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Minimum Cost Paths

USACO · 2021 · January · platinum-2

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binary-search

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Minimum Cost Paths: binary search walkthrough

Minimum Cost Paths: use the linked editorial?s binary search idea on the published sample, then verify the displayed output.

Published input5 4 1 100 100 20 20 1 1 2 1 3 1 4 1 5 1 1 2 2 2 3 2 4 2 5 2 1 3 2 3 3 3 4 3 5 3 1 4 2 4 3 4 4 4 5 4modelAlgorithm ideaSearch a monotone boundary by repeatedly testing a midpoint with the editorial?s feasibility condition.task resultExpected output0 1 2 3 4 1 5 11 19 29 2 9 20 35 54 3 13 29 49 69
  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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