Beefy Boxes and Bandwidth Generously Provided by pair Networks
Your skill will accomplish
what the force of many cannot

Comment on

( #3333=superdoc: print w/replies, xml ) Need Help??
(Tsts this Limbic~Region sabotaging our work-life balance again! ;)

Some theory:

For a minute I thought this can be trivially solved by counting the normalization of all words (<=8) from the dictionary in a hash... e.g.

DB<211> join "",sort split //,"electron" => "ceelnort" DB<212> join "",sort split //,"elector" => "ceelort"

As next step successively the count from all smaller words had to be added to covering words, e.g striking the "n" from "ceelnort" leads to "ceelort", so $count{ceelnort}+=$count{ceelort}

But than I realized that the best covering word from the dictionary is not necessarily the best solution.

take this counterexample for 3 out of 4 letters, the number showing the coverage-count

1 a 1 b 3 a b 2 a c 2 b c 4 a b d

so the word (a,b,d) is the maximum with a count 4, but the set (a,b,c) would cover 5 words!!!

(yes this also works with repeated letters)

IMHO this problem belongs to the family of Maximum coverage problem and Set_cover_problem, so finding a guarantied best solution shouldn't be trivial w/o brute force.

OTOH adapting the sort order of letters might already lead to very good solutions...

Cheers Rolf

( addicted to the Perl Programming Language)


Maybe you can use the above count hash to solve the dual problem:

"which of the n-8 letters cover the minimum of words" (n including repetition)

E.g. "d" is in only one out of 6 words with 4 letters => the remaining 3 letters cover 5 words.

"c" is only in 2 remaining words => (a,b) cover a maximum of 3 words and so on.

Not sure if this leads to the guarantied best solution, sounds to easy... =)

In reply to Re: Challenge: 8 Letters, Most Words by LanX
in thread Challenge: 8 Letters, Most Words by Limbic~Region

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
    [davido]: I find it annoying when I see "People tend to average between X and Y.", that's not an average, that's a range.
    [Corion]: Ask about the median ;)
    [jdporter]: posts like this one make me realize, ruefully, just how much my mind has deteriorated in recent years/months.
    [jdporter]: "When all your nails look like trolls, all your hammers look like trolls."

    How do I use this? | Other CB clients
    Other Users?
    Others about the Monastery: (9)
    As of 2018-06-21 16:21 GMT
    Find Nodes?
      Voting Booth?
      Should cpanminus be part of the standard Perl release?

      Results (118 votes). Check out past polls.