for my $key (keys %hash) {
	print "$key\n"
		if grep {$_ eq "banana"} @{ $hash{$key} };
}

##</code><code>##

# convert
my %hoh = map {
		$_ => { map {$_=>1} @{ $hash{$_} } }
	} keys %hash;

# debug: inspect the converted data
use Data::Dumper;
print Dumper(\%hoh);

# lookup
my $search = "banana";
for my $key (keys %hoh) {
	print "$key\n" if $hoh{$key}{$search};
}

##</code><code>##

# build inverse hash, if all values are unique
my %inverse_hash;
for my $key (keys %hash) {
	for my $val (@{ $hash{$key} }) {
		$inverse_hash{$val} = $key;
	}
}

# debug: inspect the converted data
print Dumper(\%inverse_hash);

# lookup is simple!
print $inverse_hash{banana}, "\n";

##</code><code>##

# convert to "inverse" hash of arrays (in two steps)
my %hoa;
# first, build a hash of hashes
# (this eliminates duplicates at both levels)
for my $key (keys %hash) {
	for my $val (@{ $hash{$key} }) {
		$hoa{$val}{$key}++;
	}
}
# then, convert the second level of hashes to arrays
for my $vals (values %hoa) {
	$vals = [sort keys %$vals];
}

# debug: inspect the converted data
print Dumper(\%hoa);

# lookup
print join(', ', @{ $hoa{banana} } ), "\n"