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Math::Combinatorics - Perform combinations and permutations on lists
=head1 SYNOPSIS
Available as an object oriented API.
use Math::Combinatorics;
my @n = qw(a b c);
my $combinat = Math::Combinatorics->new(count => 2,
data => [@n],
);
print "combinations of 2 from: ".join(" ",@n)."\n";
print "------------------------".("--" x scalar(@n))."\n";
while(my @combo = $combinat->next_combination){
print join(' ', @combo)."\n";
}
print "\n";
print "permutations of 3 from: ".join(" ",@n)."\n";
print "------------------------".("--" x scalar(@n))."\n";
while(my @permu = $combinat->next_permutation){
print join(' ', @permu)."\n";
}
output:
Or available via exported functions 'permute', 'combine', and 'factorial'.
use Math::Combinatorics;
my @n = qw(a b c);
print "combinations of 2 from: ".join(" ",@n)."\n";
print "------------------------".("--" x scalar(@n))."\n";
print join("\n", map { join " ", @$_ } combine(2,@n)),"\n";
print "\n";
print "permutations of 3 from: ".join(" ",@n)."\n";
print "------------------------".("--" x scalar(@n))."\n";
print join("\n", map { join " ", @$_ } permute(@n)),"\n";
Output:
combinations of 2 from: a b c
------------------------------
a b
a c
b c
permutations of 3 from: a b c
------------------------------
a b c
a c b
b a c
b c a
c a b
c b a
Output from both types of calls is the same, but the object-oriented approach consumes
much less memory for large sets.
=head1 DESCRIPTION
Combinatorics is the branch of mathematics studying the enumeration, combination,
and permutation of sets of elements and the mathematical relations that characterize
their properties. As a jumping off point, refer to:
http://mathworld.wolfram.com/Combinatorics.html
This module provides a pure-perl implementation of nCk, nCRk, nPk, nPRk, !n and n!
(combination, multiset, permutation, string, derangement, and factorial, respectively).
Functional and object-oriented usages allow problems such as the following to be solved:
=over
=item combine - nCk
http://mathworld.wolfram.com/Combination.html
"Fun questions to ask the pizza parlor wait staff: how many possible combinations
of 2 toppings can I get on my pizza?".
=item derange - !n
http://mathworld.wolfram.com/Derangement.html
"A derangement of n ordered objects, denoted !n, is a permutation in which none of the
objects appear in their "natural" (i.e., ordered) place."
=item permute - nPk
http://mathworld.wolfram.com/Permutation.html
"Master Mind Game: ways to arrange pieces of different colors in a
certain number of positions, without repetition of a color".
=back
Object-oriented usage additionally allows solving these problems by calling L</new()>
with a B<frequency> vector:
=over
=item string - nPRk
http://mathworld.wolfram.com/String.html
"Morse signals: diferent signals of 3 positions using the two symbols - and .".
$o = Math::Combinatorics->new( count=>3 , data=>[qw(. -)] , frequency=>[3,3] );
while ( my @x = $o->next_multiset ) {
my $p = Math::Combinatorics->new( data=>\@x , frequency=>[map{1} @x] );
while ( my @y = $p->next_string ) {
#do something
}
}
=item multiset/multichoose - nCRk
http://mathworld.wolfram.com/Multiset.html
"ways to extract 3 balls at once of a bag with 3 black and 3 white balls".
$o = Math::Combinatorics->new( count=>3 , data=>[qw(white black)] , frequency=>[3,3] );
while ( my @x = $o->next_multiset ) {
#do something
}
=back
=head2 EXPORT
the following export tags will bring a single method into the caller's
namespace. no symbols are exported by default. see pod documentation below for
method descriptions.
combine
derange
multiset
permute
string
factorial
=head1 AUTHOR
Allen Day <allenday@ucla.edu>, with algorithmic contributions from Christopher Eltschka and
Tye.
Copyright (c) 2004-2005 Allen Day. All rights reserved. This program is free software; you
can redistribute it and/or modify it under the same terms as Perl itself.
=head1 ACKNOWLEDGEMENTS
A sincere thanks to everyone for helping to make this a better module. After initial
development I've only had time to accept patches and improvements. Math::Combinatorics
continues to be developed and improved by the community. Contributors of note include:
For adding new features: Carlos Rica, David Coppit, Carlos Segre, Lyon Lemmens
For bug reports: Ying Yang, Joerg Beyer, Marc Logghe, Yunheng Wang,
Torsten Seemann, Gerrit Haase, Joern Behre, Lyon Lemmens, Federico Lucifredi
=head1 BUGS / TODO
Report them to the author.
