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- Received: 2006/10/11
- Draft: 2006/10/17 - 2006/12/16
- Revised: 2006/11/06

- Changed so that the algorithms are required to call
`key`arguments no more than once per element.As a consequence, the pair allocation constraints for

`sort!`

and`merge!`

are removed. - These procedures are stable only for
`less?`predicates which return`#f`

when applied to identical arguments. With non-empty sequence arguments,`less?`can easily be tested. Should these procedures signal an error when given reflexive predicates? Should they silently replace`less?`with(lambda (

`a``b`) (not (`less?``b``a`)))

- List and Vector versions were separated, even though Scheme has manifest types which eliminate ambiguity as to the caller's intentions.
- Four varieties of algorithms were provided (quick, heap, insert, merge) even though quick, heap, and insert sorts have no significant advantage over merge-sort.
- Sort and stable-sort varieties were included, even though an unstable sort has no performance advantage.
- Four delete-neighbor-dups procedures were included.

SRFI 32's
vector routines took optional arguments to restrict their operations
to a subrange of the vector.
SRFI 63
shared subarrays (using `make-shared-array`

or
SLIB's
`subarray`

) eliminate the need for these optional
arguments.

The present SRFI procedures take an optional procedure argument
equivalent to Common-Lisp's `&KEY` argument.

`#f`

when applied to identical arguments.
The `sorted?`

, `merge`

, and `merge!`

procedures consume
asymptotic time and space no larger than *O(N)*, where *N* is the
sum of the lengths of the sequence arguments.
The `sort`

and `sort!`

procedures consume asymptotic time
and space no larger than *O(N*log(N))*, where *N* is the length of
the sequence argument.

All five functions take an optional `key` argument corresponding
to a CL-style ``&key'` argument. A `less?` predicate with a
`key` argument behaves like:

(lambda (x y) (less?(keyx) (keyy)))

All five functions will call the `key` argument at most once per
element.

The ``!'` variants sort in place; `sort!`

returns its
`sequence` argument.

__Function:__**sorted?***sequence less?*__Function:__**sorted?***sequence less? key*-
Returns
`#t`

when the sequence argument is in non-decreasing order according to`less?`(that is, there is no adjacent pair`... x y ...`

for which`(less? y x)`

).Returns

`#f`

when the sequence contains at least one out-of-order pair. It is an error if the sequence is not a list or array (including vectors and strings).

__Function:__**merge***list1 list2 less?*__Function:__**merge***list1 list2 less? key*- Merges two sorted lists, returning a freshly allocated list as its result.

__Function:__**merge!***list1 list2 less?*__Function:__**merge!***list1 list2 less? key*-
Merges two sorted lists, re-using the pairs of
`list1`and`list2`to build the result. The result will be either`list1`or`list2`.

__Function:__**sort***sequence less?*__Function:__**sort***sequence less? key*-
Accepts a list or array (including vectors and strings) for
`sequence`; and returns a completely new sequence which is sorted according to`less?`. The returned sequence is the same type as the argument`sequence`. Given valid arguments, it is always the case that:(sorted? (sort

`sequence``less?`)`less?`) => #t

__Function:__**sort!***sequence less?*__Function:__**sort!***sequence less? key*-
Returns list, array, vector, or string
`sequence`which has been mutated to order its elements according to`less?`. Given valid arguments, it is always the case that:(sorted? (sort!

