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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;
}
[download]```
\$ time ./abigails.pl
ONE = 435; THREE = 17955; SIX = 820; TEN = 153.
0.06user 0.00system 0:00.07elapsed 83%CPU

\$ time ./mine.pl
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!

-Blake

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