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|
;;; "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
;;; (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 (sort:sorted? seq less?)
(cond
((null? seq)
#t)
((vector? seq)
(let ((n (vector-length seq)))
(if (<= n 1)
#t
(do ((i 1 (+ i 1)))
((or (= i n)
(less? (vector-ref seq i)
(vector-ref seq (- i 1))))
(= i n)) )) ))
(else
(let loop ((last (car seq)) (next (cdr seq)))
(or (null? next)
(and (not (less? (car next) last))
(loop (car next) (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 vectors. See below.
(define (sort:merge a b less?)
(cond
((null? a) b)
((null? b) a)
(else (let loop ((x (car a)) (a (cdr a)) (y (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? y x)
(if (null? b)
(cons y (cons x a))
(cons y (loop x a (car b) (cdr b)) ))
;; x <= y
(if (null? a)
(cons x (cons y b))
(cons x (loop (car a) (cdr a) y b)) )) )) ))
;;; (merge! a b less?)
;;; 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 vectors.
(define (sort:merge! a b less?)
(define (loop r a b)
(if (less? (car b) (car a))
(begin
(set-cdr! r b)
(if (null? (cdr b))
(set-cdr! b a)
(loop b a (cdr b)) ))
;; (car a) <= (car b)
(begin
(set-cdr! r a)
(if (null? (cdr a))
(set-cdr! a b)
(loop a (cdr a) b)) )) )
(cond
((null? a) b)
((null? b) a)
((less? (car b) (car a))
(if (null? (cdr b))
(set-cdr! b a)
(loop b a (cdr b)))
b)
(else ; (car a) <= (car b)
(if (null? (cdr a))
(set-cdr! a b)
(loop a (cdr a) b))
a)))
;;; (sort! sequence less?)
;;; sorts the list or vector 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.
(define (sort:sort! seq less?)
(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?)))
((= n 2)
(let ((x (car seq))
(y (cadr seq))
(p seq))
(set! seq (cddr seq))
(if (less? y x) (begin
(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
'()) ))
(if (vector? seq)
(let ((n (vector-length seq))
(vec seq))
(set! seq (vector->list seq))
(do ((p (step n) (cdr p))
(i 0 (+ i 1)))
((null? p) vec)
(vector-set! vec i (car p)) ))
;; otherwise, assume it is a list
(step (length seq)) ))
;;; (sort sequence less?)
;;; sorts a vector 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:sort seq less?)
(if (vector? seq)
(list->vector (sort:sort! (vector->list seq) less?))
(sort:sort! (append seq '()) less?)))
;;; eof
(define sorted? sort:sorted?)
(define merge sort:merge)
(define merge! sort:merge!)
(define sort sort:sort)
(define sort! sort:sort!)
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