* Need more extensive unit tests.
* tests for new()'s frequency argment
* A known bug (more of a missing feature, actually) does not allow parameterization of k
for nPk in permute(). it is assumed k == n. L</permute()> for details. You can work
around this by making calls to both L</permute()> and L</combine()>
* Lots of really interesting stuff from Mathworld.Wolfram.com. MathWorld rocks! Expect
to see implementation of more concepts from their site, e.g.:
http://mathworld.wolfram.com/BellNumber.html
http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
http://mathworld.wolfram.com/Word.html
* Other combinatorics stuff
http://en.wikipedia.org/wiki/Catalan_number
http://en.wikipedia.org/wiki/Stirling_number
=head1 SEE ALSO
L<Set::Scalar>
L<Set::Bag>
L<String::Combination> (alas misnamed, it actually returns permutations on a string).
http://perlmonks.thepen.com/29374.html
http://groups.google.com/groups?selm=38568F79.13680B86%40physik.tu-muenchen.de&output=gplain
=cut
package Math::Combinatorics;
use strict;
use Data::Dumper;
require Exporter;
our @ISA = qw(Exporter);
our @EXPORT = qw( combine derange factorial permute );
our $VERSION = '0.09';
=head1 EXPORTED FUNCTIONS
=head2 combine()
Usage : my @combinations = combine($k,@n);
Function: implements nCk (n choose k), or n!/(k!*(n-k!)).
returns all unique unorderd combinations of k items from set n.
items in n are assumed to be character data, and are
copied into the return data structure (see "Returns" below).
Example : my @n = qw(a b c);
my @c = combine(2,@n);
print join "\n", map { join " ", @$_ } @c;
# prints:
# b c
# a c
# a b
Returns : a list of arrays, where each array contains a unique combination
of k items from n
Args : a list of items to be combined
Notes : data is internally assumed to be alphanumeric. this is necessary
to efficiently generate combinations of large sets. if you need
combinations of non-alphanumeric data, or on data
C<sort {$a cmp $b}> would not be appropriate, use the
object-oriented API. See L</new()> and the B<compare> option.
Identical items are assumed to be non-unique. That is, calling
C<combine(1,'a','a') yields two sets: {a}, and {a}. See
L</next_multiset() if this is not the desired behavior.
=cut
sub combine {
my($k,@n) = @_;
my @result = ();
my $c = __PACKAGE__->new(data => [@n], count => $k);
while(my(@combo) = $c->next_combination){
push @result, [@combo];
}
return @result;
}
=head2 derange()
Usage : my @deranges = derange(@n);
Function: implements !n, a derangement of n items in which none of the
items appear in their originally ordered place.
Example : my @n = qw(a b c);
my @d = derange(@n);
print join "\n", map { join " ", @$_ } @d;
# prints:
# a c b
# b a c
# b c a
# c a b
# c b a
Returns : a list of arrays, where each array contains a derangement of
k items from n (where k == n).
Args : a list of items to be deranged.
Note : k should really be parameterizable. this will happen
in a later version of the module. send me a patch to
make that version come out sooner.
Notes : data is internally assumed to be alphanumeric. this is necessary
to efficiently generate combinations of large sets. if you need
combinations of non-alphanumeric data, or on data
C<sort {$a cmp $b}> would not be appropriate, use the
object-oriented API. See L</new()>, and the B<compare> option.
=cut
sub derange {
my(@n) = @_;
my @result = ();
my $c = __PACKAGE__->new(data => [@n]);
while(my(@derange) = $c->next_derangement){
push @result, [@derange];
}
return @result;
}
=head2 next_derangement()
Usage : my @derangement = $c->next_derangement();
Function: get derangements for @data.
Returns : returns a permutation of items from @data (see L</new()>),
where none of the items appear in their natural order. repeated calls
retrieve all unique derangements of @data elements. a returned empty
list signifies all derangements have been iterated.
Args : none.
