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Moo Decomposition

USACO · 2025 · US Open · gold-1

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dynamic-programming · sorting · combinatorics

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

sample trace

Moo Decomposition: dynamic programming walkthrough

Moo Decomposition: use the linked editorial?s dynamic programming, sorting idea on the published sample, then verify the displayed output.

Published input2 6 1 MOOMOO 2 6 1 MMOOOO 1 4 2 MMOO 1 4 100 MMOOmodelAlgorithm ideaTrack smaller states that summarize partial solutions. For each state, combine the legal predecessor states; the full-task state gives the result.task resultExpected output1 6 4 976371285
  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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