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Missing method: How to delete from Okasaki's red-black trees
Balanced-tree-based maps are a workhorse in functional programming. Because of their disarming simplicity, Chris Okasaki's purely functional red-black trees are a popular means for implementing such maps. In his book, self-balancing binary search trees are less than a page of code. Except that delete is left as an exercise to the reader. Unfortunately, deletion is tricky. Stefan Kahrs devised a wi
Purely Functional Left-Leaning Red-Black Trees
We show that the idea of left-leaning reduces one pattern matching in the insertion operation of Okasaki's purely functional red-black trees. We proved in Coq that the invariants of left-leaning red-black trees stand for our purely functional algorithm of the insertion operation. Our benchmark shows that our algorithm is slightly faster than Okasaki's algorithm in some cases. History In 1979, Guib
サービス終了ã®ãŠçŸ¥ã‚‰ã›
サービス終了ã®ãŠçŸ¥ã‚‰ã› ã„ã¤ã‚‚Yahoo! JAPANã®ã‚µãƒ¼ãƒ“スをã”利用ã„ãŸã ãèª ã«ã‚ã‚ŠãŒã¨ã†ã”ã–ã„ã¾ã™ã€‚ ãŠå®¢æ§˜ãŒã‚¢ã‚¯ã‚»ã‚¹ã•ã‚ŒãŸã‚µãƒ¼ãƒ“スã¯æœ¬æ—¥ã¾ã§ã«ã‚µãƒ¼ãƒ“スを終了ã„ãŸã—ã¾ã—ãŸã€‚ 今後ã¨ã‚‚Yahoo! JAPANã®ã‚µãƒ¼ãƒ“スをã”愛顧ãã ã•ã„ã¾ã™ã‚ˆã†ã€ã‚ˆã‚ã—ããŠé¡˜ã„ã„ãŸã—ã¾ã™ã€‚
Red-Black Tree by Java -- ã“ã‚Œã§åˆ†ã‹ã£ãŸèµ¤é»’木
ã“ã®ãƒšãƒ¼ã‚¸ã¯ã€ãƒžãƒƒãƒ—ã¨å‘¼ã°ã‚Œã‚‹ãƒ‡ãƒ¼ã‚¿æ§‹é€ ã®å®Ÿè£…ã®ï¼‘ã¤ã§ã‚る赤黒木 (２色木ã€red-black tree)ã«ã¤ã„ã¦è§£èª¬ã™ã‚‹ãƒšãƒ¼ã‚¸ã§ã™ã€‚赤黒木ã¯ã€è¦ç´ 㮠挿入・削除・検索ãªã©ã®æ“作㌠\(O(\log n)\) ã®è¨ˆç®—é‡ã§å®Ÿè¡Œå‡ºæ¥ã‚‹å¹³è¡¡æœ¨ ã§ã™(\(n\) ã¯è¦ç´ æ•°)。赤黒木ã¯ã‚„ã£ã¦ã„ã‚‹ã“ã¨ã¯å˜ç´”ãªã®ã§ã™ãŒã€ã¨ã«ã‹ã å ´åˆåˆ†ã‘ãŒãŸãã•ã‚“ã‚ã£ã¦ã€ç¿’å¾—ã—よã†ã¨ã—ãªãŒã‚‰ã‚‚ãã˜ã‘ã¦ã—ã¾ã£ãŸäººã‚‚ 多ã„ã®ã§ã¯ãªã„ã§ã—ょã†ã‹ï¼Ÿ ã—ã‹ã—ã€ã”安心ãã ã•ã„。ã“ã®ãƒšãƒ¼ã‚¸ã¯å ´åˆåˆ†ã‘を出æ¥ã‚‹ã ã‘減らã—〠挿入æ“作ã§ï¼”パターンã€å‰Šé™¤æ“作ã§ï¼˜ãƒ‘ターンã•ãˆç†è§£ã™ã‚Œã°èµ¤é»’木ãŒåˆ†ã‹ã‚‹ よã†ã«æ›¸ã‹ã‚Œã¦ã„ã¾ã™ã€‚削除æ“作ã«é–¢ã—ã¦ã¯ã€å·¦å³å¯¾ç§°ã®ãƒ‘ターンをçœã‘㰠４パターンç†è§£ã™ã‚Œã°ãŠãŠã‚€ã OK ã§ã™ã€‚ã“ã‚Œã‹ã‚‰èµ¤é»’木を勉強ã—よã†ã¨ã„ã†äºº ã¯ã‚‚ã¡ã‚ã‚“ã€ä¸€åº¦ã¯å‹‰å¼·ã—ãŸãŒæŒ«æŠ˜ã—ã¦ã—ã¾ã£ãŸã¨ã„ã†äººã‚‚是éžã¨ã‚‚èªã‚“ã§ã¿ã¦ ãã ã•ã„。 ã€æº–備】 ã¾
Common Lispã§èµ¤é»’木 - 壊れãŸè¨ˆç®—æ©Ÿ
Haskellã§ã®èµ¤é»’木ã®å®Ÿè£…ã®ç¾Žã—ã•ã«æ„Ÿå‹•ã—㟠data Color = R | B data RedBlackSet a = E | T Color (RedBlackSet a) a (RedBlackSet a) balance B (T R (T R a x b) y c) z d = T R (T B a x b) y (T B c z d) balance B (T R a x (T R b y c)) z d = T R (T B a x b) y (T B c z d) balance B a x (T R (T R b y c) z d) = T R (T B a x b) y (T B c z d) balance B a x (T R b y (T R c z d)) = T R (T B a x b) y (T B c z d) balance color a x
