rb-tree

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Sorted dictionary data structures based on red-black trees.

The rb-tree library is based on the SML/NJ library implementation of red-black trees, which is in turn based on Chris Okasaki's implementation of red-black trees. The delete function is based on the description in Cormen, Leiserson, and Rivest.

The present implementation code defines a persistent map typeclass that implements an ordered dictionary mapping of keys to values.

Looking up an arbitrary or the min/max keys, and deleting the min/max keys require no more key comparisons than the depth of the tree, which is O(log n) where n is the total number of keys in the tree.

Procedures

The persistent map instance is created by procedure rb-tree-map:

rb-tree-map:procedure

where KEY-COMPARE-PROC is a user-supplied function that takes two keys and returns a negative, positive, or zero number depending on how the first key compares to the second.

Optional keyword argument insdel-key-compare can be used to specify different key comparison predicates for the insertion and deletion operations.

The <PersistentMap> typeclass contains the following operations:

empty: returns a new empty tree
empty? TREE: returns #t if the given tree is empty
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)
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)
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.
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.
size TREE: returns the size (the number of associations) in the tree
put TREE KEY VALUE: returns a new tree object that contains the given association
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
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.
for-each-descending TREE: returns a procedure LAMBDA PROC that will apply the given procedure PROCto each (key . value) association of the tree, in the descending order of keys.
map TREE: returns a procedure LAMBDA PROC that will apply the given procedure PROCto 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.
mapi TREE: returns a procedure LAMBDA PROC that will apply the given procedure PROCto 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.
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).
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).
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).
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).
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.
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.
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.
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.
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)....
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)....

Examples

(use rb-tree typeclass)

(define (++ x) (fx+ 1 x))
(define (-- x) (fx- x 1))

(let ((m (rb-tree-map (lambda (x y) (- x y)))))
   (with-instance ((<PersistentMap> m))
     
     (let* ((compute-assoc (lambda (key) (cons key (++ key))))
            (min-key -1) (max-key 10)
            (t 
             (let recur  ((t (empty)) (i min-key))
               (let ((t1 (put t i (cdr (compute-assoc i)))))
                 (if (< i max-key) (recur t1 (++ i)) t1))))
            )
           
      (print ((get t) (++ min-key)))

      (print ((get t) (-- min-key) 'notfound))

      ;; checking traversing in ascending order
      (let ((expected-key min-key))
       ((for-each-ascending t)
        (lambda (association)
          (print (equal? association (compute-assoc expected-key)))
         (set! expected-key (++ expected-key)))))
 )
))

5.0: Using typeclass interface, discarded ephemeral map
4.2: Ensure test script returns proper exit status
4.0: Divided API in persistent and ephemeral maps
3.1: Added get-value operation
3.0: Ability to specify different predicates for lookup, insert, delete operations
2.9: Documentation converted to wiki format
2.8: Added matchable as dependency
2.7: Bug fix in dispatch-on-key
2.6: Ported to Chicken 4
2.5: Fixes to for-each-ascending/descending
2.3: Build script updated for better cross-platform compatibility
2.2: Added fold-limit procedures
2.1: Added fold-partial procedures
2.0: Added side-effect-free put and delete procedures
1.0: Initial release

License

Copyright 2007-2013 Ivan Raikov and the Okinawa Institute of Science and Technology.

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

A full copy of the GPL license can be found at
<http://www.gnu.org/licenses/>.

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