#!/usr/bin/perl -w
# Copyright 2011 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 5.010;
use strict;
use List::Util 'min','max';
# uncomment this to run the ### lines
#use Smart::Comments;
sub min_maybe {
return min(grep {defined} @_);
}
sub max_maybe {
return max(grep {defined} @_);
}
sub print_table {
my ($name, $aref) = @_;
print "my \@$name = (";
my $entry_width = max (map {length($_//'undef')} @$aref);
foreach my $i (0 .. $#$aref) {
printf "%*s", $entry_width, $aref->[$i]//'undef';
if ($i == $#$aref) {
print ");\n";
} else {
print ",";
if ($entry_width >= 2 && ($i % 25) == 4) {
print " # ".($i-4);
}
if (($i % 25) == 24
|| $entry_width >= 2 && ($i % 5) == 4) {
print "\n ".(" " x length($name));
} elsif (($i % 5) == 4) {
print " ";
}
}
}
}
sub make_state {
my ($transpose, $rot) = @_;
$transpose %= 2;
$rot %= 4;
unless ($rot == 0 || $rot == 2) {
die "bad rotation $rot";
}
return 25*($rot/2 + 2*$transpose);
}
my @next_state;
my @digit_to_x;
my @digit_to_y;
my @yx_to_digit;
my @min_digit;
my @max_digit;
foreach my $transpose (0, 1) {
foreach my $rot (0, 2) {
my $state = make_state ($transpose, $rot);
### $state
foreach my $orig_digit (0 .. 24) {
my $digit = $orig_digit;
# if ($rev) {
# $digit = 24-$digit;
# }
my $xo;
my $yo;
my $new_rot = $rot;
my $new_transpose = $transpose;
my $inc_rot = 0;
if ($digit == 0) {
$xo = 0;
$yo = 0;
} elsif ($digit == 1) {
$xo = 1;
$yo = 0;
} elsif ($digit == 2) {
$xo = 2;
$yo = 0;
$new_transpose ^= 1;
} elsif ($digit == 3) {
$xo = 2;
$yo = 1;
$new_transpose ^= 1;
} elsif ($digit == 4) {
$xo = 2;
$yo = 2;
$new_transpose ^= 1;
} elsif ($digit == 5) {
$xo = 1;
$yo = 2;
$inc_rot = 2;
$new_transpose ^= 1;
} elsif ($digit == 6) {
$xo = 1;
$yo = 1;
$inc_rot = 2;
} elsif ($digit == 7) {
$xo = 0;
$yo = 1;
$inc_rot = 2;
} elsif ($digit == 8) {
$xo = 0;
$yo = 2;
$new_transpose ^= 1;
} elsif ($digit == 9) {
$xo = 0;
$yo = 3;
$new_transpose ^= 1;
} elsif ($digit == 10) {
$xo = 0;
$yo = 4;
} elsif ($digit == 11) {
$xo = 1;
$yo = 4;
} elsif ($digit == 12) {
$xo = 1;
$yo = 3;
$inc_rot = 2;
$new_transpose ^= 1;
} elsif ($digit == 13) {
$xo = 2;
$yo = 3;
$new_transpose ^= 1;
} elsif ($digit == 14) {
$xo = 2;
$yo = 4;
} elsif ($digit == 15) {
$xo = 3;
$yo = 4;
} elsif ($digit == 16) {
$xo = 4;
$yo = 4;
} elsif ($digit == 17) {
$xo = 4;
$yo = 3;
$inc_rot = 2;
} elsif ($digit == 18) {
$xo = 3;
$yo = 3;
$inc_rot = 2;
$new_transpose ^= 1;
} elsif ($digit == 19) {
$xo = 3;
$yo = 2;
$inc_rot = 2;
$new_transpose ^= 1;
} elsif ($digit == 20) {
$xo = 4;
$yo = 2;
} elsif ($digit == 21) {
$xo = 4;
$yo = 1;
$inc_rot = 2;
} elsif ($digit == 22) {
$xo = 3;
$yo = 1;
$inc_rot = 2;
$new_transpose ^= 1;
} elsif ($digit == 23) {
$xo = 3;
$yo = 0;
$inc_rot = 2;
$new_transpose ^= 1;
} elsif ($digit == 24) {
