Recall that the hash join algorithm $($for the natural inner join A I B$)$ basically adds the join attribute of B to the hash table, then hashes on A into the same table. If a match is found, then the join on that attribute succeeds. If no match is found, the join on that attribute does not succeed, but the attribute of A is not added to the hash table.

Briefly list the changes necessary to this algorithm for to handle a full outer join.