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Painting Fence Posts

USACO · 2024 · US Open · silver-2

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binary-search · prefix-sums · sorting

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

sample trace

Painting Fence Posts: binary search walkthrough

Painting Fence Posts: use the linked editorial?s binary search, prefix sums idea on the published sample, then verify the displayed output.

Published input5 4 3 1 1 5 3 5 1 1 2 1 1 5 1 5 3 4 3 1 3 5 2 1 2 1 3 2 3 3 2 8 1 1 1 2 0 2 0 3 0 0 0 1 2 3 2 0 1 1 2 1 1 0 1 3 1 12 0 0 2 0 2 1 1 1 1 2 3 2 3 3 1 3 1 4 2 4 2 5 0 5 2 2 0 2modelAlgorithm ideaSearch a monotone boundary by repeatedly testing a midpoint with the editorial?s feasibility condition.task resultExpected output1 2 2 1 1 0 0 0 1 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0
  1. 1

    Range

    Set the candidate interval for the quantity the task asks to minimize or maximize.
  2. 2

    Test

    Evaluate the task?s feasibility condition at the midpoint.
  3. 3

    Narrow

    Keep the half containing the true boundary until the answer is determined.
  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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