=cut
sub next_derangement {
my $self = shift;
my $data = $self->data();
my $cursor = $self->_permutation_cursor();
my $values = @$cursor;
if($self->{pin}){
$self->{pin} = 0;
my $i;
for ($i = 1; $i < $values; $i += 2) {
$$cursor[$i - 1] = $i;
$$cursor[$i] = $i - 1;
}
if ($values % 2 != 0) {
$$cursor[$values - 1] = $values - 3;
$$cursor[$values - 2] = $values - 1;
}
goto RESULT;
}
else {
my $values = @$cursor;
my $i;
my @found; # stores for each element if it has been found previously
for ($i = 0; $i < $values; $i++) { $found[$i] = 0 }
my $e;
my $elemfound = 0;
for ($i = $values - 1; $i > -1; $i--) {
$found[$$cursor[$i]] = 1;
if ($i > $values - 3) { # $values-1 or $values-2
if ($i == $values - 2) {
#print "i=$i (values-2)\n";##
$e = $$cursor[$i + 1];
if ($e > $$cursor[$i] && $e != $i
&& $$cursor[$i] != $i + 1) {
$$cursor[$i + 1] = $$cursor[$i];
$$cursor[$i] = $e;
#print "!\n";##
goto RESULT;
}
}
next;
}
for ($e = $$cursor[$i] + 1; $e < $values; $e++) {
if ($found[$e] && $e != $i) {
$elemfound = 1;
last;
}
}
last if ($elemfound);
}
if ($elemfound) {
$$cursor[$i] = $e;
$found[$e] = 0;
$i++;
my $j;
my @elems;
for ($j = 0; $j < $values; $j++) {
if ($found[$j]) { push(@elems, $j) }
}
for ($j = 0; $j < @elems; $j++) {
if ($elems[$j] != $i) {
# if the next is the last and it will be wrong:
if ($j + 2 == @elems
&& $elems[$j + 1] == $i + 1) {
# interchange them:
$$cursor[$i] = $elems[$j + 1];
$$cursor[$i + 1] = $elems[$j];
last;
}
$$cursor[$i] = $elems[$j];
}
elsif ($j + 1 < @elems) {
# use the next element:
$$cursor[$i] = $elems[$j + 1];
$elems[$j + 1] = $elems[$j];
}
else { die() }
$i++;
}
goto RESULT;
}
return ();
}
RESULT:
# map cursor to data array
my @result;
foreach my $c (@$cursor){
push @result, $${ $data->[$c] };
}
return @result;
}
=head2 factorial()
Usage : my $f = factorial(4); #returns 24, or 4*3*2*1
Function: calculates n! (n factorial).
Returns : undef if n is non-integer or n < 0
Args : a positive, non-zero integer
Note : this function is used internally by combine() and permute()
=cut
sub factorial {
my $n = shift;
return undef unless $n >= 0 and $n == int($n);
my $f;
for($f = 1 ; $n > 0 ; $n--){
$f *= $n
}
return $f;
}
=head2 permute()
Usage : my @permutations = permute(@n);
Function: implements nPk (n permute k) (where k == n), or n!/(n-k)!
returns all unique permutations of k items from set n
(where n == k, see "Note" below). items in n are assumed to
be character data, and are copied into the return data
structure.
Example : my @n = qw(a b c);
my @p = permute(@n);
print join "\n", map { join " ", @$_ } @p;
# prints:
# b a c
# b c a
# c b a
# c a b
# a c b
# a b c
Returns : a list of arrays, where each array contains a permutation of
k items from n (where k == n).
Args : a list of items to be permuted.
Note : k should really be parameterizable. this will happen
in a later version of the module. send me a patch to
make that version come out sooner.
Notes : data is internally assumed to be alphanumeric. this is necessary
to efficiently generate combinations of large sets. if you need
combinations of non-alphanumeric data, or on data
C<sort {$a cmp $b}> would not be appropriate, use the
object-oriented API. See L</new()>, and the B<compare> option.
Identical items are assumed to be non-unique. That is, calling
C<permute('a','a') yields two sets: {a,a}, and {a,a}. See
L</next_string() if this is not the desired behavior.
=cut
sub permute {
my(@n) = @_;
my @result = ();
my $c = __PACKAGE__->new(data => [@n]);
while(my(@permu) = $c->next_permutation){
push @result, [@permu];
}
return @result;
}
=head1 CONSTRUCTOR
=cut
=head2 new()
Usage : my $c = Math::Combinatorics->new( count => 2, #treated as int
data => [1,2,3,4] #arrayref or anonymous array
);
Function: build a new Math::Combinatorics object.
