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https://github.com/kazu-yamamoto/llrbtree
Left-leaning red-black trees
https://github.com/kazu-yamamoto/llrbtree
Last synced: 17 days ago
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Left-leaning red-black trees
- Host: GitHub
- URL: https://github.com/kazu-yamamoto/llrbtree
- Owner: kazu-yamamoto
- License: bsd-3-clause
- Created: 2011-10-14T07:36:33.000Z (about 13 years ago)
- Default Branch: master
- Last Pushed: 2012-05-16T04:10:22.000Z (over 12 years ago)
- Last Synced: 2024-10-11T23:56:08.175Z (about 1 month ago)
- Language: Haskell
- Homepage:
- Size: 245 KB
- Stars: 48
- Watchers: 7
- Forks: 7
- Open Issues: 1
-
Metadata Files:
- Readme: README
- License: LICENSE
Awesome Lists containing this project
README
This is a purely functional left-leaning red-black tree.
Data.RBTree --- Okasaki's red-black trees
Data.RBTree.LL --- Left-leaning red-black trees
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* Histroy of imperative red-black trees
- Red-black trees (Guibas-Sedgewick, 1978)
Leo J. Guibas and Robert Sedgewik.
A dichromatic framework for balanced trees.
In Proceedings of the 19th Annual Symposium on Computer Science
pp8-21
IEEE Computer Society
1978
- Right-leaning
Arne Andersson
Balanced search trees made simple
In Proceedings of the 3rd Workshop on Algorithms and Data Structures
pp290-306.
1993
R. Sedgewick
Algorithms in Java
Parts 1-4: Fundamentals, Data Structures, Sorting, and Searching
Addison-Wesley.
- Left-leaning Red-Black Trees
Data structures seminar at Dagstuhl (Feb 2008)
http://www.cs.princeton.edu/~rs/talks/LLRB/LLRB.pdf
Analysis of Algorithms meeting at Maresias (Apr 2008)
http://www.cs.princeton.edu/~rs/talks/LLRB/RedBlack.pdf
http://algs4.cs.princeton.edu/32bst/
http://algs4.cs.princeton.edu/33balanced/RedBlackBST.java.html
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* Lines of imperative code:
- Introduction to Algorithms (original) 150 1972 (?)
- Algorithms in Java (tricky variant) 46 1978 (?)
- (left-leaning) 33 2008
----------------------------------------------------------------
* Histroy of purefly functional red-black trees
- Original
Red-Black Trees in a Functional Setting
Chris Okasaki
Journal of Functional Programming, 9(4)
pp471-477
July 1999
http://www.eecs.usma.edu/webs/people/okasaki/pubs.html#jfp99
- Dividing balance to balanceL and balanceR
Chris Okasaki
Purely Functional Data Structures
Cambridge University Press
1998
- First deletion
Kahrs, Stefan. (2001)
Red-black trees with types
Journal of functional programming, 11(04), 425–432.
- Proof in Coq
C. Filliâtre and P. Letouzey
Functors for Proofs and Programs
In Proceedings of The European Symposium on Programming
volume 2986 of Lecture Notes in Computer Science
pages 370-384, April 2004.
http://www.lri.fr/~filliatr/ftp/publis/fpp.ps.gz
Formalization of a finite sets library in Coq
http://www.lri.fr/~filliatr/fsets/
- Efficient Verified Red-Black Trees
Andrew W. Appel
Efficient Verified Red-Black Trees
September 2011
2011
http://www.cs.princeton.edu/~appel/papers/redblack.pdf
My student Max Rosmarin (Rosmarin, 2011) studied the question
of whether using the left-leaning invariant would mix well
with the Okasaki-style functional program, so as to factor the
implementations and proofs. Rosmarin demonstrated that Okasaki's
balance function can be factored into Sedgewick's three
operations. Although it is not conceptually more complex, the
factored function has more lines of code. Recall that Okasaki's
function, as I presented it here, has only 10 lines, which
is hard to improve on.
- Rosmarin, Max. 2011 (Aug.). Red-black trees in a functional context:
Left-leaning and otherwise.
Princeton University Department of Computer Science.
- The missing method: Deleting from Okasaki's red-black trees
http://matt.might.net/articles/red-black-delete/
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