Velocity Reviews > Perl > FAQ 4.51 How do I permute N elements of a list?

# FAQ 4.51 How do I permute N elements of a list?

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 03-06-2011
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4.51: How do I permute N elements of a list?

Use the "List:ermutor" module on CPAN. If the list is actually an
array, try the "Algorithm:ermute" module (also on CPAN). It's written
in XS code and is very efficient:

use Algorithm:ermute;

my @array = 'a'..'d';
my \$p_iterator = Algorithm:ermute->new ( \@array );

while (my @perm = \$p_iterator->next) {
print "next permutation: (@perm)\n";
}

For even faster execution, you could do:

use Algorithm:ermute;

my @array = 'a'..'d';

Algorithm:ermute:ermute {
print "next permutation: (@array)\n";
} @array;

Here's a little program that generates all permutations of all the words
on each line of input. The algorithm embodied in the "permute()"
function is discussed in Volume 4 (still unpublished) of Knuth's *The
Art of Computer Programming* and will work on any list:

#!/usr/bin/perl -n
# Fischer-Krause ordered permutation generator

sub permute (&@) {
my \$code = shift;
my @idx = 0..\$#_;
while ( \$code->(@_[@idx]) ) {
my \$p = \$#idx;
--\$p while \$idx[\$p-1] > \$idx[\$p];
my \$q = \$p or return;
push @idx, reverse splice @idx, \$p;
++\$q while \$idx[\$p-1] > \$idx[\$q];
@idx[\$p-1,\$q]=@idx[\$q,\$p-1];
}
}

permute { print "@_\n" } split;

The "Algorithm::Loops" module also provides the "NextPermute" and
"NextPermuteNum" functions which efficiently find all unique
permutations of an array, even if it contains duplicate values,
modifying it in-place: if its elements are in reverse-sorted order then
the array is reversed, making it sorted, and it returns false; otherwise
the next permutation is returned.

"NextPermute" uses string order and "NextPermuteNum" numeric order, so
you can enumerate all the permutations of 0..9 like this:

use Algorithm::Loops qw(NextPermuteNum);

my @list= 0..9;
do { print "@list\n" } while NextPermuteNum @list;

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