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All Pairs Similarity

USACO · 2024 · December · platinum-1

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combinatorics

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

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All Pairs Similarity: combinatorics walkthrough

All Pairs Similarity: use the linked editorial?s combinatorics idea on the published sample, then verify the displayed output.

Published input4 2 1 1 2 3modelAlgorithm ideaCount the valid arrangements by splitting them into disjoint cases or independent choices.task resultExpected output500000006 500000006 500000005 500000006
  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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