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Max Flow

USACO · 2015 · December · platinum-1

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binary-search · prefix-sums · graph-algorithms · trees · data-structures · simulation

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

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Max Flow: binary search walkthrough

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

Published input5 10 3 4 1 5 4 2 5 4 5 4 5 4 3 5 4 3 4 3 1 3 3 5 5 4 1 5 3 4modelAlgorithm ideaSearch a monotone boundary by repeatedly testing a midpoint with the editorial?s feasibility condition.task resultExpected output9
  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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