#!/usr/bin/perl -w
# Copyright 2012, 2013, 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 Test;
plan tests => 11;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::GosperSide;
# uncomment this to run the ### lines
#use Smart::Comments '###';
my $path = Math::PlanePath::GosperSide->new;
sub numeq_array {
my ($a1, $a2) = @_;
if (! ref $a1 || ! ref $a2) {
return 0;
}
my $i = 0;
while ($i < @$a1 && $i < @$a2) {
if ($a1->[$i] ne $a2->[$i]) {
return 0;
}
$i++;
}
return (@$a1 == @$a2);
}
my %dxdy_to_dir = ('2,0' => 0,
'1,1' => 1,
'-1,1' => 2,
'-2,0' => 3,
'-1,-1' => 4,
'1,-1' => 5);
# return 0 if X,Y's are straight, 2 if left, 1 if right
sub xy_turn_6 {
my ($prev_x,$prev_y, $x,$y, $next_x,$next_y) = @_;
my $prev_dx = $x - $prev_x;
my $prev_dy = $y - $prev_y;
my $dx = $next_x - $x;
my $dy = $next_y - $y;
my $prev_dir = $dxdy_to_dir{"$prev_dx,$prev_dy"};
if (! defined $prev_dir) { die "oops, unrecognised $prev_dx,$prev_dy"; }
my $dir = $dxdy_to_dir{"$dx,$dy"};
if (! defined $dir) { die "oops, unrecognised $dx,$dy"; }
return ($dir - $prev_dir) % 6;
}
# 0=left, 1=right
sub xy_left_right {
my ($prev_x,$prev_y, $x,$y, $next_x,$next_y) = @_;
my $turn = xy_turn_6 ($prev_x,$prev_y, $x,$y, $next_x,$next_y);
if ($turn == 1) {
return 0; # left;
}
if ($turn == 5) {
return 1; # right;
}
die "unrecognised turn $turn";
}
#------------------------------------------------------------------------------
# A005823 - N ternary no 1s is horizontal segment, either left or right
MyOEIS::compare_values
(anum => 'A005823',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($dx,$dy) = $path->n_to_dxdy($n);
if ($dx == 2 && $dy == 0) {
push @got, $n;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A099450 - Y at N=3^k
MyOEIS::compare_values
(anum => 'A099450',
func => sub {
my ($count) = @_;
my @got;
require Math::BigInt;
for (my $k = Math::BigInt->new(1); @got < $count; $k++) {
my ($x,$y) = $path->n_to_xy(3**$k);
push @got, $y;
}
return \@got;
});
#------------------------------------------------------------------------------
# A189673 - morphism turn 0=left, 1=right, extra initial 0
MyOEIS::compare_values
(anum => 'A189673',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Left');
my @got = (0);
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A189640 - morphism turn 0=left, 1=right, extra initial 0
MyOEIS::compare_values
(anum => 'A189640',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath_object => $path,
turn_type => 'Right');
my @got = (0);
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A060032 - turn 1=left, 2=right as bignums to 3^level
{
my $anum = 'A060032';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
my @got;
if ($bvalues) {
for (my $level = 0; @got < @$bvalues; $level++) {
require Math::BigInt;
my $big = Math::BigInt->new(0);
foreach my $n (1 .. 3**$level) {
my $digit = xy_left_right ($path->n_to_xy($n-1),
$path->n_to_xy($n),
$path->n_to_xy($n+1)) + 1;
$big = 10*$big + $digit;
}
push @got, $big;
}
if (! numeq_array(\@got, $bvalues)) {
MyTestHelpers::diag ("bvalues: ",join(',',@{$bvalues}[0..20]));
MyTestHelpers::diag ("got: ",join(',',@got[0..20]));
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - 0,1 turns");
}
#------------------------------------------------------------------------------
# A062756 - ternary count 1s, is cumulative turn
{
my $anum = 'A062756';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
my @got;
if ($bvalues) {
my $cumulative;
push @got, 0; # bvalues starts with an n=0