`sequence``less?`)`less?`) => #t

;;; "sort.scm" Defines: sorted?, merge, merge!, sort, sort! ;;; Author : Richard A. O'Keefe (based on Prolog code by D.H.D.Warren) ;;; ;;; This code is in the public domain. ;;; Updated: 11 June 1991 ;;; Modified for scheme library: Aubrey Jaffer 19 Sept. 1991 ;;; Updated: 19 June 1995 ;;; (sort, sort!, sorted?): Generalized to strings by jaffer: 2003-09-09 ;;; (sort, sort!, sorted?): Generalized to arrays by jaffer: 2003-10-04 ;;; jaffer: 2006-10-08: ;;; (sort, sort!, sorted?, merge, merge!): Added optional KEY argument. ;;; jaffer: 2006-11-05: ;;; (sorted?, merge, merge!, sort, sort!): Call KEY arg at most once ;;; per element. (require 'array) ;;; (sorted? sequence less?) ;;; is true when sequence is a list (x0 x1 ... xm) or a vector #(x0 ... xm) ;;; such that for all 1 <= i <= m, ;;; (not (less? (list-ref list i) (list-ref list (- i 1)))). ;@ (define (sorted? seq less? . opt-key) (define key (if (null? opt-key) identity (car opt-key))) (cond ((null? seq) #t) ((array? seq) (let ((dimax (+ -1 (car (array-dimensions seq))))) (or (<= dimax 1) (let loop ((idx (+ -1 dimax)) (last (key (array-ref seq dimax)))) (or (negative? idx) (let ((nxt (key (array-ref seq idx)))) (and (less? nxt last) (loop (+ -1 idx) nxt)))))))) ((null? (cdr seq)) #t) (else (let loop ((last (key (car seq))) (next (cdr seq))) (or (null? next) (let ((nxt (key (car next)))) (and (not (less? nxt last)) (loop nxt (cdr next))))))))) ;;; (merge a b less?) ;;; takes two lists a and b such that (sorted? a less?) and (sorted? b less?) ;;; and returns a new list in which the elements of a and b have been stably ;;; interleaved so that (sorted? (merge a b less?) less?). ;;; Note: this does _not_ accept arrays. See below. ;@ (define (merge a b less? . opt-key) (define key (if (null? opt-key) identity (car opt-key))) (cond ((null? a) b) ((null? b) a) (else (let loop ((x (car a)) (kx (key (car a))) (a (cdr a)) (y (car b)) (ky (key (car b))) (b (cdr b))) ;; The loop handles the merging of non-empty lists. It has ;; been written this way to save testing and car/cdring. (if (less? ky kx) (if (null? b) (cons y (cons x a)) (cons y (loop x kx a (car b) (key (car b)) (cdr b)))) ;; x <= y (if (null? a) (cons x (cons y b)) (cons x (loop (car a) (key (car a)) (cdr a) y ky b)))))))) (define (sort:merge! a b less? key) (define (loop r a kcara b kcarb) (cond ((less? kcarb kcara) (set-cdr! r b) (if (null? (cdr b)) (set-cdr! b a) (loop b a kcara (cdr b) (key (cadr b))))) (else ; (car a) <= (car b) (set-cdr! r a) (if (null? (cdr a)) (set-cdr! a b) (loop a (cdr a) (key (cadr a)) b kcarb))))) (cond ((null? a) b) ((null? b) a) (else (let ((kcara (key (car a))) (kcarb (key (car b)))) (cond ((less? kcarb kcara) (if (null? (cdr b)) (set-cdr! b a) (loop b a kcara (cdr b) (key (cadr b)))) b) (else ; (car a) <= (car b) (if (null? (cdr a)) (set-cdr! a b) (loop a (cdr a) (key (cadr a)) b kcarb)) a)))))) ;;; takes two sorted lists a and b and smashes their cdr fields to form a ;;; single sorted list including the elements of both. ;;; Note: this does _not_ accept arrays. ;@ (define (merge! a b less? . opt-key) (sort:merge! a b less? (if (null? opt-key) identity (car opt-key)))) (define (sort:sort-list! seq less? key) (define (step n) (cond ((> n 2) (let* ((j (quotient n 2)) (a (step j)) (k (- n j)) (b (step k))) (sort:merge! a b less? car))) ((= n 2) (let ((x (car seq)) (y (cadr seq)) (p seq)) (set! seq (cddr seq)) (cond ((less? (car y) (car x)) (set-car! p y) (set-car! (cdr p) x))) (set-cdr! (cdr p) '()) p)) ((= n 1) (let ((p seq)) (set! seq (cdr seq)) (set-cdr! p '()) p)) (else '()))) (define (key-wrap! lst) (cond ((null? lst)) (else (set-car! lst (cons (key (car lst)) (car lst))) (key-wrap! (cdr lst))))) (define (key-unwrap! lst) (cond ((null? lst)) (else (set-car! lst (cdar lst)) (key-unwrap! (cdr lst))))) (key-wrap! seq) (set! seq (step (length seq))) (key-unwrap! seq) seq) (define (rank-1-array->list array) (define dimensions (array-dimensions array)) (do ((idx (+ -1 (car dimensions)) (+ -1 idx)) (lst '() (cons (array-ref array idx) lst))) ((< idx 0) lst))) ;;; (sort! sequence less?) ;;; sorts the list, array, or string sequence destructively. It uses ;;; a version of merge-sort invented, to the best of my knowledge, by ;;; David H. D. Warren, and first used in the DEC-10 Prolog system. ;;; R. A. O'Keefe adapted it to work destructively in Scheme. ;;; A. Jaffer modified to always return the original pair. ;@ (define (sort! seq less? . opt-key) (define key (if (null? opt-key) identity (car opt-key))) (cond ((array? seq) (let ((dims (array-dimensions seq))) (do ((sorted (sort:sort-list! (rank-1-array->list seq) less? key) (cdr sorted)) (i 0 (+ i 1))) ((null? sorted) seq) (array-set! seq (car sorted) i)))) (else ; otherwise, assume it is a list (let ((ret (sort:sort-list! seq less? key))) (if (not (eq? ret seq)) (do ((crt ret (cdr crt))) ((eq? (cdr crt) seq) (set-cdr! crt ret) (let ((scar (car seq)) (scdr (cdr seq))) (set-car! seq (car ret)) (set-cdr! seq (cdr ret)) (set-car! ret scar) (set-cdr! ret scdr))))) seq)))) ;;; (sort sequence less?) ;;; sorts a array, string, or list non-destructively. It does this ;;; by sorting a copy of the sequence. My understanding is that the ;;; Standard says that the result of append is always "newly ;;; allocated" except for sharing structure with "the last argument", ;;; so (append x '()) ought to be a standard way of copying a list x. ;@ (define (sort seq less? . opt-key) (define key (if (null? opt-key) identity (car opt-key))) (cond ((array? seq) (let ((dims (array-dimensions seq))) (define newra (apply make-array seq dims)) (do ((sorted (sort:sort-list! (rank-1-array->list seq) less? key) (cdr sorted)) (i 0 (+ i 1))) ((null? sorted) newra) (array-set! newra (car sorted) i)))) (else (sort:sort-list! (append seq '()) less? key))))

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Editor: David Van Horn