Returns : a Math::Combinatorics object
Args : count - required for combinatoric functions/methods. number of elements to be
present in returned set(s).
data - required for combinatoric B<AND> permutagenic functions/methods. this is the
set elements are chosen from. B<NOTE>: this array is modified in place; make
a copy of your array if the order matters in the caller's space.
frequency - optional vector of data frequencies. must be the same length as the B<data>
constructor argument. These two constructor calls here are equivalent:
$a = 'a';
$b = 'b';
Math::Combinatorics->new( count=>2, data=>[\$a,\$a,\$a,\$a,\$a,\$b,\$b] );
Math::Combinatorics->new( count=>2, data=>[\$a,\$b], frequency=>[5,2] );
so why use this? sometimes it's useful to have multiple identical entities in
a set (in set theory jargon, this is called a "bag", See L<Set::Bag>).
compare - optional subroutine reference used in sorting elements of the set. examples:
#appropriate for character elements
compare => sub { $_[0] cmp $_[1] }
#appropriate for numeric elements
compare => sub { $_[0] <=> $_[1] }
#appropriate for object elements, perhaps
compare => sub { $_[0]->value <=> $_[1]->value }
The default sort mechanism is based on references, and cannot be predicted.
Improvements for a more flexible compare() mechanism are most welcome.
=cut
sub new {
my($class,%arg) = @_;
my $self = bless {}, $class;
$self->{compare} = $arg{compare} || sub { $_[0] cmp $_[1] };
$self->{count} = $arg{count};
#convert bag to set
my $freq = $arg{frequency};
if(ref($freq) eq 'ARRAY' and scalar(@$freq) == scalar(@{$arg{data}})){
$self->{frequency}++;
my @bag = @{$arg{data}};
my @set = ();
#allow '0 but defined' elements (Yunheng Wang)
foreach my $type ( @bag ) {
my $f = shift @$freq;
next if $f < 1;
for(1..$f){
#we push on a reference to make sure, for instance, that objects
#are identical and not copied
push @set, \$type;
}
}
$arg{data} = \@set;
}
elsif(!ref($freq)){
$arg{data} = [map { \$_ } @{$arg{data}}];
}
#warn join ' ', @{$arg{data}};
#OK, this is hokey, but I don't have time to fix it properly right now.
#We want to allow both user-specified sorting as well as our own
#reference-based internal sorting -- the latter only because unit tests
#are failing if we don't have it. Additionally, we don't want to require
#the triple derefernce necessary for comparison of the pristine data in
#the user-supplied compare coderef. The solution for now is to do an
#if/else. If you're staring at this please fix it!
my $compare = $self->{compare};
if ( defined $arg{compare} ) {
$self->{data} = [sort {&$compare($$$a,$$$b)} map {\$_} @{$arg{data}}];
}
else {
$self->{data} = [sort {&$compare($a,$b)} map {\$_} @{$arg{data}}];
}
#warn Dumper($self->{data});
$self->{cin} = 1;
$self->{pin} = 1;
return $self;
}
=head1 OBJECT METHODS
=cut
=head2 next_combination()
Usage : my @combo = $c->next_combination();
Function: get combinations of size $count from @data.
Returns : returns a combination of $count items from @data (see L</new()>).
repeated calls retrieve all unique combinations of $count elements.
a returned empty list signifies all combinations have been iterated.
Note : this method may only be used if a B<frequency> argument is B<NOT>
given to L</new()>, otherwise use L</next_multiset()>.
Args : none.
