#!/usr/bin/perl -w
# Copyright 2014 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 List::Util 'min','max';
use Test;
plan tests => 87;
use lib 't';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use lib 'xt';
use MyOEIS;
use Memoize;
# uncomment this to run the ### lines
# use Smart::Comments;
use Math::PlanePath::HilbertCurve;
my $path = Math::PlanePath::HilbertCurve->new;
#------------------------------------------------------------------------------
# count of segments by direction claimed in the POD
{
my %want = ('0,1' => [ 0, 1, 4, 19, 64, 271, 1024, 4159, 16384, ], # dir=1=N
'1,0' => [ 0, 1, 5, 16, 71, 256, 1055, 4096, 16511, ], # dir=2=E
'0,-1' => [ 0, 0, 4, 12, 64, 240, 1024, 4032, 16384, ], # dir=3=S
'-1,0' => [ 0, 1, 2, 16, 56, 256, 992, 4096, 16256, ], # dir=4=W
);
my %count = ('0,1' => 0,
'1,0' => 0,
'0,-1' => 0,
'-1,0' => 0);
my $n = 0;
foreach my $k (0 .. $#{$want{'0,1'}}) {
my $n_end = 4**$k-1;
while ($n < $n_end) {
my ($dx,$dy) = $path->n_to_dxdy($n++);
$count{"$dx,$dy"}++;
### count: "n=$n $dx,$dy"
}
### count now: "$count{'0,1'}, $count{'1,0'} $count{'0,-1'} $count{'-1,0'}"
foreach my $dxdy (keys %want) {
my $pod = $want{$dxdy}->[$k];
my $count = $count{$dxdy};
ok ($pod, $count, "$dxdy samples");
my $func = c_func($dxdy,$k);
ok ($func, $count, "$dxdy func=$func count=$count");
}
}
}
sub c_func {
my ($dxdy, $k) = @_;
if ($dxdy eq '0,1') { # dir=1=N
if ($k == 0) { return 0; }
if ($k % 2) { return 4**($k-1) + 2**($k-1) - 1; }
return 4**($k-1);
}
if ($dxdy eq '1,0') { # dir=2=E
if ($k == 0) { return 0; }
if ($k % 2) { return 4**($k-1); }
return 4**($k-1) + 2**($k-1) - 1;
}
if ($dxdy eq '0,-1') { # dir=3=S
if ($k == 0) { return 0; }
if ($k % 2) { return 4**($k-1) - 2**($k-1); }
return 4**($k-1);
}
if ($dxdy eq '-1,0') { # dir=4=W
if ($k == 0) { return 0; }
if ($k % 2) { return 4**($k-1); }
return 4**($k-1) - 2**($k-1);
}
}
#------------------------------------------------------------------------------
exit 0;