Towers of Hanoi in Scheme (recursive)

问题:

I wrote the following code in scheme today, but the evaluation is wrong. Please don't tell me I suck at programming, I understand that this is a classic recursion problem, but I am having trouble with it:

(define (towers-of-hanoi n source temp dest)
 (if (= n 1)
  (begin (display "Move the disk from ")
         (display source) 
         (display " to " )
         (display dest)
         (newline))
 (begin (towers-of-hanoi (- n 1) source temp dest)
        (display "Move the disk from ") 
        (display source)
        (display " to ")
        (display dest)
        (newline)
  (towers-of-hanoi(- n 1) temp source dest))))

I expected the code to work, and when I debug it I just confuse myself even more. Can anyone help me?

回答1:

In your code, the last recursive call appears to be wrong, and there is a problem with the order of the procedure's parameters. Try this instead:

(define (towers-of-hanoi n source dest temp)
  (if (= n 1)
      (begin 
        (display "Move the disk from ")
        (display source) 
        (display " to " )
        (display dest)
        (newline))
      (begin 
        (towers-of-hanoi (- n 1) source temp dest)
        (display "Move the disk from ") 
        (display source)
        (display " to ")
        (display dest)
        (newline)
        (towers-of-hanoi (- n 1) temp dest source))))

I noticed that you've been asking questions tagged as racket, here's a more idiomatic and shorter version of the same code, for Racket:

(define (towers-of-hanoi n source dest temp)
  (cond [(= n 1)
         (printf "Move the disk from ~a to ~a~n" source dest)]
        [else
         (towers-of-hanoi (sub1 n) source temp dest)
         (printf "Move the disk from ~a to ~a~n" source dest)
         (towers-of-hanoi (sub1 n) temp dest source)]))

Either way, it works as expected:

(towers-of-hanoi 3 "source" "dest" "temp")

Move the disk from source to dest
Move the disk from source to temp
Move the disk from dest to temp
Move the disk from source to dest
Move the disk from temp to source
Move the disk from temp to dest
Move the disk from source to dest