Beefy Boxes and Bandwidth Generously Provided by pair Networks
Perl Monk, Perl Meditation
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??
One other thing to notice is that a particular distribution can be identified by a binary string of length equal to one less than the number of categories, and a number of 1-bits equal to one less than the number of columns. Each 0-bit denotes that the next category is in the same column as the prior category, while a 1-bit denotes that the next category begins the next column over. Since the first category is forced into the first column, and the last category is forced into the last column, we get two freebies there.

So the total number of distributions of N categories into M columns is equal to the number of combinations of N-1 things taken M-1 at a time.

Dunno if this helps, but it should keep you from brute forcing more than you need. {grin}

In fact, for your particular dataset (6 categories, 4 columns), you shouldn't need to brute force more than (5 items taken 3 at a time which is) 10 tries.

Wow, that's less than I thought! But it desk checks properly. All you need is a good generating algorithm, and you can brute force this!

-- Randal L. Schwartz, Perl hacker


In reply to •Re: Puzzle: need a more general algorithm by merlyn
in thread Puzzle: need a more general algorithm by Ovid

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!
  • 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
  • Outside of code tags, you may need to use entities for some characters:
            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?
    Username:
    Password:

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

    How do I use this? | Other CB clients
    Other Users?
    Others wandering the Monastery: (4)
    As of 2014-10-24 07:21 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      For retirement, I am banking on:










      Results (130 votes), past polls