source: project/wiki/eggref/5/rb-tree @ 36325

Last change on this file since 36325 was 36325, checked in by iraikov, 11 months ago

removed fx from example in rb-tree doc

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1[[tags:egg]]
2[[toc:]]
3
4== rb-tree
5
6Sorted dictionary data structures based on red-black trees.
7
8
9== Documentation
10
11The {{rb-tree}} library is based on the SML/NJ library implementation
12of red-black trees, which is in turn based on Chris Okasaki's
13implementation of red-black trees.  The delete function is based on
14the description in Cormen, Leiserson, and Rivest.
15
16The present implementation code defines a persistent map [[typeclass]]
17that implements an ordered dictionary mapping of keys to values.
18
19Looking up an arbitrary or the min/max keys, and deleting the min/max
20keys require no more key comparisons than the depth of the tree, which
21is {{O(log n)}} where {{n}} is the total number of keys in the tree.
22
23=== Procedures
24
25The persistent map instance is created by procedure {{rb-tree-map}}:
26
27<procedure>rb-tree-map:: KEY-COMPARE-PROC [insdel-key-compare: KEY-COMPARE-PROC] -> <PersistentMap></procedure>
28
29where KEY-COMPARE-PROC is a user-supplied function that takes two keys
30and returns a negative, positive, or zero number depending on how the
31first key compares to the second.
32
33Optional keyword argument {{insdel-key-compare}} can be used to
34specify different key comparison predicates for the insertion and
35deletion operations.
36
37The {{<PersistentMap>}} typeclass contains the following operations:
38
39; {{empty}} : returns a new empty tree
40; {{empty? TREE}} : returns {{#t}} if the given tree is empty
41; {{get TREE}} : returns a procedure of the form {{(LAMBDA KEY . DEFAULT-CLAUSE}} which searches the given tree for an association with a given {{KEY}}, and returns a (key . value) pair of the found association. If an association with {{KEY}} cannot be located in the  tree, the procedure returns the result of evaluating the {{DEFAULT-CLAUSE}}. If the default clause is omitted, an error is signalled. {{KEY}} must be comparable to the keys in the  tree by a key-compare predicate (which has been specified when the  tree was created)
42; {{get-value TREE}} : returns a procedure of the form {{(LAMBDA KEY . DEFAULT-CLAUSE}} which searches the tree for an association with a given {{KEY}}, and returns the value of (key . value) pair of the found association. If an association with {{KEY}} cannot be located in the  tree, the procedure returns the result of evaluating the {{DEFAULT-CLAUSE}}. If the default clause is omitted, an error is signalled. {{KEY}} must be comparable to the keys in the  tree by a key-compare predicate (which has been specified when the  tree was created)
43; {{get-min TREE}} : returns a (key . value) pair for an association in the tree with the smallest key. If the  tree is empty, an error is signalled.
44; {{get-max TREE}} : returns a (key . value) pair for an association in the tree with the largest key. If the tree is empty, an error is signalled.
45; {{size TREE}} : returns the size (the number of associations) in the tree
46; {{put TREE KEY VALUE}} : returns a new  tree object that contains the given association
47; {{delete TREE KEY . DEFAULT-CLAUSE}} : if the specified key is found, it returns a new tree object that no longer contains the association specified by that key, while the original tree object is unmodified. If the key is not found, the procedure returns the result of evaluating {{DEFAULT-CLAUSE}}
48; {{for-each-ascending TREE}} : returns a procedure {{LAMBDA PROC}} that will apply the given procedure PROC to each (key . value) association of the tree, from the one with the smallest key all the way to the one with the max key, in an ascending order of keys.
49; {{for-each-descending TREE}} : returns a procedure {{LAMBDA PROC}} that will apply the given procedure {{PROC}}to each (key . value) association of the tree, in the descending order of keys.
