Skip to content
This repository

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP

Left-leaning red-black trees

branch: master

Fetching latest commit…

Cannot retrieve the latest commit at this time

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

----------------------------------------------------------------
* 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

----------------------------------------------------------------
* 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/
	????


Something went wrong with that request. Please try again.