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Paired Up

USACO · 2021 · December · gold-1

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dynamic-programming · binary-search

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

sample trace

Paired Up: dynamic programming walkthrough

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

Published input2 5 2 1 2 3 2 4 2 5 1 7 2 1 5 2 1 2 3 2 4 2 5 1 7 2 2 15 7 3 693 10 196 12 182 14 22 15 587 31 773 38 458 39 58 40 583 41 992 84 565 86 897 92 197 96 146 99 785modelAlgorithm 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 2 2470
  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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