Link Cut Tree #124
Link Cut Tree #124
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Also, this LCT doesn't fix #117. It would need the changes from https://codeforces.com/blog/entry/67637 or the Chinese blog. |
| * Current implementation supports update value at a node, | ||
| * and query max on a path. | ||
| * Tested on: http://acm.timus.ru/problem.aspx?num=1553 | ||
| * Status: Passes existing fuzz tests (with function names modified). |
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We'll want to remove the old link-cut tree, so feel free to do that and modify the fuzz-test. Will also need to update the test to verify that max works (with max replaced by some non-commutative, non-associative function)
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Updated the fuzz-test to verify max for now. Will update it later for any new function that we decide on...
content/graph/LCT.h
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| if(c[1]) c[1]->flip ^= 1; | ||
| swap(c[0], c[1]); flip = 0; | ||
| } | ||
| // add stuff |
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remove this comment as well -- I think we can instead write in the description how to augment it ("extend push/pull").
We'll also want a more thorough explanation and/or example -- it's not clear to me in which ways the LCT is similar to a segment tree. E.g. how do I do lazy updates on entire paths in the tree? Entire subtrees? Queries on subtrees? Can I use the flip bit myself for anything? How are things ordered? It's not reasonable to answer all of these questions (we should have a link in the description!), but some more info would be useful.
content/graph/LCT.h
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| cval = val; | ||
| if(c[0]) c[0]->push(), cval = max(cval, c[0]->cval); | ||
| if(c[1]) c[1]->push(), cval = max(cval, c[1]->cval); | ||
| // add stuff |
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Does this work with non-commutative and non-associative operations?
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We've talked about this elsewhere, but it should work for non-commutative, associative functions (like a segment tree).
content/graph/LCT.h
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| if (z) z->pull(); | ||
| y->pull(); | ||
| } /// end-hash | ||
| void xiao() { |
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I agree that we should probably rename this
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"propogatePathParent" is a little much though... Will keep thinking about possible alternatives.
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could certainly shorten that to propPP if that's what we want to get across. But a nonsensical name would be fine as well
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Neat. I think the main thing I would want out of this is a more detailed view of how it can be augmented. We should try not to bloat it too much with unnecessary cruft, but right now it's hard for me to understand how to augment it with non-trivial custom stuff. I wouldn't worry too much about point 4 if it's hard to figure out, keeping it simple is good. And I don't think mixing . and -> is a problem. |
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I forgot to push my most recent changes before making the PR. It's pushed now. |
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@PotatoHashing would you still like to finish this PR? I want to get a LCT implementation - perhaps ideally this one. Alternately, I could take over for this PR if you're busy. |
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We discussed this on Discord but I should probably repeat it here. Feel free to take this over @Chillee (or anyone else interested). |
This PR is about updating the Link Cut Tree. Most of it is from MIT's LCT. This new version easily supports dynamic links and cuts, as well as queries and updates on paths (like HLD). The code has been separated so that the functions in the Node struct will change the structure of the LCT (access, splay, rotate, etc) and the functions under LinkCut will call those under Node to perform queries and updates about the tree. Alternatively, the functions under LinkCut are meant to be called by a user directly (e.g. in main) while the functions in Node aren't.
The key points are:
The current code shows an example on how to update a point on a path and query for max on a path. (It basically solves http://acm.timus.ru/problem.aspx?num=1553).
Some current possible issues.
Future work.
There's this blog on applications on LCT. It might be useful to include parts of that. Unfortunately, I can't read Chinese, so I'm leaving this incomplete for now.
https://www.cnblogs.com/flashhu/p/8324551.html
I am open to questions and suggestions.