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# Matching & Flow | ||
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## HopcroftKarp | ||
### Description | ||
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An $O(|E| \sqrt{|V|})$ bipartite matching algorithm. | ||
Basically a low constant Dinic's algorithm. | ||
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Number of matching saved in `ans`, and the corresponding matching saved in `l` and `r`. | ||
Not sure about what `a` and `p` does. | ||
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### Test Status | ||
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Tested on [Library Checker](https://judge.yosupo.jp/submission/164965) | ||
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## Dijkstra Cost Flow | ||
### Description | ||
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Successive Shortest Path Algorithm using Dijkstra's algorithm. | ||
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### Test Status | ||
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Tested on [ARC122 F](https://atcoder.jp/contests/arc122/submissions/44122501) | ||
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## Dinic | ||
### Description | ||
### Test Status | ||
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## Flow Models | ||
### Description | ||
### Test Status | ||
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## General Graph Matching | ||
### Description | ||
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Blossom Algorithm runs in $O(EV^2)$. Not sure about the complexity of ours. | ||
Can solve $|V|=500$ testcases though. | ||
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### Test Status | ||
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Tested on [Library Checker](https://judge.yosupo.jp/submission/69588) | ||
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## Global Min-Cut | ||
### Description | ||
### Test Status | ||
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## GomoryHu Tree | ||
### Description | ||
### Test Status | ||
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## Kuhn Munkres | ||
### Description | ||
### Test Status | ||
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## Minimum Cost Circulation | ||
### Description | ||
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Network simplex method. Exponential time complexity, but it runs not too slow in practice. | ||
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### Test Status | ||
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Tested on [UOJ #487](https://uoj.ac/submission/658107). | ||
**Cannot** pass [QOJ 7185](https://qoj.ac/contest/1356/problem/7185) | ||
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## Minimum Cost Max Flow | ||
### Description | ||
### Test Status | ||
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## Weighted Matching | ||
### Description | ||
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Blossom Algorithm runs in $O(EV^2)$. Not sure about the complexity of ours. | ||
Can solve $|V|=500$ testcases though. | ||
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### Test Status | ||
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Tested on [Library Checker](https://judge.yosupo.jp/submission/160271) |
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