Beefy Boxes and Bandwidth Generously Provided by pair Networks
go ahead... be a heretic

comment on

( #3333=superdoc: print w/replies, xml ) Need Help??
Another related fun 'n' interesting problem is to start with the disks placed randomly onto the three pegs and then try to sort them all onto one peg. In this version, you are allowed to place any disk onto any other disk (no size restrictions). In fact, a question on a recent algorithms Ph.D qualifying exam here at UIUC was to show that disks can be sorted in O(n log n) moves, and to also show that in fact, &Omega(n log n) moves are required in general. I won't give away how to sort the disks in O(n log n) time, but here's a hint: adapt quicksort.

If we aren't allowed to put larger disks on top of smaller disks (as in the classic example above), you need an exponential number of moves. If T(n) is the number of moves needed to sort n disks, your recursion gives the recurrence T(n) = 2T(n-1). You can verify that T(n) = 2^n.

Towers of Hanoi problems are good examples in that they are easy to visualize, and their relationship to sorting with stacks is obvious.


In reply to Re: Recursion: the Towers of Hanoi problem by blokhead
in thread Recursion: The Towers of Hanoi problem by DigitalKitty

Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":

  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.
  • Log In?

    What's my password?
    Create A New User
    and the web crawler heard nothing...

    How do I use this? | Other CB clients
    Other Users?
    Others meditating upon the Monastery: (3)
    As of 2020-10-21 02:46 GMT
    Find Nodes?
      Voting Booth?
      My favourite web site is:

      Results (212 votes). Check out past polls.