# Copyright 2012, 2013, 2014 Kevin Ryde
# This file is part of Math-NumSeq.
#
# Math-NumSeq is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-NumSeq is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
package Math::NumSeq::MaxDigitCount;
use 5.004;
use strict;
use List::Util 'max';
use vars '$VERSION', '@ISA';
$VERSION = 71;
use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;
# uncomment this to run the ### lines
#use Smart::Comments;
# use constant name => Math::NumSeq::__('...');
use constant description => Math::NumSeq::__('Maximum count of a given digit in any radix.');
use constant default_i_start => 1;
use constant parameter_info_array =>
[
{
name => 'digit',
share_key => 'digit_0',
type => 'integer',
display => Math::NumSeq::__('Digit'),
default => 0,
minimum => 0,
width => 2,
description => Math::NumSeq::__('Digit to count.'),
},
{
name => 'values_type',
share_key => 'values_type_cr',
type => 'enum',
default => 'count',
choices => ['count','radix'],
choices_display => [Math::NumSeq::__('Count'),
Math::NumSeq::__('Radix')],
description => Math::NumSeq::__('Whether to give the digit count or the radix the count occurs in.'),
},
];
sub characteristic_count {
my ($self) = @_;
return $self->{'values_type'} eq 'count';
}
sub characteristic_value_is_radix {
my ($self) = @_;
return $self->{'values_type'} eq 'radix';
}
use constant characteristic_smaller => 1;
use constant characteristic_integer => 1;
sub values_min {
my ($self) = @_;
if ($self->{'values_type'} eq 'count') {
if ($self->{'digit'} == 1) {
return 1;
}
} else { # values_type=='radix'
return 2;
}
return 0;
}
#------------------------------------------------------------------------------
# cf A033093 number of zeros in triangle of base 2 to n+1
my %oeis_anum;
$oeis_anum{'count'}->[0] = 'A062842'; # max 0s count
$oeis_anum{'count'}->[1] = 'A062843'; # max 1s count
# OEIS-Catalogue: A062842
# OEIS-Catalogue: A062843 digit=1
sub oeis_anum {
my ($self) = @_;
return $oeis_anum{$self->{'values_type'}}->[$self->{'digit'}];
}
#------------------------------------------------------------------------------
sub ith {
my ($self, $i) = @_;
### MaxDigitCount ith(): $i
if (_is_infinite($i)) {
return $i;
}
$i = abs($i);
my $digit = $self->{'digit'};
my $found_count = 0;
my $found_radix = 2;
foreach my $radix (2 .. max($i,2)) {
my $digits = _digit_split($i,$radix); # low to high
### $radix
### $digits
if (@$digits < $found_count) {
last; # fewer digits now than already found
}
my $count = grep {$_ == $digit} @$digits;
if ($count > $found_count) {
$found_count = $count;
$found_radix = $radix;
# all "ddddd" digits, is the maximum possible
# or "X0000" when digit=0 is the maximum possible
if ($count == scalar(@$digits) - ($digit==0)) {
last;
}
}
}
return ($self->{'values_type'} eq 'radix' ? $found_radix : $found_count);
}
sub _digit_split {
my ($n, $radix) = @_;
# ### _digit_split(): $n
my @ret;
while ($n) {
push @ret, $n % $radix;
$n = int($n/$radix);
}
return \@ret; # array[0] low digit
}
sub pred {
my ($self, $value) = @_;
unless ($value == int($value)) {
return 0;
}
if ($self->{'values_type'} eq 'count') {
if ($self->{'digit'} == 1) {
return ($value >= 1);
}
} else { # values_type=='radix'
if ($value == 1) {
return 0;
}
}
return ($value >= 0);
}
1;
__END__
=for stopwords Ryde Math-NumSeq radix Radix
=head1 NAME
Math::NumSeq::MaxDigitCount -- maximum count of a given digit in any radix
=head1 SYNOPSIS
use Math::NumSeq::MaxDigitCount;
my $seq = Math::NumSeq::MaxDigitCount->new (values_type => 'count');
my ($i, $value) = $seq->next;
=head1 DESCRIPTION
This is the maximum count of a given digit which occurs when i is written in
any radix. The default digit is 0.
0, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 1, 1, 1, 4, 3, 3, 2, ...
starting i=1
For example i=15 is 1 because 15 = ternary "120" which has 1 zero, and no
other base has more than that. i is "10" in base i itself so there's always
at least 1 zero, after i=1.
=head2 Radix
Option C<values_type =E<gt> 'radix'> gives the radix where the maximum
occurs,
# values_type => "radix"
2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, ...
If the maximum count occurs in more than one radix the value is the smallest
where it occurs. i=1 has no zeros in any radix and the return is 2 for
binary since the count 0 occurs in that radix.
=head2 Digit
Option C<digit =E<gt> $n> selects another digit to count, for example
# digit => 1
1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 4, 2, 2, 2, 3, ...
For example at i=7 the count is 3 since 7 in binary is "111" with 3 digit
1s.
=head1 FUNCTIONS
See L<Math::NumSeq/FUNCTIONS> for behaviour common to all sequence classes.
=over 4
=item C<$seq = Math::NumSeq::MaxDigitCount-E<gt>new ()>
=item C<$seq = Math::NumSeq::MaxDigitCount-E<gt>new (digit =E<gt> $d, values_type =E<gt> $str)>
Create and return a new sequence object.
=back
=head2 Random Access
=over
=item C<$value = $seq-E<gt>ith($i)>
Return the count or radix for the selected digit when C<$i> is written in
any radix.
=item C<$bool = $seq-E<gt>pred($value)>
Return true if C<$value> occurs in the sequence. This simply means
C<$value> an integer, but excluding 0 when seeking digit=1, or excluding 1
when seeking the radix.
=back
=head1 SEE ALSO
L<Math::NumSeq>,
L<Math::NumSeq::DigitCount>
=head1 HOME PAGE
L<http://user42.tuxfamily.org/math-numseq/index.html>
=head1 LICENSE
Copyright 2012, 2013, 2014 Kevin Ryde
Math-NumSeq is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
=cut