I've written a solution, too. :-)

I haven't been able to determine the complexity, I'm too bad in mathematics, maybe someone else could ?

However, the lower bound clearly tops all other algorithms, its g(1).
Ok, the upper bound could be g(unlimited), I'd guess.

use strict;
use List::Util qw(shuffle);

# construct a standard deck
my @card;
foreach my $suit (qw(H C S D)) {
    foreach my $value (2..10, qw(J Q K A)) {
        push @card, $value . $suit;
    }
}

# now shuffle us up a pile of cards, perhaps composed of any
# number of decks
my @pile;
my $n = 4;      # number of decks in shuffled pile
push @pile, @card for (1..$n);
@pile = shuffle @pile;


my $decks;
do {
        $decks = grab ( \@pile ); # split the pile into $n decks
        @pile = lookup( $decks ); # Look if we got it right..
} while ( @pile > 0 );
        

print "Got it!\n";

for my $a (0..$n){
        print "$_ " foreach ( @{$decks->{$a}} );
        print "\n\n";
}
# Exits here.. happily


sub grab{
        my $pile = shift;

        my $decks;
        # Grab the cards
        foreach my $card (@{$pile}){
                push @{$decks->{int(rand($n))}}, $card;
        }
        return $decks;
}

sub lookup{
        my $decks = shift;
        
        for my $a (0..$n-1) {
                my %cards; 
                foreach my $card ( @{$decks->{$a}} ){
                        if ( defined( $cards{$card} ) ){
                                damnit( $decks );
                                return throw ( $decks );
                        } else {
                                $cards{$card} = 1; # Remember this. An
+d dont forget it!
                        }
                }
        }
}

sub damnit{
        my $decks = shift;

        print "Damnit!!!\n";
        for my $a (0..$n){
                print "$_ " foreach ( @{$decks->{$a}} );
                print "\n\n";
        }
}

sub throw{
        my $decks = shift;

        my @pile;
        foreach ( values %{$decks} ){
                push @pile, @{$_};
        }
        return shuffle( @pile );            
}
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