for (my $n = $path->n_start + 1; @got < @$bvalues; $n++) {
my $turn = xy_left_right ($path->n_to_xy($n-1),
$path->n_to_xy($n),
$path->n_to_xy($n+1));
$cumulative += ($turn == 0 ? 1 : -1);
push @got, $cumulative;
}
if (! numeq_array(\@got, $bvalues)) {
MyTestHelpers::diag ("bvalues: ",join(',',@{$bvalues}[0..20]));
MyTestHelpers::diag ("got: ",join(',',@got[0..20]));
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - cumulative turn");
}
#------------------------------------------------------------------------------
# A080846 - turn 0=left, 1=right
{
my $anum = 'A080846';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
my @got;
if ($bvalues) {
for (my $n = $path->n_start + 1; @got < @$bvalues; $n++) {
push @got, xy_left_right ($path->n_to_xy($n-1),
$path->n_to_xy($n),
$path->n_to_xy($n+1));
}
if (! numeq_array(\@got, $bvalues)) {
MyTestHelpers::diag ("bvalues: ",join(',',@{$bvalues}[0..20]));
MyTestHelpers::diag ("got: ",join(',',@got[0..20]));
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - turn 0=left,1=right");
}
#------------------------------------------------------------------------------
# A038502 - taken mod 3 is 1=left, 2=right
{
my $anum = 'A038502';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
my @got;
if ($bvalues) {
@$bvalues = map { $_ % 3 } @$bvalues;
for (my $n = $path->n_start + 1; @got < @$bvalues; $n++) {
push @got, xy_left_right ($path->n_to_xy($n-1),
$path->n_to_xy($n),
$path->n_to_xy($n+1)) + 1;
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - taken mod 3 for 0,1 turns");
}
#------------------------------------------------------------------------------
# A026225 - positions of left turns
{
my $anum = 'A026225';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
{
my @got;
if ($bvalues) {
for (my $n = $path->n_start + 1; @got < @$bvalues; $n++) {
if (xy_left_right ($path->n_to_xy($n-1),
$path->n_to_xy($n),
$path->n_to_xy($n+1))
== 0) {
push @got, $n;
}
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - left turns");
}
{
my @got;
if ($bvalues) {
for (my $n = 1; @got < @$bvalues; $n++) {
if (digit_above_low_zeros($n) == 1) {
push @got, $n;
}
}
if (! numeq_array(\@got, $bvalues)) {
MyTestHelpers::diag ("bvalues: ",join(',',@{$bvalues}[0..20]));
MyTestHelpers::diag ("got: ",join(',',@got[0..20]));
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - N where lowest non-zero 1");
}
}
#------------------------------------------------------------------------------
# A026179 - positions of right turns
{
my $anum = 'A026179';
my ($bvalues, $lo, $filename) = MyOEIS::read_values($anum);
{
my @got;
if ($bvalues) {
push @got, 1; # extra 1 ...
for (my $n = $path->n_start + 1; @got < @$bvalues; $n++) {
if (xy_left_right ($path->n_to_xy($n-1),
$path->n_to_xy($n),
$path->n_to_xy($n+1))
== 1) {
push @got, $n;
}
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - right turns");
}
{
my @got = (1);
if ($bvalues) {
for (my $n = 1; @got < @$bvalues; $n++) {
if (digit_above_low_zeros($n) == 2) {
push @got, $n;
}
}
if (! numeq_array(\@got, $bvalues)) {
MyTestHelpers::diag ("bvalues: ",join(',',@{$bvalues}[0..20]));
MyTestHelpers::diag ("got: ",join(',',@got[0..20]));
}
}
skip (! $bvalues,
numeq_array(\@got, $bvalues),
1, "$anum - N where lowest non-zero 2");
}
}
sub digit_above_low_zeros {
my ($n) = @_;
if ($n == 0) {
return 0;
}
while (($n % 3) == 0) {
$n = int($n/3);
}
return ($n % 3);
}
#------------------------------------------------------------------------------
exit 0;