92 lines
2.4 KiB
Text
92 lines
2.4 KiB
Text
---
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id: max-flow
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title: "Maximum Flow"
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author: Benjamin Qi
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prerequisites:
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- bfs
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description: Introduces maximum flow as well as flow with lower bounds.
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frequency: 1
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---
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import { Problem } from "../models";
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export const metadata = {
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problems: {
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maxSam: [
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new Problem("CSES", "Download Speed", "1694", "Easy", false, ["Max Flow"], ""),
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],
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flow: [
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new Problem("CSES", "Distinct Routes", "1711", "Easy", false, ["Max Flow"], ""),
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],
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match: [
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new Problem("CSES", "School Dance", "1696", "Easy", false, ["Max Flow"], ""),
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new Problem("Old Gold", "Cow Steepchase", "93", "Easy", false, ["Max Flow"], ""),
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],
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dinic: [
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new Problem("SPOJ", "Fast Flow", "FASTFLOW", "Easy", false, [], ""),
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new Problem("YS", "Bipartite Matching", "bipartitematching", "Easy", false, [], ""),
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],
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minEx: [
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new Problem("CSES", "Coin Grid", "1709", "Easy", false, [], ""),
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],
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cut: [
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new Problem("CSA", "Fashion", "fashion", "Normal", false, [], ""),
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new Problem("CF", "Card Game", "problemset/problem/808/F", "Normal", false, [], ""),
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new Problem("CF", "Goods Transportation", "problemset/problem/724/E", "Hard", false, [], ""),
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new Problem("AC", "ARC E - MUL", "http://arc085.contest.atcoder.jp/tasks/arc085_c", "Hard", false, [], ""),
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]
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}
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};
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## Maximum Flow
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<Problems problems={metadata.problems.maxSam} />
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### Tutorial
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<Resources>
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<Resource source="CPC" title="10 - Network Flow" url="10_graphs_3_network_flow"> </Resource>
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<Resource source="CPH" title="20 - Flows & Cuts"> </Resource>
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</Resources>
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### Problems
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<Problems problems={metadata.problems.flow} />
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## Bipartite Matching
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<Problems problems={metadata.problems.match} />
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## Dinic's Algorithm
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<Problems problems={metadata.problems.dinic} />
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Hopcroft-Karp Bipartite Matching?
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<Optional title="Faster Flow">
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There exist faster flow algorithms such as **Push-Relabel**. Also see the following blog post:
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- [Chilli: Dinic's with Scaling](https://codeforces.com/blog/entry/66006)
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However, the standard implementation of Dinic's is (almost) always fast enough.
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</Optional>
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## Min-Cut Max Flow
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<Problems problems={metadata.problems.minEx} />
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(show equivalence)
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Konig's?
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- [Closure Problem](https://en.wikipedia.org/wiki/Closure_problem)?
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Dilworth stuff, antichains?
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https://maps20.kattis.com/problems/thewrathofkahn
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## Problems
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<Problems problems={metadata.problems.cut} />
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