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Uddered but not Herd

USACO · 2021 · January · gold-1

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dynamic-programming · combinatorics

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

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Uddered but not Herd: dynamic programming walkthrough

Uddered but not Herd: use the linked editorial?s dynamic programming, combinatorics idea on the published sample, then verify the displayed output.

Published inputmildredreemodelAlgorithm ideaTrack smaller states that summarize partial solutions. For each state, combine the legal predecessor states; the full-task state gives the result.task resultExpected output3
  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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