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Farmer John's Favorite Permutation

USACO · 2024 · US Open · bronze-3

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combinatorics

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

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Farmer John's Favorite Permutation: combinatorics walkthrough

Farmer John's Favorite Permutation: use the linked editorial?s combinatorics idea on the published sample, then verify the displayed output.

Published input5 2 1 2 2 4 1 1 1 4 2 1 1 4 3 2 1modelAlgorithm ideaCount the valid arrangements by splitting them into disjoint cases or independent choices.task resultExpected output1 2 -1 -1 3 1 2 4 1 2 3 4
  1. 1

    Cases

    Partition the possible configurations so each valid outcome belongs to one case.
  2. 2

    Count

    Count each case using the independent choices identified by the task.
  3. 3

    Combine

    Sum the disjoint case counts and apply any required modulus or bound.
  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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