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# Integer::Partition.pm |
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# |
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# Copyright (c) 2007-2013 David Landgren |
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# All rights reserved |
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package Integer::Partition; |
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use strict; |
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use warnings; |
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use vars qw/$VERSION/; |
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$VERSION = '0.05'; |
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=head1 NAME |
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Integer::Partition - Generate all integer partitions of an integer |
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=head1 VERSION |
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This document describes version 0.05 of Integer::Partition, released |
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2013-06-23. |
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=head1 SYNOPSIS |
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use Integer::Partition; |
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my $i = Integer::Partition->new(4); |
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while (my $p = $i->next) { |
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print join( ' ', @$p ), $/; |
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} |
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# produces |
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4 |
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3 1 |
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2 2 |
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2 1 1 |
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1 1 1 1 |
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my $j = Integer::Partition->new(5, {lexicographic => 1}); |
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while (my $p = $j->next) { |
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print join( ' ', @$p ), $/; |
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} |
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# produces |
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1 1 1 1 1 |
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2 1 1 1 |
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2 2 1 |
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3 1 1 |
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3 2 |
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4 1 |
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=head1 DESCRIPTION |
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C takes an integer number and produces an object |
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that can be used to generate all possible integer partitions of the |
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original number in either forward or reverse lexicographic order. |
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=head1 METHODS |
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=over 8 |
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=item new |
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Creates a new C object. Takes an integer as a |
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parameter. By default, the partitions appear in reverse order, as |
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the algorithm is slightly faster. Forward ordering uses a different, |
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slightly slower algorithm (which is nonetheless much faster than |
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any existing algorithm). |
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=cut |
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sub new { |
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1
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my $class = shift; |
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my $n = shift; |
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if (!defined $n) { |
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require Carp; |
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Carp::croak("missing or undefined input"); |
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} |
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elsif ($n =~ /\D/ or $n < 1) { |
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require Carp; |
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Carp::croak("$n is not a positive integer"); |
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} |
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elsif ($n != int($n)) { |
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require Carp; |
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Carp::croak("$n is not an integer"); |
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} |
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my $arg = shift; |
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my $forward = 0; |
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if (defined $arg and ref($arg) eq 'HASH' and exists $arg->{lexicographic}) { |
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$forward = $arg->{lexicographic}; |
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} |
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my @x; |
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if ($forward) { |
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@x = (1) x ($n+1); |
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$x[0] = -1; |
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} |
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else { |
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@x = (1) x $n; |
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$x[0] = $n; |
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} |
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my $self = { |
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n => $n, |
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x => \@x, |
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h => $forward ? 1 : 0, |
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m => $forward ? $n - 1 : 0, |
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count => 0, |
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forward => $forward, |
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}; |
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return bless $self, $class; |
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} |
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=item next |
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Returns the partition, or C when all partitions have been |
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generated. |
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=cut |
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sub next { |
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1
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my $self = shift; |
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if ($self->{forward}) { |
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if (++$self->{count} == 1) { |
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return [@{$self->{x}}[1..$self->{n}]]; |
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} |
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elsif ($self->{x}[1] == $self->{n}) { |
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return; |
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} |
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elsif ($self->{count} == 2) { |
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$self->{x}[1] = 2; |
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return [@{$self->{x}}[1..$self->{n}-1]]; |
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} |
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else { |
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if ($self->{m} - $self->{h} > 1) { |
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$self->{x}[++$self->{h}] = 2; |
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--$self->{m}; |
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} |
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else { |
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my $j = $self->{m} - 2; |
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while ($self->{x}[$j] == $self->{x}[$self->{m}-1]) { |
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$self->{x}[$j--] = 1; |
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} |
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$self->{h} = $j + 1; |
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$self->{x}[$self->{h}] = $self->{x}[$self->{m}-1] + 1; |
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my $r = $self->{x}[$self->{m}] |
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+ $self->{x}[$self->{m} - 1] * ($self->{m} - $self->{h} - 1); |
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$self->{x}[$self->{m}] = 1; |
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$self->{x}[$self->{m}-1] = 1 if $self->{m} - $self->{h} > 1; |
