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#!/usr/bin/perl -w
# Copyright 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/>.
# Usage: perl rationals-tree.pl
#
# Print the RationalsTree paths in tree form.
#
use 5.004;
use strict;
use List::Util 'max';
use Math::PlanePath::RationalsTree;
use Math::PlanePath::FractionsTree;
sub print_as_fractions {
my ($path) = @_;
my $n = $path->n_start;
foreach (1) {
my ($x,$y) = $path->n_to_xy($n++);
print centre("$x/$y",64);
}
print "\n";
print " /------------- -------------\\\n";
foreach (1 .. 2) {
my ($x,$y) = $path->n_to_xy($n++);
print centre("$x/$y",32);
}
print "\n";
print " /---- ----\\ /---- ----\\\n";
foreach (1 .. 4) {
my ($x,$y) = $path->n_to_xy($n++);
print centre("$x/$y",16);
}
print "\n";
print " / \\ / \\ / \\ / \\\n";
foreach (1 .. 8) {
my ($x,$y) = $path->n_to_xy($n++);
print centre("$x/$y",8);
}
print "\n";
print " / \\ / \\ / \\ / \\ / \\ / \\ / \\ / \\\n";
foreach (16 .. 31) {
my ($x,$y) = $path->n_to_xy($n++);
print centre("$x/$y",4);
}
print "\n";
print "\n";
}
sub centre {
my ($str, $width) = @_;
my $extra = max (0, $width - length($str));
my $left = int($extra/2);
my $right = $extra - $left;
return ' 'x$left . $str . ' 'x$right;
}
sub xy_to_cfrac_str {
my ($x,$y) = @_;
my @quotients;
while ($x > 0 && $y > 0) {
push @quotients, int($x/$y);
$x %= $y;
($x,$y) = ($y,$x);
}
return "[".join(',',@quotients)."]";
}
sub print_as_cfracs {
my ($path) = @_;
my $n = $path->n_start;
foreach (1) {
my ($x,$y) = $path->n_to_xy($n++);
print centre(xy_to_cfrac_str($x,$y), 72);
}
print "\n";
print " /--------------- ---------------\\\n";
foreach (1 .. 2) {
my ($x,$y) = $path->n_to_xy($n++);
print centre(xy_to_cfrac_str($x,$y), 36);
}
print "\n";
print " /----- -----\\ /----- -----\\\n";
foreach (1 .. 4) {
my ($x,$y) = $path->n_to_xy($n++);
print centre(xy_to_cfrac_str($x,$y), 18);
}
print "\n";
print " / \\ / \\ / \\ / \\\n";
foreach (1 .. 8) {
my ($x,$y) = $path->n_to_xy($n++);
print centre(xy_to_cfrac_str($x,$y), 9);
}
print "\n";
print "\n";
}
#------------------------------------------------------------------------------
my $rationals_type_arrayref
= Math::PlanePath::RationalsTree->parameter_info_hash()->{'tree_type'}->{'choices'};
my $fractions_type_arrayref
= Math::PlanePath::FractionsTree->parameter_info_hash()->{'tree_type'}->{'choices'};
print "RationalsTree\n";
print "-------------\n\n";
foreach my $tree_type (@$rationals_type_arrayref) {
print "$tree_type tree\n";
my $path = Math::PlanePath::RationalsTree->new
(tree_type => $tree_type);
print_as_fractions ($path);
}
print "\n";
print "FractionsTree\n";
print "-------------\n\n";
foreach my $tree_type (@$fractions_type_arrayref) {
print "$tree_type tree\n";
my $path = Math::PlanePath::FractionsTree->new
(tree_type => $tree_type);
print_as_fractions ($path);
}
print "\n";
print "-----------------------------------------------------------------------\n";
print "Or written as continued fraction quotients.\n";
print "\n";
print "RationalsTree\n";
print "-------------\n\n";
foreach my $tree_type (@$rationals_type_arrayref) {
print "$tree_type tree\n";
my $path = Math::PlanePath::RationalsTree->new
(tree_type => $tree_type);
print_as_cfracs ($path);
}
print "\n";
print "FractionsTree\n";
print "-------------\n\n";
foreach my $tree_type (@$fractions_type_arrayref) {
print "$tree_type tree\n";
my $path = Math::PlanePath::FractionsTree->new
(tree_type => $tree_type);
print_as_cfracs ($path);
}
exit 0;
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