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Falling Portals

USACO · 2020 · January · platinum-3

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binary-search · graph-algorithms · sorting

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

sample trace

Falling Portals: binary search walkthrough

Falling Portals: use the linked editorial?s binary search, graph algorithms idea on the published sample, then verify the displayed output.

Published input4 3 5 10 2 3 3 2 1modelAlgorithm ideaSearch a monotone boundary by repeatedly testing a midpoint with the editorial?s feasibility condition.task resultExpected output7/2 7/2 5/1 -1
  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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