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- Received: 2006-10-11
- Draft: 2006-10-17--2006-12-16
- Revised: 2006-11-06
- Revised: 2006-11-23
- Final: 2007-01-29
- Revised to fix errata:
- 2020-03-07 (Fix bug in sample implementation.)

- 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`)))

When SRFI 32 Sort Libraries was withdrawn, it had 28 procedures. Having many variants in a general-purpose sorting library has disadvantages:

- When there are only a few paths through the code, the code gets
thoroughly tested and its behavior well understood. When there
are many paths, most of the code is not well tested and not well
understood.
- To choose optimal sort algorithms requires nearly as much
understanding as to write them. Most users don't.
- A module with too many functions and voluminous documentation
scares off the typical user looking to just sort a 50-element
list; who then goes searching for any old sort algorithm to
reinvent the wheel.
- If some of the default sorts are unstable, then users will be
surprised that sorting their data twice results in different
orders; or that vector and list sorts return different orders.

This SRFI's sort procedures operate on lists and arrays, which includes vectors; the merge procedures operate on lists.

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 (not (less? last nxt)) (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 keyer (if key car identity)) (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? keyer))) ((= n 2) (let ((x (car seq)) (y (cadr seq)) (p seq)) (set! seq (cddr seq)) (cond ((less? (keyer y) (keyer 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))))) (cond (key (key-wrap! seq) (set! seq (step (length seq))) (key-unwrap! seq) seq) (else (step (length 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 list. ;@ (define (sort! seq less? . opt-key) (define key (if (null? opt-key) #f (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) #f (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