=cut
sub next_combination {
my $self = shift;
if ( $self->{frequency} ) {
print STDERR "must use next_multiset() if 'frequency' argument passed to constructor\n";
return ();
}
return $self->_next_combination;
}
sub _next_combination {
my $self = shift;
my $data = $self->data();
my $combo_end = $self->count();
my $begin = 0;
my $end = $#{$data} + 1;
my @result;
return () if scalar(@$data) < $self->count();
if($self->{cin}){
$self->{cin} = 0;
for(0..$self->count-1){
push @result, $${ $data->[$_] };
}
#warn 1;
return @result;
}
if ($combo_end == $begin || $combo_end == $end) {
return ();
}
my $combo = $combo_end;
my $total_set;
--$combo;
$total_set = $self->upper_bound($combo_end,$end,$data->[$combo]);
if ($total_set != $end) {
$self->swap($combo,$total_set);
for(0..$self->count-1){
push @result, $${ $data->[$_] };
}
#warn 2;
return @result;
}
--$total_set;
$combo = $self->lower_bound($begin, $combo_end, $data->[$total_set]);
if ($combo == $begin) {
$self->rotate($begin, $combo_end, $end);
#warn 3;
return ();
}
my $combo_next = $combo;
--$combo;
$total_set = $self->upper_bound($combo_end, $end, $data->[$combo]);
my $sort_pos = $end;
$sort_pos += $combo_end - $total_set - 1;
$self->rotate($combo_next, $total_set, $end);
$self->rotate($combo, $combo_next, $end);
$self->rotate($combo_end, $sort_pos, $end);
for(0..$self->count-1){
push @result, $${ $data->[$_] };
}
#warn 4;
return @result;
}
=head2 next_multiset()
Usage : my @multiset = $c->next_multiset();
Function: get multisets for @data.
Returns : returns a multiset of items from @data (see L</new()>).
a multiset is a special type of combination where the set from which
combinations are drawn contains items that are indistinguishable. use
L</next_multiset()> when a B<frequency> argument is passed to L</new()>.
repeated calls retrieve all unique multisets of @data elements. a
returned empty list signifies all multisets have been iterated.
Note : this method may only be used if a B<frequency> argument is given to
L</new()>, otherwise use L</next_combination()>.
Args : none.
=cut
sub next_multiset {
my $self = shift;
if ( ! $self->{frequency} ) {
print STDERR "must use next_combination() if 'frequency' argument not passed to constructor\n";
return ();
}
my $data = $self->data();
my $compare = $self->compare();
while ( my @combo = $self->_next_combination ) {
my $x = join '', map {scalar($$_)} sort @$data;
my $y = join '', map {scalar($_) } sort @combo;
next if $self->{'cache_multiset'}{$y}++;
return @combo;
}
$self->{'cache_multiset'} = undef;
return ();
}
=head2 next_permutation()
Usage : my @permu = $c->next_permutation();
Function: get permutations of elements in @data.
Returns : returns a permutation of items from @data (see L</new()>).
repeated calls retrieve all unique permutations of @data elements.
a returned empty list signifies all permutations have been iterated.
Note : this method may only be used if a B<frequency> argument is B<NOT>
given to L</new()>, otherwise use L</next_string()>.
Args : none.
=cut
sub next_permutation {
my $self = shift;
if ( $self->{frequency} ) {
print STDERR "must use next_string() if 'frequency' argument passed to constructor\n";
return ();
}
return $self->_next_permutation;
}
sub _next_permutation {
my $self = shift;
my $data = $self->data();
if($self->{pin}){
$self->{pin} = 0;
return map {$$$_} @$data;
}
my $cursor = $self->_permutation_cursor();
my $last= $#{$cursor};
if($last < 1){
return ();
}
# Find last item not in reverse-sorted order:
my $i = $last - 1;
$i-- while 0 <= $i && $cursor->[$i] >= $cursor->[$i+1];
if($i == -1){
return ();
}
# Re-sort the reversely-sorted tail of the list:
@{$cursor}[$i+1..$last] = reverse @{$cursor}[$i+1..$last]
if $cursor->[$i+1] > $cursor->[$last];
# Find next item that will make us "greater":
my $j = $i+1;
$j++ while $cursor->[$i] >= $cursor->[$j];
# Swap:
@{$cursor}[$i,$j] = @{$cursor}[$j,$i];
# map cursor to data array
my @result;
foreach my $c (@$cursor){
push @result, $${ $data->[$c] };
}
return @result;
}
=head2 next_string()
Usage : my @string = $c->next_string();
Function: get strings for @data.
Returns : returns a multiset of items from @data (see L</new()>).
a multiset is a special type of permutation where the set from which
combinations are drawn contains items that are indistinguishable. use
L</next_permutation()> when a B<frequency> argument is passed to L</new()>.
repeated calls retrieve all unique multisets of @data elements. a
returned empty list signifies all strings have been iterated.
Note : this method may only be used if a B<frequency> argument is given to
L</new()>, otherwise use L</next_permutation()>.
Args : none.
