#!/usr/bin/perl -w
# Copyright 2010, 2011, 2012, 2013 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath 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-PlanePath 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-PlanePath. If not, see <http://www.gnu.org/licenses/>.
use 5.004;
use strict;
use Test;
plan tests => 10;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::CoprimeColumns;
# uncomment this to run the ### lines
# use Smart::Comments '###';
my $path = Math::PlanePath::CoprimeColumns->new;
#------------------------------------------------------------------------------
# A127368 - Y coordinate of coprimes, 0 for non-coprimes
{
my $anum = 'A127368';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
my $good = 1;
my $count = 0;
if ($bvalues) {
my $x = 1;
my $y = 1;
for (my $i = 0; $i < @$bvalues; $i++) {
my $want = $bvalues->[$i];
my $got = (Math::PlanePath::CoprimeColumns::_coprime($x,$y)
? $y : 0);
if ($got != $want) {
MyTestHelpers::diag ("wrong _coprime($x,$y)=$got want=$want at i=$i of $filename");
$good = 0;
}
$y++;
if ($y > $x) {
$x++;
$y = 1;
}
$count++;
}
}
ok ($good, 1, "$anum count $count");
}
MyOEIS::compare_values
(anum => q{A127368},
func => sub {
my ($count) = @_;
my @got;
OUTER: for (my $x = 1; ; $x++) {
foreach my $y (1 .. $x) {
if ($path->xy_is_visited($x,$y)) {
push @got, $y;
} else {
push @got, 0;
}
last OUTER if @got >= $count;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A179594 - column of nxn unvisited block
# is X here but Y in A179594 since it goes as rows of coprimes rather than
# columns
MyOEIS::compare_values
(anum => 'A179594',
max_count => 3,
func => sub {
my ($count) = @_;
my @got;
my $x = 1;
for (my $size = 1; @got < $count; $size++) {
for ( ; ! have_unvisited_square($x,$size); $x++) {
}
push @got, $x;
}
return \@got;
});
# return true if there's a $size by $size unvisited square somewhere in
# column $x
sub have_unvisited_square {
my ($x, $size) = @_;
### have_unvisited_square(): $x,$size
my $count = 0;
foreach my $y (2 .. $x) {
if (have_unvisited_line($x,$y,$size)) {
$count++;
if ($count >= $size) {
### found at: "x=$x, y=$y count=$count"
return 1;
}
} else {
$count = 0;
}
}
return 0;
}
# return true if $x,$y is the start (the leftmost point) of a $size length
# line of unvisited points
sub have_unvisited_line {
my ($x,$y, $size) = @_;
foreach my $i (0 .. $size-1) {
if ($path->xy_is_visited($x,$y)) {
return 0;
}
$x++;
}
return 1;
}
#------------------------------------------------------------------------------
# A002088 - totient sum along X axis, or diagonal of n_start=1
MyOEIS::compare_values
(anum => 'A002088',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::CoprimeColumns->new (n_start => 1);
my @got = (0, 1);
for (my $x = 2; @got < $count; $x++) {
push @got, $path->xy_to_n($x,$x-1);
}
return \@got;
});
MyOEIS::compare_values
(anum => qq{A002088},
func => sub {
my ($count) = @_;
my @got;
for (my $x = 1; @got < $count; $x++) {
push @got, $path->xy_to_n($x,1);
}
return \@got;
});
#------------------------------------------------------------------------------
# A054428 - inverse, permutation SB N -> coprime columns N
MyOEIS::compare_values
(anum => 'A054428',
func => sub {
my ($count) = @_;
my @got;
require Math::PlanePath::RationalsTree;
my $sb = Math::PlanePath::RationalsTree->new (tree_type => 'SB');
for (my $n = 0; @got < $count; $n++) {
my $sn = insert_second_highest_bit_one($n);
my ($x,$y) = $sb->n_to_xy ($sn);
### sb: "$x/$y"
my $cn = $path->xy_to_n($x,$y);
if (! defined $cn) {
die "oops, SB $x,$y";
}
push @got, $cn+1;
}
return \@got;
});
sub insert_second_highest_bit_one {
my ($n) = @_;
my $str = sprintf ('%b', $n);
substr($str,1,0) = '1';
return oct("0b$str");
}
# # ### assert: delete_second_highest_bit(1) == 1
# # ### assert: delete_second_highest_bit(2) == 1
# ### assert: delete_second_highest_bit(4) == 2
# ### assert: delete_second_highest_bit(5) == 3
#------------------------------------------------------------------------------
# A054427 - permutation coprime columns N -> SB N
MyOEIS::compare_values
(anum => 'A054427',
func => sub {
my ($count) = @_;
my @got;
require Math::PlanePath::RationalsTree;
my $sb = Math::PlanePath::RationalsTree->new (tree_type => 'SB');
my $n = 0;
while (@got < $count) {
my ($x,$y) = $path->n_to_xy ($n++);
### frac: "$x/$y"
my $sn = $sb->xy_to_n($x,$y);
push @got, delete_second_highest_bit($sn) + 1;
}
return \@got;
});
sub delete_second_highest_bit {
my ($n) = @_;
my $bit = 1;
my $ret = 0;
while ($bit <= $n) {
$ret |= ($n & $bit);
$bit <<= 1;
}
$bit >>= 1;
$ret &= ~$bit;
$bit >>= 1;
$ret |= $bit;
# ### $ret
# ### $bit
return $ret;
}
# ### assert: delete_second_highest_bit(1) == 1
# ### assert: delete_second_highest_bit(2) == 1
### assert: delete_second_highest_bit(4) == 2
### assert: delete_second_highest_bit(5) == 3
#------------------------------------------------------------------------------
# A121998 - list of <=k with a common factor
MyOEIS::compare_values
(anum => 'A121998',
func => sub {
my ($count) = @_;
my @got;
OUTER: for (my $x = 2; ; $x++) {
for (my $y = 1; $y <= $x; $y++) {
if (! $path->xy_is_visited($x,$y)) {
push @got, $y;
last OUTER unless @got < $count;
}
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A054521 - by columns 1 if coprimes, 0 if not
{
my $anum = 'A054521';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
{
my $good = 1;
my $count = 0;
if ($bvalues) {
my $x = 1;
my $y = 1;
for (my $i = 0; $i < @$bvalues; $i++) {
my $want = $bvalues->[$i];
my $got = (Math::PlanePath::CoprimeColumns::_coprime($x,$y)
? 1 : 0);
if ($got != $want) {
MyTestHelpers::diag ("wrong _coprime($x,$y)=$got want=$want at i=$i of $filename");
$good = 0;
}
$y++;
if ($y > $x) {
$x++;
$y = 1;
}
$count++;
}
}
ok ($good, 1, "$anum count $count");
}
}
MyOEIS::compare_values
(anum => q{A054521},
func => sub {
my ($count) = @_;
my @got;
OUTER: for (my $x = 1; ; $x++) {
foreach my $y (1 .. $x) {
if ($path->xy_is_visited($x,$y)) {
push @got, 1;
} else {
push @got, 0;
}
last OUTER if @got >= $count;
}
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;