[[tag: eggs]]
== llrb-tree

Left–leaning red–black trees.  A general version and some customized
to the key types "fixnum", "string" and "symbol" are provided.

== Overview

A left-leaning red–black (LLRB) tree is a type of self-balancing binary search tree.
It is a variant of the red–black tree and guarantees the same asymptotic complexity for operations.

This egg implements an API to LLRB-trees (mostly) compatible to srfi-69 Hashtables
plus some procedures resembling the API of assoc-Lists.

Note that this egg is mainly intended to used to replace assoc-Lists.

== API

<procedure>(make-llrb-treetype COMPARATOR)</procedure>

Define a treetype of keys matching COMPARATOR (from SRFI-128).

<procedure>(make-llrb-treetype KEY? EQUAL LESS)</procedure>

Define a treetype of keys matching the KEY? predicate using EQUAL as
equivalence predicate and LESS as ordering predicate.

Note: the search key is passed to EQUAL and LESS as the first
parameter, the key of the element of the tree as second parameter.

<procedure>(llrb-treetype? X)</procedure>

Test X to be an llrb-treetype.

The procedures "*{{binding-set}}*" have ananologous definitions
specialized to the key type.  Those specialized procedure names are
prefixed by the key type (i.e. {{fixnum-}}, {{string-}} and
{{symbol-}}).

Procedures prefixed with {{symbol-}}, {{fixnum-}}, {{string-}} are
defined for most of the following.  Those are specialized to the
respective key type.

<procedure>(string-empty-binding-set)</procedure>
<procedure>(fixnum-empty-binding-set)</procedure>
<procedure>(symbol-empty-binding-set)</procedure>
<procedure>(empty-binding-set type)</procedure>

Return an empty binding set.

<procedure>(make-binding-set TYPE . pairs)</procedure>

Undocumented (API pending review).

Create an empty set of bindings of TYPE populate it with bindings from
`pairs`.


<procedure>(binding-set-empty? set)</procedure>

Test whether or not the set has no associations.

<procedure>(binding-set-ref/default set key default)</procedure>

Returns the value bound to {{key}} in {{set}} or {{default}} value if
not found.

<procedure>(binding-set-ref set key [failure] [success])</procedure>

Extracts the value associated to key in "binding-set", invokes the
procedure {{success}} on it, and returns its result; if {{success}} is
not provided, then the value itself is returned. If key is not
contained in {{set}} and {{failure}} is supplied, then {{failure}} is
invoked on no arguments and its result is returned. Otherwise, it is
an error.

<procedure>(binding-set-insert set key value)</procedure>

Extend {{set}} with a binding {{key}}-{{value}}, return the extended
set.

<procedure>(binding-set-delete key set)</procedure>

Deletes association from {{set}} with given {{key}}, return the new set.

<procedure>(binding-set-update set key update default)</procedure>

Return a set with the binding of {{key}} replaced. {{update}} and
{{default}} are procedures with the same semantics and in hash-table-update!.

<procedure>(binding-set-cons key value set)</procedure>

Same as {{binding-set-insert}} with API as alist-cons (srfi-1).

<procedure>(binding-set-fold proc nil set)</procedure>

{{Proc}} must be a procedure of three arguments.  It is invoked for
each element with the key, value and the accumulated value (nil for
the first element).

<procedure>(binding-set-union inner outer)</procedure>

Return a merged set.  All bindings in {{inner}} shadow those in
{{outer}}.



<procedure>(make-table type)</procedure>

Create a table with an empty set of bindings according to {{type}}.

<procedure>(string-make-table)</procedure>
<procedure>(fixnum-make-table)</procedure>
<procedure>(symbol-make-table)</procedure>

Create a table with an empty set of bindings.  Specialized to the key
type.

<procedure>(table? x)</procedure>

Test whether or not the object is a LLRB-table.

<procedure>(table-empty? table)</procedure>

Test {{table}} to have no bidings.

<procedure>(table-copy table)</procedure>

Create a copy of {{table}} initially sharing all bindings.

<procedure>(table-delete! table key)</procedure>

Delete the binding for {{key}} from the bindings in the table.

<procedure>(table-set! table key value)</procedure>

Set the {{value}} for {{key}} in {{table}}.

