$ perl -Mstrict -Mwarnings -E '
    my %bag = ( A => 4, B => 2, C => 3, D => 1 );
    my @distribution;

    for my $key (sort { $bag{$b} <=> $bag{$a} } keys %bag) {
        my $base_offset = int(@distribution / ($bag{$key} + 1)); 
        my $offset = $base_offset;

        for (1 .. $bag{$key}) {
            next unless $_ % 2;
            splice @distribution, $offset, 0, $key;

            if ($_ < $bag{$key}) {
                splice @distribution, -$offset, 0, $key;
            }

            $offset += $base_offset + 1;
        }   
    }   

    say "@distribution";
'
A C B A D C A B C A