1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
|
;;;; "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)))
(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)
|
