Beefy Boxes and Bandwidth Generously Provided by pair Networks
Syntactic Confectionery Delight
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??

I'm not sure quite how you might take advantage of it for optimisation, but the possible decompositions are restricted by the mod 3 equivalences. That is:

T_n == 1 (mod 3) when n == 1 (mod 3) T_n == 0 (mod 3) otherwise
so if we split the T_n sequence into A_n (== 0) and B_n (== 1) the possible decompositions are restricted such that:
if n == 0 (mod 3), require A A A or B B B if n == 1 (mod 3), require A A B if n == 2 (mod 3), require A B B

You can get similar restrictions by considering other prime moduli, but 3 is likely to be the most beneficial because it has a shorter than possible cycle in T_n.

Also, a word of warning on your p_tri() routine - the final result relies on comparing a floating point number for equality, normally considered a bad idea. It would be preferable to do the test instead by calculating from $t back up to the last known integer value, something like:

sub p_tri { my $num = shift; my $x = 8 * $num + 1; my $t = int((sqrt($x) + 1)/2); return +((2 * $t - 1) * (2 * $t - 1) == $x) ? 0 : --$t; }

Hugo


In reply to Re: Triangle Numbers Revisited by hv
in thread Triangle Numbers Revisited by Limbic~Region

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
  • 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?
    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 meditating upon the Monastery: (8)
    As of 2015-07-28 06:21 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      The top three priorities of my open tasks are (in descending order of likelihood to be worked on) ...









      Results (252 votes), past polls