93 lines
3.7 KiB
Text
93 lines
3.7 KiB
Text
---
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id: LCT
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title: "Link Cut Tree"
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author: Benjamin Qi
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description: "?"
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prerequisites:
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- Advanced - Treaps
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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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lctSam: [
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new Problem("YS", "Vertex Add Path Sum", "dynamic_tree_vertex_add_path_sum", "Normal", false, ["LCT"], ""),
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],
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lct: [
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new Problem("SPOJ", "Dynamic Connectivity", "DYNACON1", "Intro", false, ["LCT"], "technically, LCT isn't needed because the queries are offline"),
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new Problem("CF", "Silence's Sounds", "contest/1109/problem/F", "Easy", false, ["LCT"], "test connectivity"),
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new Problem("YS", "Vertex Add Path Composite", "dynamic_tree_vertex_set_path_composite", "Normal", false, ["LCT"], ""),
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new Problem("SPOJ", "Dynamic LCA", "DYNALCA", "Normal", false, ["LCT"], ""),
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new Problem("DMOJ", "Squirrel Cities", "wac4p7", "Normal", false, ["LCT"], "link, cut, min edge along path"),
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new Problem("HR", "Balanced Tokens", "https://www.hackerrank.com/contests/pwshpc-online-round/challenges/pwsh-tokens/problem", "Normal", false, ["LCT"], ""),
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new Problem("CSES", "CEOI - Treasure Hunt", "https://cses.fi/174/list/", "Normal", false, ["LCT"], ""),
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new Problem("DMOJ", "Dynamic Tree Test (Easy)", "ds5easy", "Hard", false, ["LCT"], ""),
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new Problem("CF", "Train Tracking", "contest/1344/problem/E", "Hard", false, ["LCT"], "* switching can be done with LCT access, set min on path with lazy prop * [Solution](https://codeforces.com/contest/1344/submission/79212522)"),
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new Problem("CF", "Tree or not Tree", "contest/117/problem/E", "Hard", false, ["LCT"], "tree + one edge"),
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new Problem("CF", "CERC 17 D", "gym/101620", "Hard", false, ["LCT"], "LCT not needed, but can directly apply solution from The Applicant"),
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new Problem("ojuz", "IOI - Dancing Elephants", "IOI11_elephants", "Hard", false, [], ""),
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],
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subSam: [
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new Problem("YS", "Vertex Add Subtree Sum", "dynamic_tree_vertex_add_subtree_sum", "Normal", false, ["LCT"], ""),
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],
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sub: [
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new Problem("CF", "Pastoral Oddities", "contest/603/problem/E", "Normal", false, ["LCT"], ""),
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new Problem("YS", "Subtree Add Subtree Sum", "dynamic_tree_subtree_add_subtree_sum", "Hard", false, ["LCT"], ""),
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new Problem("CF", "Old Driver Tree", "contest/1172/problem/E", "Hard", false, ["LCT"], ""),
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new Problem("DMOJ", "Dynamic Tree Test", "ds5", "Very Hard", false, ["LCT"], ""),
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]
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}
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};
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## Splay Tree
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### Tutorial
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- [Splay Tree Paper](https://www.cs.cmu.edu/~sleator/papers/self-adjusting.pdf)
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- [Stanford Presentation](https://web.stanford.edu/class/archive/cs/cs166/cs166.1146/lectures/08/Slides08.pdf)
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(Implementation?)
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- [Euler Tour Tree](https://codeforces.com/blog/entry/18369)
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## Link Cut Tree - Paths
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<problems-list problems={metadata.problems.lctSam} />
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### Tutorial
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- [MIT](http://courses.csail.mit.edu/6.851/spring12/scribe/L19.pdf)
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- [CTSC 2014 Translation](https://www.overleaf.com/read/zbbwngftkrkx?fbclid=IwAR1VJmGscfSZJHejVqU5_2Nlm8-R09pFlU7PpEg_i3CXEd0Qw-dzliSn5RI)
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(Implementation?)
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### Problems
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<problems-list problems={metadata.problems.lct} />
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### USACO Camp
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(Maybe add descriptions since problems not publicly viewable.)
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* [The Applicant](https://probgate.org/viewproblem.php?pid=578)
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* tree + one edge
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* [Cows Play on a Tree](https://probgate.org/viewproblem.php?pid=259)
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* reverse tree paths
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* HLD + Treap
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* or two LCTs, one for real tree labels and one for query labels
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## Link Cut Tree - Subtrees
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<problems-list problems={metadata.problems.subSam} />
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### Tutorial
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- [CF](https://codeforces.com/blog/entry/67637)
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### Problems
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<problems-list problems={metadata.problems.sub} />
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