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As a consequence, the pair allocation constraints for
sort! and merge! are removed.
#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When SRFI 32 Sort Libraries was withdrawn, it had 28 procedures.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:
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? (key x) (key y)))
All five functions will call the key argument at most once per element.
The `!' variants sort in place; sort! returns its
sequence argument.
#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).
(sorted? (sort sequence less?) less?) => #t
(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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