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The Best Subsequence

USACO · 2025 · February · gold-2

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greedy · binary-search · prefix-sums · sorting

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

sample trace

The Best Subsequence: greedy walkthrough

The Best Subsequence: use the linked editorial?s greedy, binary search idea on the published sample, then verify the displayed output.

Published input5 3 9 1 5 2 4 3 3 1 5 5 1 5 4 1 5 3 1 5 2 1 5 1 2 5 4 2 5 3 2 5 2 2 5 1 9 1 1 7 9 1 8 8 30 1 1 1 30 1 30 30modelAlgorithm ideaProcess choices in the order justified by the editorial and maintain the invariant that each accepted choice remains safe.task resultExpected output21 13 7 3 1 5 5 3 1 3 73741816
  1. 1

    Order

    Arrange candidates by the criterion used by the task?s greedy strategy.
  2. 2

    Choose

    Accept the next locally safe option while preserving the feasibility invariant.
  3. 3

    Finish

    Read the accumulated result and check it against the 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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