Is using a HashSet the fastest way to combine two ArrayList(s) and omit duplicates?
ArrayList a1, a2; // fill them with junk
HashSet hash = new HashSet(a1);
hash.addAll(a2);
You could just do
ArrayList a1, a2; // fill with junk
a1.removeAll( a2 ); // removes duplicates
a1.addAll( a2 ); // combines lists
You might also want to use LinkedLists instead of ArrayLists in order to avoid costly removing-from-an-array operations, and the annoying array-growing operation. Anyhoo, as long as your chosen collection implements the java.util.Collection interface, you can do the above.
Exact testing needs to be done, but I do think that HashSet version should be an order of magnitude faster.
In theory HashSet insert is O(1) and ArrayList remove of single element is O(n). So here we have O(n) versus O(n^2) complexity, a BIG difference.
Of course, for small n, other costs will be important. But I do not expect that remove version will be faster for anything over 5-6 elements.
If both ArrayLists are sorted, the fastest way is coding a loop that iterates both arrays in parallel and for each iteration, copies the lower-ordering element to a new array.