 #!/usr/bin/perl
use strict;
use warnings;
use 5.014;
=head1 DESCRIPTION
In a 3x2 crosshatched grid, a total of 37 different rectangles could be
situated within that grid as indicated in the sketch.
There are 5 grids smaller than 3x2, vertical and horizontal dimensions being
important, i.e. 1x1, 2x1, 3x1, 1x2 and 2x2. If each of them is crosshatched,
the following number of different rectangles could be situated within those
smaller grids:
1x1: 1 2x1: 4 3x1: 8 1x2: 4 2x2: 18
Adding those to the 37 of the 3x2 grid, a total of 72 different rectangles
could be situated within 3x2 and smaller grids.
How many different rectangles could be situated within 47x43 and smaller grids?
=cut
# A 2dimensional cache.
# $Rects_Coefficients_Cache[$rect_x][$rect_y] = { min => $min, offset => $offset};
# Formula for step is calculated at 2*$board_dim + $offset
my @Rects_Coefficients_Cache;
# A 4dimensional cache:
# 0  board large dim.
# 1  board small dim.
# 2  rect large dim.
# 3  rect large dim.
# Each value is:
# {
#
# Cache for the boards:
# $Boards_Cache[$board_x][$board_y] = { 'num_unique' => , 'rects' => \@rects, }
# rects is:
# $rects[$rect_x][$rect_y]
my @Boards_Cache;
sub get_unique_rects
{
# $x >= $y >= $rect_x , $rect_y
my ($x, $y, $rect_x, $rect_y) = @_;
my $board_struct = ($Boards_Cache[$x][$y] //= +{});
if (! defined($board_struct>{num_unique}))
{
# Calculate the unique rectangles.
$board_struct>{rects} //= [];
}
return $board_struct;
}
sub get_total_rects
{
my ($x, $y) = @_;
my $sum = 0;
foreach my $xx (1 .. $x)
{
foreach my $yy (1 .. $y)
{
$sum += $xx * $yy * ($x  $xx + 1) * ($y  $yy + 1);
}
}
return {num_straight_rects => $sum};
}
my ($x, $y) = @ARGV;
# my $num_rects = get_rects(47, 43, 47, 43);
my $num_straight_rects = get_total_rects($x, $y)>{num_straight_rects};
print "Straight Rects = $num_straight_rects\n";
