The EIS reference is the best definition: "a rook must land on each square exactly once, but may start and end anywhere and may intersect it's own path". (For the non-chess players, the rook may move from a given square to any other square in the same row or the same column.)

The data structure I'm using takes advantage of the fact that any given position is equivalent to one in which rows and/or columns are arbitrarily reordered, in an attempt to maximise the benefits of memoizing calculated values; the rearrange() function under discussion is trying to do precisely that reordering.

I don't know enough graph theory to guess whether a graph-based approach would gain me anything; I think I'm happy with my data structure (though there may well be a better way), but I understand it rather better than I've been able to explain it so far.

Hugo

In reply to Re^4: better algorithm: bitwise reordering by hv
in thread better algorithm: bitwise reordering by hv

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.