50; {{map TREE}} : returns a procedure {{LAMBDA PROC}} that will apply the given procedure {{PROC}}to the value component of each association in the  tree, in the ascending order of keys, and will construct a copy of the tree that contains the values returned by that procedure.
51; {{mapi TREE}} : returns a procedure {{LAMBDA PROC}} that will apply the given procedure {{PROC}}to each (key . value) association in the  tree, in the ascending order of keys, and will construct a copy of the tree that contains the values returned by that procedure.
52; {{fold TREE}} : returns a procedure {{LAMBDA PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-n . value-n) ... (key-2 . value-2) (key-1 . value-1) }} the procedure returns the result of the successive function applications {{(PROC value-1 (PROC value-2 ... (PROC value-n INITIAL)}}.
53; {{foldi TREE}} : returns a procedure {{LAMBDA PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-n . value-n) ... (key-2 . value-2) (key-1 . value-1) }} the procedure returns the result of the successive function applications {{(PROC key-1 value-1 (PROC key-2 value-2 ... (PROC key-n value-n INITIAL)}}.
54; {{fold-right TREE}} : returns a procedure {{LAMBDA PROC INITIAL}} such that, given the associations in the tree ordered by the ascending order of keys: {{(key-1 . value-1) (key-2 . value-2) ... (key-n . value-n) }} the procedure returns the result of the successive function applications {{(PROC value-n ... (PROC value-2 (PROC value-1 INITIAL)}}.
55; {{foldi-right TREE}} : returns a procedure {{LAMBDA PROC INITIAL}} such that, given the associations in the tree ordered by the ascending order of keys: {{(key-1 . value-1) (key-2 . value-2) ... (key-n . value-n) }} the procedure returns the result of the successive function applications {{(PROC key-n value-n ... (PROC key-2 value-2 (PROC key-1 value-1 INITIAL)}}.
56; {{fold-partial TREE}} : returns a procedure {{LAMBDA PRED PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-n . value-n) ... (key-2 . value-2) (key-1 . value-1) }} the procedure returns the result of the successive function applications {{(PROC value-i ... (PROC value-n INITIAL)}}, where {{i <= n}} and {{(PRED x)}} holds true for all {{x = (value-n) ... (value-i)}}. In other words, this function acts like {{fold}} on the ordered subset of the values {{x}} in the tree such that {{(PRED x)}} is true.
57; {{foldi-partial TREE}} : returns a procedure {{LAMBDA PRED PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-n . value-n) ... (key-2 . value-2) (key-1 . value-1) }} the procedure returns the result of the successive function applications {{(PROC key-i value-i ... (PROC key-n value-n INITIAL)}}, where {{i <= n}} and {{(PRED xk x)}} holds true for all {{x = (value-n) ... (value-i)}} and {{xk = (key-n) ... (key-i)}}. In other words, this function acts like {{foldi}} on the ordered subset of the key-value pairs {{(k . x)}} in the tree such that {{(PRED k x)}} is true.
58; {{fold-right-partial TREE}} : returns a procedure {{LAMBDA PRED PROC INITIAL}} such that, given the associations in the tree ordered by the ascending order of keys: {{(key-1 . value-1) (key-2 . value-2) ... (key-n . value-n) }} the procedure returns the result of the successive function applications {{(PROC value-1 ... (PROC value-i INITIAL)}}, where {{i <= n}} and {{(PRED x)}} holds true for all {{x = (value-1) ... (value-i)}}. In other words, this function acts like {{fold-right}} on the ordered subset of the values {{x}} in the tree such that {{(PRED x)}} is true.
59; {{foldi-right-partial TREE}} : returns a procedure {{LAMBDA PRED PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-1 . value-1) (key-2 . value-2) ... (key-1 . value-1) }} the procedure returns the result of the successive function applications {{(PROC key-1 value-1 ... (PROC key-i value-i INITIAL)}}, where {{i <= n}} and {{(PRED xk x)}} holds true for all {{x = (value-1) ... (value-i)}} and {{xk = (key-1) ... (key-i)}}. In other words, this function acts like {{foldi-right}} on the ordered subset of the key-value pairs {{(k . x)}} in the tree such that {{(PRED k x)}} is true.