optima - 高速パターンマッãƒãƒ©ã‚¤ãƒ–ラリ - Qiita
開発ãŒæˆç†Ÿã—ã¦ããŸã®ã§ã€ã“ã“らã§æ‹™ä½œã®ãƒ‘ターンマッãƒãƒ©ã‚¤ãƒ–ラリã€optimaを日本語ã§è§£èª¬ã—ãŸã„ã¨æ€ã†ã€‚ãŸã ã—解説ã¨ã¯è¨€ã£ã¦ã‚‚ã€è©³ç´°ãªä»•æ§˜ã‚’ã らã らã¨è§£èª¬ã™ã‚‹ã‚ˆã†ãªã“ã¨ã¯ã—ãªã„。むã—ã‚「ãªãœãƒ‘ターンマッãƒãªã®ã‹ã€ã‚’è¸ã¾ãˆãŸä¸Šã§ã€ç°¡å˜ãªå…¥é–€ã¨ä½¿ç”¨ä¾‹ã‚’示ã™ã“ã¨ã§ã€ãƒ‘ターンマッãƒã®é‡è¦æ€§ã‚’èªè˜ã—ã¦ã‚‚らã†ã®ãŒç‹™ã„ã 。ãªãŠã€è©³ç´°ãªä»•æ§˜ã«ã¤ã„ã¦ã¯ãƒžãƒ‹ãƒ¥ã‚¢ãƒ«ã‚’å‚ç…§ã•ã‚ŒãŸã„。 ãªãœãƒ‘ターンマッãƒãªã®ã‹ Common Lispã«ã¯ãƒ‘ターンマッãƒãƒ©ã‚¤ãƒ–ラリãŒå¤šæ•°å˜åœ¨ã™ã‚‹ãŒã€ãã®å¤§åŠã¯å˜ã«ãƒ‘ターンマッãƒãŒä¾¿åˆ©ã ã‹ã‚‰ã¨ã„ã†è¦–点ã—ã‹æŒã£ã¦ã„ãªã„。ãŸã—ã‹ã«ãƒ‘ターンマッãƒã¯ä¾¿åˆ©ã§ã‚ã‚‹ãŒã€ä¾¿åˆ©ãªã ã‘ã§ã¯äººã€…ã¯ãれを使ãŠã†ã¨ã¯ã—ãªã„。より本質的ãªè¦–点を与ãˆã‚‹å¿…è¦ãŒã‚ã‚‹ã ã‚ã†ã€‚ OCamlã‚„Haskellãªã©ã®é–¢æ•°åž‹è¨€èªžã§ã¯ã€ã‚らゆるデータã¯ã€ä»£æ•°çš„データ型ã¨ã—ã¦å®šç¾©ã•ã‚Œã€ãã‚Œã«ã¨ã‚‚ãªã†ãƒ‡ãƒ¼ã‚¿ã‚³ãƒ³ã‚¹ãƒˆãƒ©ã‚¯ã‚¿ã«ã‚ˆã£ã¦æ§‹æˆã•ã‚Œã‚‹
Left-Leaning Red-Black Trees Considered Harmful
Left-Leaning Red-Black Trees Considered Harmful Eddie Kohler Robert Sedgewick’s left-leaning red-black trees are supposedly simpler to implement than normal red-black trees: In this paper, we describe a new variant of red-black trees that meets many of the original design goals and leads to substantially simpler code for insert/delete, less than one-fourth as much code as in implementations in com
Balanced Trees, Part 4: Left Leaning Red-Black Trees
Balanced Trees, Part 4: Left Leaning Red-Black Trees Overview While searching around for info about balanced trees, I found some new papers by Robert Sedgewick, describing an algorithm called Left Leaning Red-Black (LLRB) trees. Since Sedgewick (along with Guibas back in 1978) helped come up with the abstraction for red-black trees, I assumed this would be a good algorithm to test. However... Ther
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Data.Tree.RBTree
Deletion in Left Leaning Red Black Trees
Left-Leaning Red-Black Tree by Java
http://www.sampou.org/cgi-bin/haskell.cgi?Programming%3A%B6%CC%BC%EA%C8%A2%3A%A4%BD%A4%CE%C2%BE
rb.h -- Red-black tree implementation
http://algs4.cs.princeton.edu/32bst/
Red Black Tree using optima in Common Lisp
https://www.cs.kent.ac.uk/people/staff/smk/redblack/
Red Black Tree for Common Lisp.
Balanced Trees, Part 5: Performance
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