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Re: (Efficiency Golf) Triangular numbers

by blakem (Monsignor)
on May 31, 2001 at 22:30 UTC ( #84685=note: print w/replies, xml ) Need Help??

in reply to (Efficiency Golf) Triangular numbers

Since others are posting, here is my original code. It uses a slightly different tactic, which I hoped would be a bit of an optimization (though I don't think it actually was) When I generate my triangular numbers, I also calculate a "pattern mask", i.e.

THREE => 'abcdd'
55345 => 'aabca'
66456 => 'aabca'
98766 => 'abcdd' (aha, same as THREE's)
So: wordmask('THREE') eq wordmask(98766);

This was supposed to eliminate running repeated regexes against the same numbers. Anyway, it complicates the code a bit and others have submitted faster solutions using the same basic algorithm. Anyway here is the code:

#!/usr/bin/perl use strict; # Calculate some "masks" outside the loops my (%nummasks,%wordmasks); map{my $k=.5*$_*($_+1); $nummasks{$k}=wordmask($k)}1..446; # ok, this +line was tweaked from another poster map{$wordmasks{$_}=wordmask($_)}('ONE','THREE','SIX','TEN'); # Loop through the THREE candidates for my $three (keys %nummasks) { next unless $nummasks{$three} eq $wordmasks{'THREE'}; my @three = split(//,$three); # Loop through the TEN candidates for my $ten (keys %nummasks) { next unless $nummasks{$ten} eq $wordmasks{'TEN'}; my @ten = split(//,$ten); next unless $ten[0] == $three[0] && $ten[1] == $three[3]; my %used = map{$_,1} (@three); next if $used{$ten[2]}; # Loop through the ONE candidates for my $one (keys %nummasks) { next unless $nummasks{$one} eq $wordmasks{'ONE'}; my @one = split(//,$one); next unless $one[1] == $ten[2] && $one[2] == $ten[1]; my %used = map{$_,1} (@three,@ten); next if $used{$one[0]}; # Find a SIX and we've solved it for my $six (keys %nummasks) { next unless $nummasks{$six} eq $wordmasks{'SIX'}; my @six = split(//,$six); my %used = map{$_,1} (@three,@ten,@one); next if $used{$six[0]} || $used{$six[1]} || $used{$six[2]}; print "ONE:\t$one\nTHREE:\t$three\nSIX:\t$six\nTEN:\t$ten\n"; } } } } sub wordmask { # generate a "pattern mask", 56675 => abbca my $mask = shift; my $letter = 'a'; while ($mask =~ /([^a-z])/) { $mask =~ s/$1/$letter/g; $letter++; } return $mask; }
$ time ./
ONE = 435; THREE = 17955; SIX = 820; TEN = 153.
0.06user 0.00system 0:00.07elapsed 83%CPU

$ time ./
ONE: 435 THREE: 17955 SIX: 820 TEN: 153
0.25user 0.01system 0:00.26elapsed 98%CPU

So, Abigail's beats mine by a factor of about 4.5!


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