=cut
sub next_string {
my $self = shift;
my $data = $self->data();
if ( ! $self->{frequency} ) {
print STDERR "must use next_permutation() if 'frequency' argument not passed to constructor\n";
return ();
}
while ( my @permu = $self->_next_permutation ) {
my $x = join '', map {scalar($$_)} @$data;
my $y = join '', map {scalar($_) } @permu;
next if $self->{'cache_string'}{$y}++;
return @permu;
}
$self->{'cache_string'} = undef;
return ();
}
=head1 INTERNAL FUNCTIONS AND METHODS
=head2 sum()
Usage : my $sum = sum(1,2,3); # returns 6
Function: sums a list of integers. non-integer list elements are ignored
Returns : sum of integer items in arguments passed in
Args : a list of integers
Note : this function is used internally by combine()
=cut
sub sum {
my $sum = 0;
foreach my $i (@_){
$sum += $i if $i == int($i);
}
return $sum;
}
=head2 compare()
Usage : $obj->compare()
Function: internal, undocumented. holds a comparison coderef.
Returns : value of compare (a coderef)
=cut
sub compare {
my($self,$val) = @_;
return $self->{'compare'};
}
=head2 count()
Usage : $obj->count()
Function: internal, undocumented. holds the "k" in nCk or nPk.
Returns : value of count (an int)
=cut
sub count {
my($self) = @_;
return $self->{'count'};
}
=head2 data()
Usage : $obj->data()
Function: internal, undocumented. holds the set "n" in nCk or nPk.
Returns : value of data (an arrayref)
=cut
sub data {
my($self) = @_;
return $self->{'data'};
}
=head2 swap()
internal, undocumented.
=cut
sub swap {
my $self = shift;
my $first = shift;
my $second = shift;
my $data = $self->data();
my $temp = $data->[$first];
$data->[$first] = $data->[$second];
$data->[$second] = $temp;
}
=head2 reverse()
internal, undocumented.
=cut
sub reverse {
my $self = shift;
my $first = shift;
my $last = shift;
my $data = $self->data();
while (1) {
if ($first == $last || $first == --$last) {
return;
} else {
$self->swap($first++, $last);
}
}
}
=head2 rotate()
internal, undocumented.
=cut
sub rotate {
my $self = shift;
my $first = shift;
my $middle = shift;
my $last = shift;
my $data = $self->data();
if ($first == $middle || $last == $middle) {
return;
}
my $first2 = $middle;
do {
$self->swap($first++, $first2++);
if ($first == $middle) {
$middle = $first2;
}
} while ($first2 != $last);
$first2 = $middle;
while ($first2 != $last) {
$self->swap($first++, $first2++);
if ($first == $middle) {
$middle = $first2;
} elsif ($first2 == $last) {
$first2 = $middle;
}
}
}
=head2 upper_bound()
internal, undocumented.
=cut
sub upper_bound {
my $self = shift;
my $first = shift;
my $last = shift;
my $value = shift;
my $compare = $self->compare();
my $data = $self->data();
my $len = $last - $first;
my $half;
my $middle;
while ($len > 0) {
$half = $len >> 1;
$middle = $first;
$middle += $half;
if (&$compare($value,$data->[$middle]) == -1) {
$len = $half;
} else {
$first = $middle;
++$first;
$len = $len - $half - 1;
}
}
return $first;
}
=head2 lower_bound()
internal, undocumented.
=cut
sub lower_bound {
my $self = shift;
my $first = shift;
my $last = shift;
my $value = shift;
my $compare = $self->compare();
my $data = $self->data();
my $len = $last - $first;
my $half;
my $middle;
while ($len > 0) {
$half = $len >> 1;
$middle = $first;
$middle += $half;
if (&$compare($data->[$middle],$value) == -1) {
$first = $middle;
++$first;
$len = $len - $half - 1;
} else {
$len = $half;
}
}
return $first;
}
=head2 _permutation_cursor()
Usage : $obj->_permutation_cursor()
Function: internal method. cursor on permutation iterator order.
Returns : value of _permutation_cursor (an arrayref)
Args : none
=cut
sub _permutation_cursor {
my($self,$val) = @_;
if(!$self->{'_permutation_cursor'}){
my $data = $self->data();
my @tmp = ();
my $i = 0;
push @tmp, $i++ foreach @$data;
$self->{'_permutation_cursor'} = \@tmp;
}
return $self->{'_permutation_cursor'};
}
1;
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