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DFS Order

USACO · 2025 · January · platinum-1

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prefix-sums · graph-algorithms · trees

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

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DFS Order: prefix sums walkthrough

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

Published input4 1 2 3 40 6 11 5 -1 10 -2 10 -7 10 -6 -4 -5 10 4 -1 -2 300 4 -5 6modelAlgorithm ideaStore cumulative aggregates so a range can be answered from two prefix values instead of rescanning its elements.task resultExpected output10 5 9
  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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