Question

我有以下连接列表：

(define routelist
  (list
      (list'a 'b)
      (list'a 'c)
      (list'b 'e)
      (list'b 'f)
      (list'b 'c)
      (list'a 'd)
      (list'e 'f)
      (list'f 'g)))

找到'a和'g之间的路线。此页面显示了Prolog中的解决方案：http://www.anselm.edu/homepage/mmalita/culpro/graf1.html

我可以管理以下解决方案，但它是迭代的：

(define (mainpath routelist start end (outl '()))
  (if (equal? start end)
      (println "Same start and end points.")
  (for ((item routelist)) 
    (when (equal? start (list-ref item 0))
          (set! outl (cons start outl))
          (if (equal? end (list-ref item 1))
              (begin 
                ; PATH FOUND:
                (set! outl (cons end outl))
                (println (reverse outl)))
              (begin 
                (mainpath (rest routelist) (list-ref item 1) end outl)
                (set! outl (rest outl))))))))

(mainpath routelist 'a 'g)

输出：

'(a b e f g)
'(a b f g)

如何在Racket中实现功能性解决方案？

Answer 1

这是一个非常简单的解决方案：

(define (mainpath routelist start end)
  (define (neighbors node)
    (map second (filter (lambda (x) (eq? (first x) node)) routelist)))
  (define (visit node visited)
    (when (not (member node visited))
      (when (eq? node end)
        (println (reverse (cons node visited))))
      (let ((new-visited (cons node visited)))
        (map (lambda (x) (visit x new-visited)) (neighbors node)))))
  (visit start '())
  "No more paths")

这个递归函数，也可以管理带有循环的图形，保存已沿当前路径访问过的节点列表，并在访问了从起始节点可到达的所有节点时停止。当前节点是结束节点时，将打印当前路径。

Answer 2

使用DFS算法就行了。

(define (mainpath routelist start end)
  (letrec ([next-nodes (λ (node)
                        (for/list ([al routelist]
                                   #:when (eq? node (first al)))
                                  (second al)))]
           [path (λ (node vlist)
                   (let ([new-list (cons node vlist)])
                     (when (eq? node end)
                       (println (reverse new-list)))
                     (for ([next (next-nodes node)]
                           #:unless (memq next vlist))
                          (path next new-list))))])
    (path start '())))

寻找Racket中2点之间的路径

2 个答案: