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Paint by Letters

USACO · 2021 · January · platinum-3

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prefix-sums · graph-algorithms · trees · data-structures

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

sample trace

Paint by Letters: prefix sums walkthrough

Paint by Letters: use the linked editorial?s prefix sums, graph algorithms idea on the published sample, then verify the displayed output.

Published input4 8 9 ABBAAAAA ABAAAABA CAADABBA AAAAAAAA 1 1 4 8 3 5 3 8 1 3 2 4 1 4 2 5 1 1 3 3 4 4 4 4 2 6 4 8 3 5 4 6 1 6 3 8modelAlgorithm ideaStore cumulative aggregates so a range can be answered from two prefix values instead of rescanning its elements.task resultExpected output6 3 2 1 4 1 3 2 2
  1. 1

    Accumulate

    Build the running total or count across the input order.
  2. 2

    Query

    Subtract the prefix before a range from the prefix at its end.
  3. 3

    Finish

    Apply the task?s boundary adjustment and compare with the sample result.
  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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