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Add source for tree reroot fold #67

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Feb 25, 2024
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Add source for tree reroot fold #67

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9 changes: 5 additions & 4 deletions src/RerootFold.hs
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Original file line number Diff line number Diff line change
Expand Up @@ -12,15 +12,16 @@ g :: b -> c -> b must be commutative, in the sense that
(b `g` c1) `g` c2 = (b `g` c2) `g` c1

Sources:
* Informal discussions. I am unable to find a good published source for this technique :(
* pajenegod, "The Ultimate Reroot Template"
https://codeforces.com/blog/entry/124286

Implementation notes:
* Thanks to Haskell's laziness it is possible to write a more concise implementation with a single
dfs, but this seems to be slower in practice. Here is a possible implementation:
https://gist.github.com/meooow25/6460e45327355106cedbcf3bd5166cd6
* Reroot problems can often be solved in O(n) time, if there is a way to *take way* the contribution
of a node from an accumulated value. Avoiding this requirement, it takes O(n log n) but is far
simpler.
* Reroot problems can often be solved in O(n) time, if there is a way to *take away* the
contribution of a node from an accumulated value. Avoiding this requirement, it takes O(n log n)
but is far simpler.

foldReroot
Returns the same tree with each vertex accompanied by the fold of the tree if that vertex is made
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