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
|
;; (graph topological-sort) -- topological sorting
;; Written 1995 by Mikael Durfeldt.
;; This file is based on tsort.scm from SLIB, and is in the public domain.
;;; Commentary:
;; The algorithm is inspired by Cormen, Leiserson and Rivest (1990)
;; ``Introduction to Algorithms'', chapter 23.
;;; Code:
(define-module (graph topological-sort)
#:export (topological-sort
topological-sortq
topological-sortv)
#:use-module (math primes))
(define (topological-sort-helper dag insert lookup)
(if (null? dag)
'()
(let* ((adj-table (make-hash-table
(car (primes> (length dag) 1))))
(sorted '()))
(letrec ((visit
(lambda (u adj-list)
;; Color vertex u
(insert adj-table u 'colored)
;; Visit uncolored vertices which u connects to
(for-each (lambda (v)
(let ((val (lookup adj-table v)))
(if (not (eq? val 'colored))
(visit v (or val '())))))
adj-list)
;; Since all vertices downstream u are visited
;; by now, we can safely put u on the output list
(set! sorted (cons u sorted)))))
;; Hash adjacency lists
(for-each (lambda (def)
(insert adj-table (car def) (cdr def)))
(cdr dag))
;; Visit vertices
(visit (caar dag) (cdar dag))
(for-each (lambda (def)
(let ((val (lookup adj-table (car def))))
(if (not (eq? val 'colored))
(visit (car def) (cdr def)))))
(cdr dag)))
sorted)))
(define (topological-sort dag)
"Returns a list of the objects in the directed acyclic graph, @var{dag}, topologically sorted. Objects are
compared using @code{equal?}. The graph has the form:
@lisp
(list (obj1 . (dependents-of-obj1))
(obj2 . (dependents-of-obj2)) ...)
@end lisp
...specifying, for example, that @code{obj1} must come before all the objects in @code{(dependents-of-obj1)} in
the sort."
(topological-sort-helper dag hash-set! hash-ref))
(define (topological-sortq dag)
"Returns a list of the objects in the directed acyclic graph, @var{dag}, topologically sorted. Objects are
compared using @code{eq?}. The graph has the form:
@lisp
(list (obj1 . (dependents-of-obj1))
(obj2 . (dependents-of-obj2)) ...)
@end lisp
...specifying, for example, that @code{obj1} must come before all the objects in @code{(dependents-of-obj1)} in
the sort."
(topological-sort-helper dag hashq-set! hashq-ref))
(define (topological-sortv dag)
"Returns a list of the objects in the directed acyclic graph, @var{dag}, topologically sorted. Objects are
compared using @code{eqv?}. The graph has the form:
@lisp
(list (obj1 . (dependents-of-obj1))
(obj2 . (dependents-of-obj2)) ...)
@end lisp
...specifying, for example, that @code{obj1} must come before all the objects in @code{(dependents-of-obj1)} in
the sort."
(topological-sort-helper dag hashv-set! hashv-ref))
;;; arch-tag: 9ef30b53-688a-43fc-b208-df78d5b38c74
|
