Dear DIY-Monks,

The following is a bit OT, but bear with me please. I need to fit some skirting boards in my house. So I have measured out all the bits of wall and now need to know many pieces of skirting board I need to buy, so that the amount left over once I have completed the work is minimized. This is obviously an example of the general problem of having a set of numbers and trying to find the minimum number of groups, the sum of whose members does not exceed a certain value. I am currently a bit stuck regarding an elegant approach to this problem.

I can conceive of a sort of brute force approach of just trying out a whole bunch of combinations, but there must be a more intelligent way. I assume that the best way could depend of the distribution of the numbers, e.g. whether I have and even spread or, say, large numbers and small numbers with not much in between. On the one hand I am sure some of you can tell me what the proper name of this problem is, so that I can google for information about it more easily. On the other hand, I am sure that some of you have good ideas about how to go about solving the problem in a perly way.

Thanks,

loris

Update: This is homework, but only in the literal, DIY-sense.

"It took Loris ten minutes to eat a satsuma . . . twenty minutes to get from one end of his branch to the other . . . and an hour to scratch his bottom. But Slow Loris didn't care. He had a secret . . ." (from "Slow Loris" by Alexis Deacon)

In reply to "The Skirting Board Problem" by loris

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.