2020-06-22 14:26:06 +00:00
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---
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2020-06-25 15:52:19 +00:00
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id: max-flow
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2020-06-22 14:26:06 +00:00
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title: "Maximum Flow"
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author: Benjamin Qi
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prerequisites:
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2020-06-22 20:51:12 +00:00
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- Gold - Breadth First Search
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2020-06-22 14:26:06 +00:00
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description: Introduces maximum flow as well as flow with lower bounds.
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2020-06-26 18:00:32 +00:00
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frequency: 1
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2020-06-22 14:26:06 +00:00
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---
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Has not been the solution to any platinum problem, but appeared in old gold.
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2020-06-28 02:11:09 +00:00
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- [Fast Flow](http://www.spoj.com/problems/FASTFLOW/) [](107)
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- [YS - Bipartite Matching](https://judge.yosupo.jp/problem/bipartitematching)
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2020-06-22 14:26:06 +00:00
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## Maximum Flow
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- [CSES Download Speed](https://cses.fi/problemset/task/1694)
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### Tutorial
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- [CPC.10](https://github.com/SuprDewd/T-414-AFLV/tree/master/10_graphs_3_network_flow)
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- CPH (20, Flows & Cuts)
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- Topics
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- Bipartite Matching?
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- Edmonds-Karp Algorithm
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- Min-Cut Max-Flow Theorem
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- [Closure Problem](https://en.wikipedia.org/wiki/Closure_problem)
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2020-06-28 02:11:09 +00:00
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## Bipartite Matching
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- [School Dance](https://cses.fi/problemset/task/1696)
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- matching
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Old Gold - Cow Steepchase http://www.usaco.org/index.php?page=viewproblem2&cpid=93
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## Min-Cut Max Flow
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- [Coin Grid](https://cses.fi/problemset/task/1709)
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Dilworth stuff
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https://maps20.kattis.com/problems/thewrathofkahn
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### Dinic's Algorithm
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* Hopcroft-Karp Bipartite Matching?
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<optional-content 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-content>
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### Problems
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- [CSES Distinct Routes](https://cses.fi/problemset/task/1711)
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- [Goods Transportation](http://codeforces.com/problemset/problem/724/E) [](52)
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- [ARC 85 MUL](http://arc085.contest.atcoder.jp/tasks/arc085_c) [](67)
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- [Fashion](https://csacademy.com/contest/rmi-2017-day-1/task/fashion/statement/) [](95)
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- [Card Game](http://codeforces.com/problemset/problem/808/F) [](135)
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## Flow with Lower Bounds
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2020-06-26 21:12:04 +00:00
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### Tutorial
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- [CMU Slides](https://www.cs.cmu.edu/~ckingsf/bioinfo-lectures/flowext.pdf)
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2020-06-26 21:12:04 +00:00
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### Problems
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- [Diverse Singing](https://codeforces.com/group/ZFgXbZSjvp/contest/274398/problem/C)
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- [Captain America](https://codeforces.com/contest/704/problem/D)
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- [Incorrect Flow](https://codeforces.com/contest/708/problem/D)
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- [Multi-Path Story](https://atcoder.jp/contests/jag2013summer-day4/tasks/icpc2013summer_day4_i)
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- [WAC 4 - Hungry Squirrels](https://dmoj.ca/problem/wac4p6)
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