If you run this for larger boards (say 13 or 15, which takes quite some time) then you can easily see the general pattern of solutions you get (7n-3 steps for board size 2n+1 or 2n+2). You could write a program that generates that solution, that way you'd get a simple program to generate a solution that's quite good. If you actually wanted to prove that that solution is optimal, I don't know an algorithm that's much better than this brute force one. You could of course optimize this brute force solution to run a few orders of magnitude faster if you really needed to run it for large boards.

In reply to Re^2: Block-sliding puzzle by ambrus
in thread Block-sliding puzzle by ambrus

Title:
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, details, 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, summary, 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.