use warnings;
use strict;
use List::Util 'shuffle';
use sort '_mergesort';

#create the 
!$ARGV[0] and print  "No input for array size" and exit;
my @array1  = shuffle 1..$ARGV[0];
my @array2   = shuffle 1..$ARGV[0];

my @sortedA = sort {$a<=>$b} (@array1);
my @sortedB = sort {$a<=> $b } (@array2);

our $pivot; #used in binary search..
my ($uni, $insc)= p_uni(0,$#sortedA,0,$#sortedB);
print "\n|U| = ",$uni," |I|=",$insc;



#>>>>>     UNION and INTERSECTION   <<<<<<<<
#The function p_uni()  will return an ARRAY for which
#ARRAY[0] = cardinality of union
#ARRAY[1]=cardinality of intersection
sub p_uni {

#The function process 2 ordered lists, say A and B as follows
#We split A = A1+A2 and B=B1+B2 around the middle
#Since they are ordered we know that INTERSECTION(A1,B2)=0 and INTERSECTION (A2,B1)=0, so we process them independently...
#The split array Ai is A[aLeft,aRight] - a subset of A with those indices. The same holds for bLeft and bRight.
my ($aLeft,$aRight,$bLeft, $bRight) = @_;
 my ($tmp_uni,$tmp_insc)=(0)x 2;
#If A array is too small then run a linear search and match
if($aRight-$aLeft<100)
    {
    my $search_result;
    
          for (my $i=$aLeft, my $bLeft_h = $bLeft;$i<=$aRight;$i++)
            {
                
               $search_result = bin_search(\@sortedB, $sortedA[$i],$bLeft_h,$bRight);
               $tmp_uni++;
               $tmp_insc++  if($search_result->[0]);
               $bLeft_h = $search_result->[1];
                
            }
          
       return ($aRight-$aLeft+1-$tmp_insc+$bRight-$bLeft+1, $tmp_insc);
    }
#If B array is too small run a linear search and match
elsif($bRight-$bLeft<100)
    {
  
    my ($tmp_uni,$tmp_insc)=(0)x 2;
    my $search_result;
    for my $i($bLeft..$bRight)
            {
                   if(defined($sortedB[$i-1]) && $sortedB[$i-1] != $sortedB[$i]) {
                my $search_result = bin_search(\@sortedA, $sortedB[$i],$aLeft,$aRight);
                if($search_result->[0]) {$tmp_uni++; $tmp_insc++;}
                else { $tmp_uni+=1; }
                $aLeft = $search_result->[1];
                }
            }
           
        return ($aRight-$aLeft+1-$tmp_insc+$bRight-$bLeft+1, $tmp_insc);
    }

my $bPos = int(($bLeft+$bRight)/2);
my $aPos = bin_search(\@sortedA, $sortedB[$bPos],$aLeft,$aRight);

my ($a_insc,$a_uni) = p_uni($aLeft, $aPos->[1], $bLeft,$bPos);
my ($b_insc,$b_uni) = p_uni($aPos->[1]+1,$aRight,$bPos+1,$bRight);
return($a_insc+$b_insc,$a_uni+$b_uni);
}


#This is a binary search- Searches in the ordered list reference AR_REF for WHAT and between and including indices cLEFT cRIGHT..
sub bin_search {
my ($ar_ref, $what,$cLeft,$cRight) =@_;
my ($left,$right,$value)=($cLeft,$cRight,0);

while($left<=$right )
{

    $pivot = int (($left+$right)/2);
    $value = $ar_ref->[$pivot];
    
    if($value>$what)
        { 
            $right=$pivot-1;
        }
    elsif($value<$what)
        {
           $left=$pivot+1;
        }
    else 
        {
        return [1,$pivot];
        }
}

return [0,$pivot];
}