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$self->{m} = $self->{h} + $r - 1; |
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} |
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return [@{$self->{x}}[1..$self->{m}]]; |
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} |
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} |
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return [$self->{n}] unless $self->{count}++; |
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return if $self->{x}[0] == 1; |
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if ($self->{x}[$self->{h}] == 2) { |
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++$self->{m}; |
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$self->{x}[$self->{h}--] = 1; |
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} |
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else { |
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my $r = $self->{x}[$self->{h}] - 1; |
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$self->{x}[$self->{h}] = $r; |
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263
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my $t = $self->{m} - $self->{h} + 1; |
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while ($t >= $r) { |
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$self->{x}[++$self->{h}] = $r; |
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$t -= $r; |
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} |
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$self->{m} = $self->{h} + ($t ? 1 : 0); |
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$t > 1 and $self->{x}[++$self->{h}] = $t; |
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} |
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return [@{$self->{x}}[0..$self->{m}]]; |
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} |
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=item reset |
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Resets the object, which causes it to enumerate the arrangements from the |
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beginning. |
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182
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$p->reset; # begin again |
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184
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=cut |
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186
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sub reset { |
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19
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1
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5795
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my $self = shift; |
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191
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my $n = $self->{n}; |
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24
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my @x; |
190
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100
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if ($self->{forward}) { |
191
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9
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@x = (1) x ($n+1); |
192
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$x[0] = -1; |
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} |
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else { |
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@x = (1) x $n; |
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$x[0] = $n; |
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} |
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$self->{x} = \@x; |
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$self->{m} = $self->{forward} ? $n - 1 : 0, |
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100
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200
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$self->{h} = $self->{forward} ? 1 : 0, |
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$self->{count} = 0; |
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43
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return $self; |
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} |
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205
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=back |
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207
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=head1 DIAGNOSTICS |
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209
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=head2 missing or undefined input |
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211
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The C method was called without an input parameter, which |
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should be a positive integer. |
213
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214
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=head2 C is not a positive integer |
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The C method was called with zero or a negative integer. |
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=head2 C is not an integer |
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The C method was called with a number containing a decimal |
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component. Use C or C on the input if necessary. |
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=head1 NOTES |
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This module implements the Zoghbi and Stojmenovic ZS1 and ZS2 |
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algorithms for generating integer partitions. See |
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L for more |
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information. These algorithms have been proven to have constant |
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average delay, that is, the amount of effort it takes to produce |
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the next result in the series. |
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They are the fastest known algorithms known for generating integer |
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partitions (with the ZS1 reverse lexicographic order algorithm being |
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slightly faster than the ZS2 lexicographic order algorithm). |
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=head1 SEE ALSO |
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=over 8 |
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=item * |
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L |
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The Wikipedia entry on integer partitions |
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=item * |
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L |
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The original 1998 paper written by Zoghbi and Stojmenovic. |
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=back |
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=head1 BUGS |
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None known. |
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Please report all bugs at |
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Make sure you include the output from the following two commands: |
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perl -MInteger::Partition -le 'print $Integer::Partition::VERSION' |
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perl -V |
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Pull requests on Github may be issued at |
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L. |
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=head1 ACKNOWLEDGEMENTS |
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Thanks to Antoine Zoghbi and Ivan Stojmenovic, for sharing their |
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discovery with the world on the internet, and not hiding it in |
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behind some sort of pay-wall. |
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=head1 AUTHOR |
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David Landgren, copyright (C) 2007-2013. All rights reserved. |
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http://www.landgren.net/perl/ |
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If you (find a) use this module, I'd love to hear about it. If you |
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want to be informed of updates, send me a note. You know my first |
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name, you know my domain. Can you guess my e-mail address? |
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=head1 LICENSE |
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This library is free software; you can redistribute it and/or modify |
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it under the same terms as Perl itself. |
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=cut |
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'The Lusty Decadent Delights of Imperial Pompeii'; |
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__END__ |