#!/usr/bin/perl -w
# Copyright 2010, 2011, 2012, 2013, 2017, 2018 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 => 15;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::Diagonals;
#------------------------------------------------------------------------------
# A057554 -- X,Y successively
MyOEIS::compare_values
(anum => 'A057554',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $x;
if (@got < $count) {
push @got, $y;
}
}
return \@got;
});
# A057555 -- X,Y successively, x_start=1,y_start=1
MyOEIS::compare_values
(anum => 'A057555',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new (x_start=>1, y_start=>1);
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $x;
if (@got < $count) {
push @got, $y;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A057046 -- X at N=2^k
require Math::NumSeq::PlanePathN;
my $bigclass = Math::NumSeq::PlanePathN::_bigint();
{
my $path = Math::PlanePath::Diagonals->new (x_start=>1, y_start=>1);
MyOEIS::compare_values
(anum => 'A057046',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $bigclass->new(1); @got < $count; $n *= 2) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $x;
}
return \@got;
});
# A057047 -- Y at N=2^k
MyOEIS::compare_values
(anum => 'A057047',
func => sub {
my ($count) = @_;
my @got;
for (my $n = $bigclass->new(1); @got < $count; $n *= 2) {
my ($x,$y) = $path->n_to_xy($n);
push @got, $y;
}
return \@got;
});
}
#------------------------------------------------------------------------------
# A185787 -- total N in row up to Y=X diagonal
MyOEIS::compare_values
(anum => 'A185787',
max_count => 1000,
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got;
for (my $y = 0; @got < $count; $y++) {
push @got, path_rect_to_accumulation ($path, 0,$y, $y,$y);
}
return \@got;
});
#------------------------------------------------------------------------------
# A100182 -- total N in column to X=Y leading diagonal
# tetragonal anti-prism numbers (7*n^3 - 3*n^2 + 2*n)/6
MyOEIS::compare_values
(anum => 'A100182',
max_count => 1000,
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got;
for (my $x = 0; @got < $count; $x++) {
push @got, path_rect_to_accumulation ($path, $x,0, $x,$x);
}
return \@got;
});
#------------------------------------------------------------------------------
# A185788 -- total N in row to X=Y-1 before leading diagonal
MyOEIS::compare_values
(anum => 'A185788',
max_count => 1000,
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got = (0);
for (my $y = 1; @got < $count; $y++) {
push @got, path_rect_to_accumulation ($path, 0,$y, $y-1,$y);
}
return \@got;
});
#------------------------------------------------------------------------------
# A101165 -- total N in column up to Y=X-1 before leading diagonal
MyOEIS::compare_values
(anum => 'A101165',
max_count => 1000,
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got = (0);
for (my $x = 1; @got < $count; $x++) {
push @got, path_rect_to_accumulation ($path, $x,0, $x,$x-1);
}
return \@got;
});
#------------------------------------------------------------------------------
# A185506 -- accumulation array, by antidiagonals
# accumulation being total sum N in rectangle 0,0 to X,Y
MyOEIS::compare_values
(anum => 'A185506',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got;
for (my $d = $path->n_start; @got < $count; $d++) {
my ($x,$y) = $path->n_to_xy($d); # by anti-diagonals
push @got, path_rect_to_accumulation($path, 0,0, $x,$y)
}
return \@got;
});
sub path_rect_to_accumulation {
my ($path, $x1,$y1, $x2,$y2) = @_;
# $x1 = round_nearest ($x1);
# $y1 = round_nearest ($y1);
# $x2 = round_nearest ($x2);
# $y2 = round_nearest ($y2);
($x1,$x2) = ($x2,$x1) if $x1 > $x2;
($y1,$y2) = ($y2,$y1) if $y1 > $y2;
my $accumulation = 0;
foreach my $x ($x1 .. $x2) {
foreach my $y ($y1 .. $y2) {
$accumulation += $path->xy_to_n($x,$y);
}
}
return $accumulation;
}
#------------------------------------------------------------------------------
# A103451 -- turn 1=left or right, 0=straight
# but has extra n=1 whereas path first turn at starts N=2
MyOEIS::compare_values
(anum => 'A103451',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'Diagonals',
turn_type => 'LSR');
my @got = (1);
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, abs($value);
}
return \@got;
});
#------------------------------------------------------------------------------
# A103452 -- turn 1=left,0=straight,-1=right
# but has extra n=1 whereas path first turn at starts N=2
MyOEIS::compare_values
(anum => 'A103452',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'Diagonals',
turn_type => 'LSR');
my @got = (1);
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A215200 -- Kronecker(n-k,k) by rows, n>=1 1<=k<=n
# for n=6 runs n-k=5,4,3,2,1,0 for n=1 runs n-k=0
# k=1,2,3,4,5,6 k=1
# x=n-k y=k is diagonal up from X axis
MyOEIS::compare_values
(anum => q{A215200},
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new (direction => 'up',
x_start => 0,
y_start => 1);
require Math::NumSeq::PlanePathCoord;
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy ($n);
push @got, Math::NumSeq::PlanePathCoord::_kronecker_symbol($x,$y);
}
return \@got;
});
#------------------------------------------------------------------------------
# A038722 -- permutation N at transpose Y,X, n_start=1
MyOEIS::compare_values
(anum => 'A038722',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new;
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $path->xy_to_n ($y, $x);
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A038722',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::Diagonals->new (direction => 'up');
my @got;
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $path->xy_to_n ($y, $x);
}
return \@got;
});
#------------------------------------------------------------------------------
# A061579 -- permutation N at transpose Y,X
MyOEIS::compare_values
(anum => 'A061579',
func => sub {
my ($count) = @_;
my @got;
my $path = Math::PlanePath::Diagonals->new (n_start => 0);
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $path->xy_to_n ($y, $x);
}
return \@got;
});
MyOEIS::compare_values
(anum => 'A061579',
func => sub {
my ($count) = @_;
my @got;
my $path = Math::PlanePath::Diagonals->new (n_start => 0,
direction => 'up');
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $path->xy_to_n ($y, $x);
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;