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Re^2: Triangle Numbers Revisited

by Limbic~Region (Chancellor)
on Oct 14, 2004 at 04:54 UTC ( #399106=note: print w/ replies, xml ) Need Help??


in reply to Re: Triangle Numbers Revisited
in thread Triangle Numbers Revisited

FoxtrotUniform,
I couldn't sleep as I had several optimizations pop into my head I just had to try. I played around with caching known triangular numbers as well as results of known non-triangular numbers. I only got a marginal speed increase which I guessed would be the case earlier in the CB. Moving away from caching, I tried a combination of my method and your method with dramatic results:

#!/usr/bin/perl use strict; use warnings; my $file = $ARGV[0] || 'targets.txt'; open (INPUT, '<', $file) or die "Unable to open $file for reading : $! +"; while ( <INPUT> ) { chomp; get_three( $_ ); } sub get_three { my $num = shift; my $prev = p_tri( $num ); return ($num, 0, 0) if ! $prev; while ( $prev ) { my $tri_1 = ($prev * $prev + $prev) / 2; my $target = $num - $tri_1; my $next = gen_tri(); my $tri_2 = $next->(); while ( $tri_2 <= $target / 2 ) { my $tri_3 = $target - $tri_2; return $tri_1, $tri_2, $tri_3 if ! p_tri( $tri_3 ); $tri_2 = $next->(); } --$prev; } die "Something went horribly wrong : $num\n"; } sub p_tri { my $num = shift; my $x = ( sqrt( 8 * $num + 1 ) + 1 )/ 2; my $t = int $x; return $t == $x ? 0 : --$t; } sub gen_tri { my $tri = 0; my $sum; return sub { $sum += $tri++; return $sum }; } __END__ real 0m3.393s user 0m3.344s sys 0m0.050s
From 1 minute to just over 3 seconds.

Cheers - L~R


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