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Nap Sort

USACO · 2024 · January · gold-3

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dynamic-programming · binary-search · sorting · two-pointers

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

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Nap Sort: dynamic programming walkthrough

Nap Sort: use the linked editorial?s dynamic programming, binary search idea on the published sample, then verify the displayed output.

Published input4 5 1 2 4 5 100000000000 5 17 53 4 33 44 4 3 5 5 5 6 2 5 100 1 4 5modelAlgorithm ideaTrack smaller states that summarize partial solutions. For each state, combine the legal predecessor states; the full-task state gives the result.task resultExpected output6 15 5 6
  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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