$xo = 4;
$yo = 0;
} else {
die;
}
### base: "$xo, $yo"
if ($transpose) {
($xo,$yo) = ($yo,$xo);
$inc_rot = - $inc_rot;
}
$new_rot = $rot + $inc_rot;
if ($rot & 2) {
$xo = 4 - $xo;
$yo = 4 - $yo;
}
if ($rot & 1) {
($xo,$yo) = (4-$yo,$xo);
}
### rot to: "$xo, $yo"
$digit_to_x[$state+$orig_digit] = $xo;
$digit_to_y[$state+$orig_digit] = $yo;
$yx_to_digit[$state + $yo*5+$xo] = $orig_digit;
my $next_state = make_state ($new_transpose, $new_rot);
$next_state[$state+$orig_digit] = $next_state;
}
# N = (- 1/2 d^2 + 9/2 d)
# = (- 1/2*$d**2 + 9/2*$d)
# = ((9 - d)d/2
# (9-d)*d/2
# d=0 (9-0)*0/2 = 0
# d=1 (9-1)*1/2 - 1 = 8/2-1 = 3
# d=2 (9-2)*2/2 - 2 = 7-1 = 6
# d=4 (9-4)*4/2 = 5*4/2 = 10
#
foreach my $x1pos (0 .. 4) {
foreach my $x2pos ($x1pos .. 4) {
my $xkey = (9-$x1pos)*$x1pos/2 + $x2pos;
### $xkey
### assert: $xkey >= 0
### assert: $xkey < 15
foreach my $y1pos (0 .. 4) {
foreach my $y2pos ($y1pos .. 4) {
my $ykey = (9-$y1pos)*$y1pos/2 + $y2pos;
### $ykey
### assert: $ykey >= 0
### assert: $ykey < 15
my $min_digit = undef;
my $max_digit = undef;
foreach my $digit (0 .. 24) {
my $x = $digit_to_x[$digit];
my $y = $digit_to_y[$digit];
if ($rot & 2) {
$x = 4 - $x;
$y = 4 - $y;
}
if ($transpose) {
($x,$y) = ($y,$x);
}
next unless $x >= $x1pos;
next unless $x <= $x2pos;
next unless $y >= $y1pos;
next unless $y <= $y2pos;
$min_digit = min_maybe($digit,$min_digit);
$max_digit = max_maybe($digit,$max_digit);
}
my $key = $state*9 + $xkey*15 + $ykey;
### $key
if (defined $min_digit[$key]) {
die "oops min_digit[] already: state=$state key=$key y1p=$y1pos y2p=$y2pos value=$min_digit[$key], new=$min_digit";
}
$min_digit[$key] = $min_digit;
$max_digit[$key] = $max_digit;
}
}
### @min_digit
}
}
}
}
print_table ("next_state", \@next_state);
print_table ("digit_to_x", \@digit_to_x);
print_table ("digit_to_y", \@digit_to_y);
print_table ("yx_to_digit", \@yx_to_digit);
print_table ("min_digit", \@min_digit);
print_table ("max_digit", \@max_digit);
print "# state length ",scalar(@next_state)," in each of 4 tables\n\n";
### @next_state
### @digit_to_x
### @digit_to_y
### @yx_to_digit
### next_state length: scalar(@next_state)
{
my @pending_state = (0);
my $count = 0;
my @seen_state;
my $depth = 1;
$seen_state[0] = $depth;
while (@pending_state) {
my $state = pop @pending_state;
$count++;
### consider state: $state
foreach my $digit (0 .. 24) {
my $next_state = $next_state[$state+$digit];
if (! $seen_state[$next_state]) {
$seen_state[$next_state] = $depth;
push @pending_state, $next_state;
### push: "$next_state depth $depth"
}
}
$depth++;
}
for (my $state = 0; $state < @next_state; $state += 25) {
print "# used state $state depth ",$seen_state[$state]//'undef',"\n";
}
print "used state count $count\n";
}
print "\n";
exit 0;