It uses pretty little space (not just in this particular example, but in general...) considering what's doing... Think of it as an index on the joins of the three arrays...

For really big arrays using greps on every iteration would make the operation really cumbersome and memory would be used anyway for the temporaries for grep on each of the arrays... This approach allows logarithmic access to the key once the index is done, yours would be at least of order O(N^2)...

Example:

# some are shared by others...
@array1 = (1 .. 100001);
@array2 = (100001 .. 200001);
@array3 = (200001 .. 300000);

for $i ( 1 .. 100000, 1 .. 10000 ) 
{
    $a = int( rand( 3 ) ) + 1;
    # dark magic, beware...
    push @array4, ${*{"array$a"}}[$i];
}

my %which; 
do { push @{ $which{$_} } => "array1" } for @array1;
do { push @{ $which{$_} } => "array2" } for @array2;
do { push @{ $which{$_} } => "array3" } for @array3;

my @pairs = @array4;
while (my ($one,$two) = splice(@pairs,0,2)) {
   print "." if "$one and $two are in (@{$which{$one}}) and (@{$which{
+$two}}) respectively\n";
}

__END__

This renders (on my box):
4.05user 0.15system 0:04.31elapsed 97%CPU (0avgtext+0avgdata 0maxresid
+ent)k
0inputs+0outputs (0major+22995minor)pagefaults 0swaps
[download]

with bigger arrays it will grow bigger, of course, but if you have that many data you will have a lot of RAM... memory is cheap nowadays, cheaper than CPU cycles, I think...

best regards