoffs | Set per-contest by USACO; check the results page for exact thresholds. |
The contest at a glance
Bronze · 3 problems
1. Promotion Counting — from per-division before/after head counts, recover the number of promotions across each adjacent boundary (linear algebra of conservation).
2. Angry Cows — pick one bale on a number line so the expanding-radius chain reaction detonates as many bales as possible (simulate from each).
3. Mowing the Field — given an NSEW path, find the maximum regrowth time T such that no cell is revisited within T (track first-visit time per cell).
Silver · 3 problems
1. Angry Cows — with K cows of equal radius R, find the minimum R so K well-placed shots cover all bales (binary search + greedy).
2. Subsequences Summing to Sevens — longest contiguous subarray whose sum ≡ 0 (mod 7) (prefix sums + first-occurrence table).
3. Build Gates — number of regions the fence path partitions the plane into (Euler's formula on the path graph).
Gold · 3 problems
1. Angry Cows — chain-reaction version: one shot at power R triggers radius-(R−1) blasts, etc. Minimum R such that one placement detonates all (two-pointer + DP).
2. Radio Contact — FJ and Bessie walk fixed paths; at each tick each may step or wait. Minimise Σ squared distance (2D DP on path indices).
3. Lights Out — rectilinear polygon; Bessie must reach vertex 1 in the dark using only turn directions to localise. Find the worst-case extra distance (KMP-like matching on signed-turn string).
Platinum · 3 problems
1. Fort Moo — largest axis-aligned rectangle in an N×M grid whose border (one-meter frame) avoids all 'X' cells (per-row maximal runs + sweep on top row pairs).
2. Mowing the Field — Platinum version: count perpendicular crossings between segments separated by ≥ T mowing days (offline BIT on coordinate-compressed events).
3. Lights Out — Platinum version of Gold P3 with N up to 200 vertices and tighter optimality requirements (full O(N²) signal-disambiguation DP).
How to use this set
- Pick your division. Open the full division page and read the three statements before writing any code.
- Solve P1 first, P2 if time, P3 only if you're cruising. January 2016 problem 1s are usually the cheapest points.
- Time-box. 4 hours total. Don't spend more than ~90 minutes on a single problem without a working subtask submission.
- Compare to the reference C++. Each problem on the division page has a ~30–50 line reference solution. If yours is much longer, ask why.
- Verify with the editorial. Official editorials are linked from each problem page on usaco.org.