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Watering the Plants

USACO · 2025 · January · platinum-3

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dynamic-programming

The organizer’s problem statement is available at the official source link.

sample trace

Watering the Plants: dynamic programming walkthrough

Watering the Plants: use the linked editorial?s dynamic programming idea on the published sample, then verify the displayed output.

Published input3 39 69 33 30 29 3 33 82 36 19 1 8 35 89 44 1 35 3 62 50 7 86 94 62 63 9 49modelAlgorithm ideaTrack smaller states that summarize partial solutions. For each state, combine the legal predecessor states; the full-task state gives the result.task resultExpected output2070 2127 1558 676 623 4099 4114 6269 6272 6827 8827
  1. 1

    State

    Choose a compact value for each partial subproblem so later choices need only that summary.
  2. 2

    Transition

    Combine legal smaller states to compute reachability, a count, or an optimum for the next state.
  3. 3

    Finish

    Read the state representing the full task and compare it with the published sample output.
  4. 4

    Verify the sample

    Use the published sample output to check the result of this idea on the displayed input.
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