32 lines
1.4 KiB
Markdown
32 lines
1.4 KiB
Markdown
---
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id: dsu
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title: "Disjoint Set Union"
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author: Benjamin Qi, Michael Cao
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prerequisites:
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- Silver - Depth First Search
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description: The Disjoint Set Union (DSU) data structure allows you to add edges to an initially empty graph and test whether two vertices of the graph are connected.
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---
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## Tutorial
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- CPH 15.2
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- [PAPS 11.1](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
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- Chapter 10.6 of "An Introduction to the US Computing Olympiad"
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- [CSAcademy Disjoint-Set](https://csacademy.com/lesson/disjoint_data_sets)
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- [Topcoder Union Find](https://www.topcoder.com/community/data-science/data-science-tutorials/disjoint-set-data-structures/)
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- [CPC.3](https://github.com/SuprDewd/T-414-AFLV/tree/master/03_data_structures)
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- DSU Complexity Proofs (optional of course)
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- [log\*n](https://en.wikipedia.org/wiki/Proof_of_O(log*n)\_time_complexity\_of_union%E2%80%93find)
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- [a(m,n)](https://dl.acm.org/doi/pdf/10.1145/321879.321884)
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with rollback: https://codeforces.com/contest/1140/problem/F
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## Problems
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- [Mootube](http://www.usaco.org/index.php?page=viewproblem2&cpid=789)
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- same as [CSES Road Construction](https://cses.fi/problemset/task/1676)
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- [Closing the Farm](http://www.usaco.org/index.php?page=viewproblem2&cpid=646)
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- [CSES Network Breakdown](https://cses.fi/problemset/task/1677)
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- [Favorite Colors](http://www.usaco.org/index.php?page=viewproblem2&cpid=1042)
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- fairly tricky
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