<procedure>(table-ref/default table key default)</procedure>

Returns the value associated to key in {{table}}, or the {{default}}
when the {{key}} is missing.

<procedure>(table-ref table key [failure] [success])</procedure>

Extracts the value associated to key in {{table}}, invokes the
procedure {{success}} on it, and returns its result; if {{success}} is
not provided, then the value itself is returned. If key is not
contained in {{set}} and {{failure}} is supplied, then {{failure}} is
invoked on no arguments and its result is returned. Otherwise, it is
an error.

<procedure>(table-update! table key update . default)</procedure>

Note: procedures {{update}} and {{default}} should have no side
effects.  They may be called multiple times.  (This can happen if
those procedures allow other continuations/threads to update the table
before they return.  As a consequence those procedures must especially
not update the table, since this will result in an endless loop.)

<procedure>(table-fold table proc nil)</procedure>
<procedure>(table-for-each table proc)</procedure>

Intentionally minimum related operations are NOT available for
{{symbol}}, since those are supposedly unordered.

<procedure>(table-min table thunk)</procedure>

Return two values the minimal key and associated value in table.
If the table is empty {{thunk}} is invoked instead.

((FIXME: will be in constant time with little change to the
source, at the moment O(log n).))

<procedure>(table-delete-min! table)</procedure>

Delete the entry with the smalles key and return two values, the key
and associated value in table.  In case table is empty returns two
false values.

=== Auxillaries

Note: These procedures are obsolete for chicken version >= 4.10.1 at
least (they provide no more performance benefit) and will be removed
in future versions of this egg.

<procedure>(wrap-one-string-arg PROC)</procedure>

Returns a procedure caching PROC.  PROC must accept exactly one
argument, a string.

<procedure>(str2sym string)</procedure>

Calls {{string->symbol}} and caches the result.  (Surprisingly this is
faster on lookup than {{string->symbol}} itself, at least for large
numbers.)

== Examples

    #;1> (use llrb-tree)
    #;2> (define y (fixnum-make-table))
    #;3> (fixnum-table-update! y 23 add1 (lambda () 41))
    42
    #;4> (define numttype (make-llrb-treetype number? = <))
    #;5> (define nt (make-table numttype))
    #;6> (table-update! nt 42.23 add1 (lambda () 22))
    23
    #;7> (define clsttype (make-llrb-treetype
          number?
	  (lambda (a b) (let ((delta (- a b))) (and (< delta 1) (> delta 0))))
	  <))
    #;8> (define ct (make-table clsttype))
    #;9> (table-set! ct 1 '(one))
    #;10> (table-set! ct 2 '(two))
    #;11> (table-set! ct 3 '(three))
    #;12> (define (classify n) (table-update! ct n (lambda (v) `(,(car v) ,n . ,(cdr v)))))
    #;13> (classify 1.1)
    (one 1.1)
    #;14>  (classify 1.2)
    (one 1.2 1.1)
    #;15> (classify 2.1)
    (two 2.1)
    #;16> (classify 2.4)
    (two 2.4 2.1)
    #;17> (classify 3.5)
    (three 3.5)
    #;18> (table-fold ct (lambda (k v i) `((,k . ,v) . ,i)) '())
    ((1 one 1.2 1.1) (2 two 2.4 2.1) (3 three 3.5))
    #;19> (define (string-binding-set-find set proc) ;; This is not the most efficient implementation.
      (call-with-current-continuation
       (lambda (return)
	 (or
	  (string-binding-set-fold
	   (lambda (k v i)
	     (let ((hit (proc k v)))
	       (if hit (return hit) i)))
	   #f
	   set)
	  (error "no match")))))
    #;20> (string-binding-set-find (string-binding-set-cons "a" 'A (string-empty-binding-set)) (lambda (k v) (equal? k "a")))
    #t

== About this egg

=== Author

Jörg F. Wittenberger

=== Version History

0.3.7 -- Remove global scope from C symbol.

0.3.1 -- Enable srfi-128 comparators, add tests, documentation update.

0.3 -- Fixed dependency.

0.2 -- Changed API to match srfi-125

0.1 -- initial release

=== License

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.

Neither the name of the author nor the names of its contributors may
be used to endorse or promote products derived from this software
without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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