I can obtain a modest (< 10%) but consistent speedup by modifying the permutation generator so that it doesn't even generate sequences that would fail the extended precheck. Like this:
sub fannkuch {
my ( $a, $level, $split ) = ( @_, 0, 1 );
my ( $index, $ok, $copy ) = ( $level, $level + 1 == length( $a ),
+$a );
if ($ok) {
# print "Before munging: ($split) ", unpack('C*', $copy);
$index = $split - 1;
substr($copy, $index, 0) = chop($copy);
}
do {
if ($ok) {
# print "($split) ", unpack('C*', $copy);
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, 1 + $level, $split );
$split = $level + 1 if $index == $split;
}
substr( $copy, $index - 1, 2 ) = reverse substr( $copy, $index
+ -1, 2 );
} while $index--;
return $maxflips;
}
The idea is that
$split is the smallest positive number for which all the elements in
substr($copy, 0, $split) are less than or equal to
$split.
This table shows a few examples:
sequence | $split |
15342 | 1 |
21345 | 2 |
23145 | 3 |
23415 | 4 |
31425 | 4 |
31542 | 5 |
(The commented-out debugging statements may make it easier to follow what's going on. They certainly helped me to understand it as I was writing it.)
On each top-level run (i.e. where $ok is true) we can skip directly to the first permutation where the moving element (which starts out as the last one in the list) has passed the split-point.
I've also reordered the maxflips logic, which gives an additional small improvement.
On an unloaded Linux PC, I get the following results. This is the output from diff --side-by-side -W 80, with the output from BrowserUk's code on the left, and mine on the right:
[rpc142: /tmp]$ diff --side-by-side -W 80 fann-char-orig.out fann-char
+.out
Pfannkuchen(1) = 0 for: Pfannkuchen(1) = 0 for:
8.7e-05 elapsed seconds. | 1
> 0.000118 elapsed seconds.
Pfannkuchen(2) = 1 for: Pfannkuchen(2) = 1 for:
21 21
7.7e-05 elapsed seconds. | 6.4e-05 elapsed seconds.
Pfannkuchen(3) = 2 for: Pfannkuchen(3) = 2 for:
231 231
312 312
0.000134 elapsed seconds. | 0.000133 elapsed seconds.
Pfannkuchen(4) = 4 for: Pfannkuchen(4) = 4 for:
2413 2413
3142 3142
0.000307 elapsed seconds. | 0.000281 elapsed seconds.
Pfannkuchen(5) = 7 for: Pfannkuchen(5) = 7 for:
31452 31452
0.001292 elapsed seconds. | 0.001164 elapsed seconds.
Pfannkuchen(6) = 10 for: Pfannkuchen(6) = 10 for:
365142 365142
415263 415263
416523 416523
456213 456213
564132 564132
0.008305 elapsed seconds. | 0.007341 elapsed seconds.
Pfannkuchen(7) = 16 for: Pfannkuchen(7) = 16 for:
3146752 3146752
4762153 4762153
0.062369 elapsed seconds. | 0.056875 elapsed seconds.
Pfannkuchen(8) = 22 for: Pfannkuchen(8) = 22 for:
61578324 61578324
0.541676 elapsed seconds. | 0.498606 elapsed seconds.
Pfannkuchen(9) = 30 for: Pfannkuchen(9) = 30 for:
615972834 615972834
5.347029 elapsed seconds. | 4.943895 elapsed seconds.
Pfannkuchen(10) = 38 for: Pfannkuchen(10) = 38 for:
59186210473 59186210473
58.118665 elapsed seconds. | 54.24672 elapsed seconds.