60; {{fold-limit TREE}} : returns a procedure {{LAMBDA PRED PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-n . value-n) ... (key-2 . value-2) (key-1 . value-1) }} the procedure returns the result of the successive function applications {{(PROC value-i ... (PROC value-n INITIAL)}}, where {{i <= n}} and {{(PRED x)}} does not hold true for all {{x = (PROC value-n INITIAL)  ... (PROC (value-i) (PROC value-(i-1)...}}.
61; {{fold-right-limit TREE}} : returns a procedure {{LAMBDA PRED PROC INITIAL}} such that, given the associations in the tree ordered by the descending order of keys: {{(key-1 . value-1) (key-2 . value-2) ... (key-i . value-1) }} the procedure returns the result of the successive function applications {{(PROC value-i ... (PROC value-1 INITIAL)}}, where {{i <= n}} and {{(PRED x)}} does not hold true for all {{x = (PROC value-1 INITIAL)  ... (PROC (value-i) (PROC value-(i-1)...}}.
62
63
64== Examples
65
66 (import typeclass rb-tree)
67 
68 (define (++ x) (+ 1 x))
69 (define (-- x) (- x 1))
70 
71 (let ((m (rb-tree-map (lambda (x y) (- x y)))))
72    (with-instance ((<PersistentMap> m))
73     
74      (let* ((compute-assoc (lambda (key) (cons key (++ key))))
75             (min-key -1) (max-key 10)
76             (t
77              (let recur  ((t (empty)) (i min-key))
78                (let ((t1 (put t i (cdr (compute-assoc i)))))
79                  (if (< i max-key) (recur t1 (++ i)) t1))))
80             )
81           
82       (print ((get t) (++ min-key)))
83 
84       (print ((get t) (-- min-key) 'notfound))
85 
86       ;; checking traversing in ascending order
87       (let ((expected-key min-key))
88        ((for-each-ascending t)
89         (lambda (association)
90           (print (equal? association (compute-assoc expected-key)))
91          (set! expected-key (++ expected-key)))))
92  )
93 ))
94
95== About this egg
96
97
98=== Author
99
100[[/users/ivan-raikov|Ivan Raikov]]
101
102=== Version history
103
104; 5.3 : Ported to CHICKEN 5
105; 5.0 : Using typeclass interface, discarded ephemeral map
106; 4.2 : Ensure test script returns proper exit status
107; 4.0 : Divided API in persistent and ephemeral maps
108; 3.1 : Added get-value operation
109; 3.0 : Ability to specify different predicates for lookup, insert, delete operations
110; 2.9 : Documentation converted to wiki format
111; 2.8 : Added matchable as dependency
112; 2.7 : Bug fix in dispatch-on-key
113; 2.6 : Ported to Chicken 4
114; 2.5 : Fixes to for-each-ascending/descending
115; 2.3 : Build script updated for better cross-platform compatibility
116; 2.2 : Added fold-limit procedures
117; 2.1 : Added fold-partial procedures
118; 2.0 : Added side-effect-free put and delete procedures
119; 1.0 : Initial release
120
121=== License
122
123
124 Copyright 2007-2018 Ivan Raikov.
125 
126 This program is free software: you can redistribute it and/or modify
127 it under the terms of the GNU General Public License as published by
128 the Free Software Foundation, either version 3 of the License, or (at
129 your option) any later version.
130 
131 This program is distributed in the hope that it will be useful, but
132 WITHOUT ANY WARRANTY; without even the implied warranty of
133 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
134 General Public License for more details.
135 
136 A full copy of the GPL license can be found at
137 <http://www.gnu.org/licenses/>.
138
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