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Minimum Sum of Maximums

USACO · 2024 · February · platinum-2

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dynamic-programming · sorting

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

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Minimum Sum of Maximums: dynamic programming walkthrough

Minimum Sum of Maximums: use the linked editorial?s dynamic programming, sorting idea on the published sample, then verify the displayed output.

Published input3 0 1 100 10 3 1 1 100 10 3 3 1 1 100 10 2 4 2 1 3 2 4 2 3modelAlgorithm ideaTrack smaller states that summarize partial solutions. For each state, combine the legal predecessor states; the full-task state gives the result.task resultExpected output110 110 200 9
  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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