269:
29:
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291:, since 4-nodes are now prohibited. Sedgewick remarks that the implementations of LLRB 2–3 trees and LLRB 2–3–4 trees differ only in the position of a single line of code.
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All of the red-black tree algorithms that have been proposed are characterized by a worst-case search time bounded by a small constant multiple of
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Linus Ek, Ola
Holmström and Stevan Andjelkovic. May 19, 2009. Formalizing Arne Andersson trees and Left-leaning Red–Black trees in Agda
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keys, and the behavior observed in practice is typically that same multiple faster than the worst-case bound, close to the optimal
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The left-leaning property reduces the number of cases that must be considered when implementing search tree operations.
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If we impose the additional requirement that a node may not have two red children, LLRB trees become isomorphic to
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and guarantees the same asymptotic complexity for operations, but is designed to be easier to implement.
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284:. This means that for every LLRB tree, there is a unique corresponding 2–3–4 tree, and vice versa.
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from a given node to any of its descendant NIL nodes goes through the same number of black nodes.
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Julien Oster. March 22, 2011. An Agda implementation of deletion in Left-leaning Red–Black trees
280:. Unlike conventional red-black trees, the 3-nodes always lean left, making this relationship a
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A left-leaning red-black tree satisfies all the properties of a red-black tree:
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Kazu
Yamamoto. 2011.10.19. Purely Functional Left-Leaning Red–Black Trees
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nodes examined that would be observed in a perfectly balanced tree.
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Open Data
Structures - Section 9.2.2 - Left-Leaning Red–Black Trees
356:
The average size of left subtree exhibits log-oscillating behavior.
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Robert
Sedgewick. 20 Apr 2008. Animations of LLRB operations
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If a node has only one red child, it must be the left child.
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419:. Department of Computer Science, Princeton University.
250:
Additionally, the left-leaning property states that:
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328:random keys, Sedgewick's experiments suggest that:
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16:Self-balancing binary search tree data structure
466:Left-Leaning Red-Black Trees Considered Harmful
443:Robert Sedgewick. Left-Leaning Red–Black Trees
434:Robert Sedgewick. Left-leaning Red–Black Trees
272:Isomorphism between LLRB trees and 2–3–4 trees
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320:Specifically, in a left-leaning red-black
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236:A red node does not have a red child.
7:
1074:Algorithms and data structures stubs
1000:
998:
332:A random successful search examines
1022:. You can help Knowledge (XXG) by
246:The root is black (by convention).
230:Every node is either red or black.
14:
346:The average tree height is about
208:self-balancing binary search tree
1002:
264:Relation to 2–3 and 2–3–4 trees
233:A NIL node is considered black.
410:"Left-Leaning Red–Black Trees"
1:
417:Left-Leaning Red–Black Trees
370:implementation of LLRB from
22:Left-leaning red–black tree
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997:
408:Sedgewick, Robert (2008).
276:LLRB trees are isomorphic
214:. It is a variant of the
63:
26:
949:Left-child right-sibling
445:slides from October 2008
779:data partitioning trees
737:C-trie (compressed ADT)
255:
1018:-related article is a
273:
200:left-leaning red–black
282:1 to 1 correspondence
271:
959:Log-structured merge
502:Tree data structures
206:) tree is a type of
366:Robert Sedgewick's
924:Fractal tree index
519:associative arrays
438:Direct link to PDF
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212:Robert Sedgewick
210:, introduced by
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164:Space complexity
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58:Robert Sedgewick
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598:Order statistic
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69:Time complexity
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757:Ternary search
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428:External links
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372:his 2008 paper
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216:red–black tree
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73:big O notation
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934:Hash calendar
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709:van Emde Boas
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699:Skew binomial
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578:Binary search
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306:in a tree of
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1069:Search trees
1024:expanding it
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609:Left-leaning
608:
515:dynamic sets
510:Search trees
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361:Bibliography
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909:Exponential
897:Other trees
341:− 0.5
324:built from
278:2–3–4 trees
54:Invented by
1063:Categories
1012:algorithms
853:Priority R
603:Palindrome
392:References
222:Properties
88:Worst case
939:iDistance
818:implicit
806:Hilbert R
801:Cartesian
684:Fibonacci
618:Scapegoat
613:Red–black
386:Pat Morin
289:2–3 trees
79:Operation
954:Link/cut
666:Binomial
593:Interval
322:2–3 tree
295:Analysis
46:Invented
914:Fenwick
878:Segment
777:Spatial
694:Pairing
689:Leftist
611:)
583:Dancing
576:)
574:Optimal
83:Average
964:Merkle
929:Fusion
919:Finger
843:Octree
833:Metric
767:Y-fast
762:X-fast
752:Suffix
671:Brodal
661:Binary
343:nodes.
239:Every
153:O(log
144:O(log
140:Delete
130:O(log
121:O(log
117:Insert
107:O(log
98:O(log
94:Search
1010:This
974:Range
944:K-ary
904:Cover
747:Radix
732:Ctrie
724:Tries
653:Heaps
633:Treap
623:Splay
588:HTree
543:(a,b)
533:2–3–4
413:(PDF)
348:2 ln
170:Space
1020:stub
979:SPQR
858:Quad
786:Ball
742:Hash
714:Weak
704:Skew
679:-ary
368:Java
312:log
301:log
241:path
204:LLRB
49:2008
41:tree
37:Type
1014:or
984:Top
838:MVP
796:BSP
548:AVL
528:2–3
334:log
71:in
1065::
969:PQ
883:VP
873:R*
868:R+
848:PH
822:-d
814:-d
791:BK
638:UB
563:B*
558:B+
538:AA
436:.
415:.
400:^
384:,
198:A
183:O(
174:O(
1051:e
1044:t
1037:v
1026:.
888:X
863:R
828:M
824:)
820:k
816:(
812:k
677:d
628:T
607:(
572:(
568:B
553:B
521:)
517:/
513:(
494:e
487:t
480:v
447:.
440:.
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350:N
339:N
336:2
326:N
314:N
308:N
303:N
202:(
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185:n
178:)
176:n
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155:n
148:)
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134:)
132:n
125:)
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111:)
109:n
102:)
100:n
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