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|
;;;; "priorque.scm" priority queues for Scheme.
;;; Copyright (C) 1992, 1993, 1994, 1995, 1997 Aubrey Jaffer
;
;Permission to copy this software, to modify it, to redistribute it,
;to distribute modified versions, and to use it for any purpose is
;granted, subject to the following restrictions and understandings.
;
;1. Any copy made of this software must include this copyright notice
;in full.
;
;2. I have made no warranty or representation that the operation of
;this software will be error-free, and I am under no obligation to
;provide any services, by way of maintenance, update, or otherwise.
;
;3. In conjunction with products arising from the use of this
;material, there shall be no use of my name in any advertising,
;promotional, or sales literature without prior written consent in
;each case.
;;@code{(require 'priority-queue)}
;;@ftindex priority-queue
;;
;;@noindent
;;This algorithm for priority queues is due to
;;@cite{Introduction to Algorithms}
;;by T. Cormen, C. Leiserson, R. Rivest.
;;1989 MIT Press.
(require 'record)
;; Record type.
(define heap:rtd (make-record-type "heap" '(array size heap<?)))
;; Reference an element.
(define heap:ref
(let ((ra (record-accessor heap:rtd 'array)))
(lambda (a i)
(vector-ref (ra a) (+ -1 i)))))
;; Set an element.
(define heap:set!
(let ((ra (record-accessor heap:rtd 'array)))
(lambda (a i v)
(vector-set! (ra a) (+ -1 i) v))))
;; Exchange two elements.
(define heap:exchange
(let ((aa (record-accessor heap:rtd 'array)))
(lambda (a i j)
(set! i (+ -1 i))
(set! j (+ -1 j))
(let* ((ra (aa a))
(tmp (vector-ref ra i)))
(vector-set! ra i (vector-ref ra j))
(vector-set! ra j tmp)))))
(define heap:heap<? (record-accessor heap:rtd 'heap<?))
(define heap:set-size!
(let ((aa (record-accessor heap:rtd 'array))
(am (record-modifier heap:rtd 'array))
(sm (record-modifier heap:rtd 'size)))
(lambda (a s)
(let ((ra (aa a)))
(if (> s (vector-length ra))
(let ((nra (make-vector (+ s (quotient s 2)))))
(do ((i (+ -1 (vector-length ra)) (+ -1 i)))
((negative? i) (am a nra))
(vector-set! nra i (vector-ref ra i)))))
(sm a s)))))
(define (heap:parent i) (quotient i 2))
(define (heap:left i) (* 2 i))
(define (heap:right i) (+ 1 (* 2 i)))
(define (heap:heapify a i)
(let* ((l (heap:left i))
(r (heap:right i))
(largest (if (and (<= l (heap:length a))
((heap:heap<? a) (heap:ref a i) (heap:ref a l)))
l
i)))
(cond ((and (<= r (heap:length a))
((heap:heap<? a) (heap:ref a largest) (heap:ref a r)))
(set! largest r)))
(cond ((not (= largest i))
(heap:exchange a i largest)
(heap:heapify a largest)))))
;;;; Externals
;;@body
;;Returns a binary heap suitable which can be used for priority queue
;;operations.
(define make-heap
(let ((cstr (record-constructor heap:rtd '(array size heap<?))))
(lambda (pred<?)
(cstr (make-vector 4) 0 pred<?))))
;;@args heap
;;Returns the number of elements in @1.
(define heap-length (record-accessor heap:rtd 'size))
;;@args heap item
;;Inserts @2 into @1. @2 can be inserted multiple
;;times. The value returned is unspecified.
(define (heap-insert! a key)
(define i (+ 1 (heap:length a)))
(heap:set-size! a i)
(do ()
((not (and (> i 1)
((heap:heap<? a) (heap:ref a (heap:parent i)) key))))
(heap:set! a i (heap:ref a (heap:parent i)))
(set! i (heap:parent i)))
(heap:set! a i key))
;;@args heap
;;Returns the item which is larger than all others according to the
;;@var{pred<?} argument to @code{make-heap}. If there are no items in
;;@1, an error is signaled.
(define (heap-extract-max! a)
(if (< (heap:length a) 1)
(slib:error "heap underflow" a))
(let ((max (heap:ref a 1)))
(heap:set! a 1 (heap:ref a (heap:length a)))
(heap:set-size! a (+ -1 (heap:length a)))
(heap:heapify a 1)
max))
;; Internal protect.
(define heap:length heap-length)
|
