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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 1))
+ (vector-ref seq i)))
+ (= 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!)