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.

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;
}

[download]

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.

[download]

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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