use strict;
use warnings;
use Data::Dumper;

my $area = [ [ 10, 20 ] ];
my $rect = [ [ 5, 12 ], [ 4, 8 ], [ 12, 2 ] ];

foreach my $r (@$rect) {
    my $leftover = [];
    foreach (@$area) {
        my ($n1, $n2) = fit_rect_in_area($r, $_);
        next if !defined $n1;
        $leftover = [ @$leftover, @$n1, @$n2 ];
    }
    $area = $leftover;
}

#
#  +------------------------+
#  |                        |
#  |                        |
#  +---------------+        |
#  |               |        |
#  |               |        |
#  +---------------+--------+
#
#  two left over area options =>
#
#  +------------------------+     +--------+
#  |                        |  +  |        |
#  |                        |     |        |
#  +------------------------+     +--------+
#
#  or
#
#  +---------------+     +--------+
#  |               |  +  |        |
#  |               |     |        |
#  +---------------+     |        |
#                        |        |
#                        |        |
#                        +--------+
#

sub fit_rect_in_area
{
    my ($rect, $area) = @_;
    if (canfit($rect, $area)) {
        print rectstr($rect) . " can fit inside " . rectstr($area) . "\n";
        my ($n1, $n2) = fitrect($rect, $area);
        print "leftover option 1: " . join(" and ", map { rectstr($_) } @{$n1}) . "\n";
        print "leftover option 2: " . join(" and ", map { rectstr($_) } @{$n2}) . "\n";
        return ($n1, $n2);
    } elsif (canfit(rotate($rect), $area)) {
        print rectstr($rect) . " can fit inside " . rectstr($area) . " after rotation\n";
        my ($n1, $n2) = fitrect(rotate($rect), $area);
        print "leftover option 1: " . join(" and ", map { rectstr($_) } @{$n1}) . "\n";
        print "leftover option 2: " . join(" and ", map { rectstr($_) } @{$n2}) . "\n";
        return ($n1, $n2);
    } else {
        print rectstr($rect) . " can not fit inside " . rectstr($area) . "\n";
        return ();
    }
}

# place rect on area
sub fitrect
{
    my ($rect, $area) = @_;

    my $a1 = [ $area->[0] - $rect->[0], $area->[1] ];
    my $a2 = [ $rect->[0], $area->[1] - $rect->[1] ];

    my $b1 = [ $area->[0] - $rect->[0], $rect->[1] ];
    my $b2 = [ $area->[0], $area->[1] - $rect->[1] ];

    return ([ $a1, $a2 ], [ $b1, $b2 ]);
}

# check if a rect can fit
sub canfit
{
    my ($rect, $area) = @_;
    return $rect->[0] <= $area->[0] && $rect->[1] <= $area->[1];
}

# rotate a rectangle
sub rotate
{
    my $rect = shift;
    return [ $rect->[1], $rect->[0] ];
}

# return textual representation of rectangle
sub rectstr
{
    my $rect = shift;
    return sprintf "R(W=%d, H=%d)", $rect->[0], $rect->[1];
}

##</code><code>##

R(W=5, H=12) can fit inside R(W=10, H=20)
leftover option 1: R(W=5, H=20) and R(W=5, H=8)
leftover option 2: R(W=5, H=12) and R(W=10, H=8)
R(W=4, H=8) can fit inside R(W=5, H=20)
leftover option 1: R(W=1, H=20) and R(W=4, H=12)
leftover option 2: R(W=1, H=8) and R(W=5, H=12)
R(W=4, H=8) can fit inside R(W=5, H=8)
leftover option 1: R(W=1, H=8) and R(W=4, H=0)
leftover option 2: R(W=1, H=8) and R(W=5, H=0)
R(W=4, H=8) can fit inside R(W=5, H=12)
leftover option 1: R(W=1, H=12) and R(W=4, H=4)
leftover option 2: R(W=1, H=8) and R(W=5, H=4)
R(W=4, H=8) can fit inside R(W=10, H=8)
leftover option 1: R(W=6, H=8) and R(W=4, H=0)
leftover option 2: R(W=6, H=8) and R(W=10, H=0)
R(W=12, H=2) can not fit inside R(W=1, H=20)
R(W=12, H=2) can fit inside R(W=4, H=12) after rotation
leftover option 1: R(W=2, H=12) and R(W=2, H=0)
leftover option 2: R(W=2, H=12) and R(W=4, H=0)
R(W=12, H=2) can not fit inside R(W=1, H=8)
R(W=12, H=2) can fit inside R(W=5, H=12) after rotation
leftover option 1: R(W=3, H=12) and R(W=2, H=0)
leftover option 2: R(W=3, H=12) and R(W=5, H=0)
R(W=12, H=2) can not fit inside R(W=1, H=8)
R(W=12, H=2) can not fit inside R(W=4, H=0)
R(W=12, H=2) can not fit inside R(W=1, H=8)
R(W=12, H=2) can not fit inside R(W=5, H=0)
R(W=12, H=2) can not fit inside R(W=1, H=12)
R(W=12, H=2) can not fit inside R(W=4, H=4)
R(W=12, H=2) can not fit inside R(W=1, H=8)
R(W=12, H=2) can not fit inside R(W=5, H=4)
R(W=12, H=2) can not fit inside R(W=6, H=8)
R(W=12, H=2) can not fit inside R(W=4, H=0)
R(W=12, H=2) can not fit inside R(W=6, H=8)
R(W=12, H=2) can not fit inside R(W=10, H=0)