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;;; "tsort.scm" Topological sort
;;; Copyright (C) 1995 Mikael Djurfeldt
;;; This code is in the public domain.
;;; The algorithm is inspired by Cormen, Leiserson and Rivest (1990)
;;; "Introduction to Algorithms", chapter 23
(require 'hash-table)
(require 'primes)
;;@code{(require 'topological-sort)} or @code{(require 'tsort)}
;;@ftindex topological-sort
;;@ftindex tsort
;;@noindent
;;The algorithm is inspired by Cormen, Leiserson and Rivest (1990)
;;@cite{Introduction to Algorithms}, chapter 23.
;;@body
;;@defunx topological-sort dag pred
;;where
;;@table @var
;;@item dag
;;is a list of sublists. The car of each sublist is a vertex. The cdr is
;;the adjacency list of that vertex, i.e. a list of all vertices to which
;;there exists an edge from the car vertex.
;;@item pred
;;is one of @code{eq?}, @code{eqv?}, @code{equal?}, @code{=},
;;@code{char=?}, @code{char-ci=?}, @code{string=?}, or @code{string-ci=?}.
;;@end table
;;
;;Sort the directed acyclic graph @1 so that for every edge from
;;vertex @var{u} to @var{v}, @var{u} will come before @var{v} in the
;;resulting list of vertices.
;;
;;Time complexity: O (|V| + |E|)
;;
;;Example (from Cormen):
;;@quotation
;;Prof. Bumstead topologically sorts his clothing when getting
;;dressed. The first argument to @0 describes which
;;garments he needs to put on before others. (For example,
;;Prof Bumstead needs to put on his shirt before he puts on his
;;tie or his belt.) @0 gives the correct order of dressing:
;;@end quotation
;;
;;@example
;;(require 'tsort)
;;@ftindex tsort
;;(tsort '((shirt tie belt)
;; (tie jacket)
;; (belt jacket)
;; (watch)
;; (pants shoes belt)
;; (undershorts pants shoes)
;; (socks shoes))
;; eq?)
;;@result{}
;;(socks undershorts pants shoes watch shirt belt tie jacket)
;;@end example
(define (tsort dag pred)
(if (null? dag)
'()
(let* ((adj-table (make-hash-table
(car (primes> (length dag) 1))))
(insert (hash-associator pred))
(lookup (hash-inquirer pred))
(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 tsort)
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