Actually, this:

$unique_ids = scalar(grep {defined $_} @normal_array);
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will not find the number of unique IDs in @normal_array, it'll simply count how many elements of @normal_array are defined. I recommend using the uniq function from List::MoreUtils.

Applying it to a hash of arrays is straightforward: just iterate through the keys, and apply it to each element of your hash (i.e., each array). Using your example:

foreach (sort keys %HoA) {
    say "$_: ", join ",", uniq @{ $HoA{$_} };
}
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Output:

flintstones: fred,barney,nick,john
jetsons: george,jane,elroy,mike,elias
simpsons: homer,marge,bart,jack
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If you can't or don't want to use this module, the Perl Cookbook has several solutions (Recipe 4.6, p. 102).

I recommend using the uniq function from List::MoreUtils. ... If you can't or don't want to use this module ...

Anonymonk: ... just take a look at the code in it to see how it works; i.e., Steal This Code!

Great thanks,
can you also tell me how I can count the unique elements per key of the Hash of Arrays?

Sure. uniq returns a list of unique elements, and lists evaluate to their number of elements in scalar context, so if you replace the line inside the foreach with e.g. this:

    say "$_: ", scalar uniq @{ $HoA{$_} };
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Then you'll get the number of unique items. (You could equally well assign to a variable for further processing, of course, and if you assign to a scalar, the explicit scalar won't be necessary, though it also won't hurt and may serve to make it a bit clearer what's going on.)