135 lines
4.7 KiB
Scheme
135 lines
4.7 KiB
Scheme
;;; (sorted? sequence less?)
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;;; is true when sequence is a list (x0 x1 ... xm) or a vector #(x0 ... xm)
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;;; such that for all 1 <= i <= m,
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;;; (not (less? (list-ref list i) (list-ref list (- i 1)))).
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(define (sorted? seq less?)
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(cond
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((null? seq)
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#t)
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((vector? seq)
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(let ((n (vector-length seq)))
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(if (<= n 1)
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#t
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(do ((i 1 (+ i 1)))
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((or (= i n)
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(less? (vector-ref seq (- i 1))
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(vector-ref seq i)))
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(= i n)) )) ))
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(else
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(let loop ((last (car seq)) (next (cdr seq)))
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(or (null? next)
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(and (not (less? (car next) last))
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(loop (car next) (cdr next)) )) )) ))
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;;; (merge a b less?)
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;;; takes two lists a and b such that (sorted? a less?) and (sorted? b less?)
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;;; and returns a new list in which the elements of a and b have been stably
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;;; interleaved so that (sorted? (merge a b less?) less?).
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;;; Note: this does _not_ accept vectors. See below.
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(define (merge a b less?)
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(cond
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((null? a) b)
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((null? b) a)
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(else (let loop ((x (car a)) (a (cdr a)) (y (car b)) (b (cdr b)))
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;; The loop handles the merging of non-empty lists. It has
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;; been written this way to save testing and car/cdring.
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(if (less? y x)
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(if (null? b)
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(cons y (cons x a))
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(cons y (loop x a (car b) (cdr b)) ))
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;; x <= y
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(if (null? a)
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(cons x (cons y b))
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(cons x (loop (car a) (cdr a) y b)) )) )) ))
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;;; (merge! a b less?)
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;;; takes two sorted lists a and b and smashes their cdr fields to form a
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;;; single sorted list including the elements of both.
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;;; Note: this does _not_ accept vectors.
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(define (merge! a b less?)
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(define (loop r a b)
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(if (less? (car b) (car a))
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(begin
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(set-cdr! r b)
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(if (null? (cdr b))
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(set-cdr! b a)
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(loop b a (cdr b)) ))
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;; (car a) <= (car b)
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(begin
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(set-cdr! r a)
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(if (null? (cdr a))
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(set-cdr! a b)
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(loop a (cdr a) b)) )) )
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(cond
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((null? a) b)
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((null? b) a)
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((less? (car b) (car a))
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(if (null? (cdr b))
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(set-cdr! b a)
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(loop b a (cdr b)))
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b)
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(else ; (car a) <= (car b)
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(if (null? (cdr a))
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(set-cdr! a b)
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(loop a (cdr a) b))
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a)))
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;;; (sort! sequence less?)
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;;; sorts the list or vector sequence destructively. It uses a version
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;;; of merge-sort invented, to the best of my knowledge, by David H. D.
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;;; Warren, and first used in the DEC-10 Prolog system. R. A. O'Keefe
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;;; adapted it to work destructively in Scheme.
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(define (sort! seq less?)
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(define (step n)
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(cond
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((> n 2)
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(let* ((j (quotient n 2))
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(a (step j))
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(k (- n j))
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(b (step k)))
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(merge! a b less?)))
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((= n 2)
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(let ((x (car seq))
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(y (cadr seq))
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(p seq))
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(set! seq (cddr seq))
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(if (less? y x) (begin
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(set-car! p y)
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(set-car! (cdr p) x)))
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(set-cdr! (cdr p) '())
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p))
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((= n 1)
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(let ((p seq))
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(set! seq (cdr seq))
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(set-cdr! p '())
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p))
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(else
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'()) ))
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(if (vector? seq)
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(let ((n (vector-length seq))
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(vector seq)) ; save original vector
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(set! seq (vector->list seq)) ; convert to list
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(do ((p (step n) (cdr p)) ; sort list destructively
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(i 0 (+ i 1))) ; and store elements back
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((null? p) vector) ; in original vector
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(vector-set! vector i (car p)) ))
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;; otherwise, assume it is a list
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(step (length seq)) ))
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;;; (sort sequence less?)
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;;; sorts a vector or list non-destructively. It does this by sorting a
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;;; copy of the sequence
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(define (sort seq less?)
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(if (vector? seq)
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(list->vector (sort! (vector->list seq) less?))
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(sort! (append seq '()) less?)))
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