Re: Triangle Numbers Revisited

[TedPride]

EDIT: For some reason, a few numbers such as 1035 are causing errors (Can't take sqrt of -1, <STDIN> line 1.) Going to have to hunt down the bug and fix it...

EDIT: Just needed a slight change to the first line after BING to prevent tget calls for 0:

use strict;
use warnings;

my ($i, $j, $inum, $jnum, $left);

$| = 1; print "Enter the number to check : ";
my $inp = <STDIN>;

BING:
for ($i = tget($inp-2); $i; $i--) {
    $inum = tmake($i);
    $left = tget($inp - $inum - 1) + 1;
    for ($j = 1; $j < $left; $j++) {
        $jnum = tmake($j);
        last BING if (tis($inp - $inum - $jnum));
    }
}
print "       Your triangles are : $inum $jnum "
      . ($inp - $inum - $jnum) . "\n";

sub tget { return int(sqrt(1 + $_[0] * 2) - .5); }
sub tmake { return (.5 * $_[0] * ($_[0] + 1)); }
sub tis { my $n = shift; return ($n == tmake(tget($n))); }

Incidently, I ran a looped version of this for all numbers 3-100000, and only the following could not be made with sums of three triangles:

4, 6, 11, 20, 29

As far as I can tell, all integers after 29 can be made with at least one sum of three triangles. The number of sums increases as you go along.

[Limbic~Region]

TedPride,
Good catch! I didn't have time to track it down myself this morning as I was supposed to be getting ready for work. For the purposes of the original thread, it appears that 0 was being allowed as a triangular number. With that allowance, all numbers can indeed be the sum of 3 triangles.

As far as speed, you are right that this is quite fast. If it was not fast enough in a real problem you would likely use C as tachyon, the cheater, did ;-)
I have no idea about how to figure out the big O of either solution, but I did want to mention that my solution is more than a constant factor faster in case you decided to spend the time optimizing. At 5_000 random targets between 1 and 5_000_000 it was twice as fast, but for 10_000 random targets between 1 and 987_654_321 it was three times as fast. I didn't want to come off as offensive - I just like silly challenges like this.