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Some more micro-optimization, proably getting into foolish optimization at this point. Reduced unnecesary copying of variables, performing some calculations used many times outside the loop, added a special check for sequences that start with n.

The line checking for sequences starting with n needs some explanation. It is probably the most obscure.

There are two givens for this algorithm.

  • If ($next == $length) then ($level + 1 == $length).
  • $maxflips DOES NOT get reset between runs.

So: if the first character is n then the minimum $maxflips{n} is $maxflips{n-1} + 1. It is impossible to have a sequence to take less than length - 1 flips, so if $length - 1 is less than $maxflips{n-1} then it impossible for a sequence that starts with n to have more than $maxflips{n-1} + 1. Therefore, no need to check them.

Rather than compare $length to $maxflips + 1, since $level == $length - 1, I save the calculation in the loop and compare $level to $maxflips.

sub fannkuch { my ( $copy, $level, $split ) = ( @_, 0, 1 ); my ( $index, $next ) = ( $level, $level + 1 ); my $length = length($copy); if ($next == $length) { ($index, $split) = ($split - 1, $level); substr($copy, $index, 0) = chop($copy); } do { if ($next == $length) { unless ( ord($copy) == $length and $level < $maxflips ) { my $q = $copy; my ( $k, $flips ); for ( $flips = 0; ( $k = ord( $q ) ) != 1; $flips++ ) +{ substr( $q, 0, $k ) = reverse substr( $q, 0, $k ); } if ( $flips >= $maxflips ) { if ( $flips == $maxflips) { push @max_sequence, $copy; } else { $maxflips = $flips; @max_sequence = ($copy); } } } } else { fannkuch( $copy, $next, $split ); } substr( $copy, $index - 1, 2 ) = reverse substr( $copy, $index + - 1, 2 ); $split = $next if $index == $split; } while $index--; return $maxflips; }

Side by side with your code: It is only about a 4-6% increase, but it is repeatable.

Your sub My sub Pfannkuchen(1) = 0 for: Pfannkuchen(1) = 0 for: 1 1 0.000351 elapsed seconds. 0.000274 elapsed seconds. Pfannkuchen(2) = 1 for: Pfannkuchen(2) = 1 for: 21 21 0.000196 elapsed seconds. 0.00016 elapsed seconds. Pfannkuchen(3) = 2 for: Pfannkuchen(3) = 2 for: 231 231 312 312 0.000275 elapsed seconds. 0.000225 elapsed seconds. Pfannkuchen(4) = 4 for: Pfannkuchen(4) = 4 for: 2413 2413 3142 3142 0.000348 elapsed seconds. 0.000288 elapsed seconds. Pfannkuchen(5) = 7 for: Pfannkuchen(5) = 7 for: 31452 31452 0.000701 elapsed seconds. 0.000634 elapsed seconds. Pfannkuchen(6) = 10 for: Pfannkuchen(6) = 10 for: 365142 365142 415263 415263 416523 416523 456213 456213 564132 564132 0.00376 elapsed seconds. 0.003357 elapsed seconds. Pfannkuchen(7) = 16 for: Pfannkuchen(7) = 16 for: 3146752 3146752 4762153 4762153 0.025629 elapsed seconds. 0.023704 elapsed seconds. Pfannkuchen(8) = 22 for: Pfannkuchen(8) = 22 for: 61578324 61578324 0.226504 elapsed seconds. 0.209445 elapsed seconds. Pfannkuchen(9) = 30 for: Pfannkuchen(9) = 30 for: 615972834 615972834 2.209246 elapsed seconds. 2.088572 elapsed seconds. Pfannkuchen(10) = 38 for: Pfannkuchen(10) = 38 for: 59186210473 59186210473 24.218115 elapsed seconds. 23.077981 elapsed seconds.

In reply to Re^2: Speed/Efficiency tweaks for a fannkuch benchmark script? by thundergnat
in thread Speed/Efficiency tweaks for a fannkuch benchmark script? by thundergnat

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