full table scan for an OR in a WHERE statement

Question

So I have this query

EXPLAIN SELECT r.* FROM r_table r
        LEFT JOIN f_table f ON f.id = r.fid
        LEFT JOIN f_table ff ON r.fid = 0 AND r.type = 'f' AND r.id = ff.id
      WHERE (r.fid = 0 AND ff.cid = 421563) OR (r.fid <> 0 AND f.cid = 421563);

And it's performing a full table scan on table r

Explain output:

1   SIMPLE      r   ALL Index1              2314    Using where
1   SIMPLE      f   eq_ref  PRIMARY PRIMARY 4   r.fid   1   Using where
1   SIMPLE      ff  eq_ref  PRIMARY PRIMARY 4   r.id    1   Using where

How can I modify this query to make it not perform a full table scan? I know that I can probably use UNION nonetheless I'd rather not do UNION unless necessary.

EDIT

Rewriting the query into a UNION indeed worked...here's the UNION query

EXPLAIN SELECT r.* FROM r_table r
        LEFT JOIN f_table f ON r.fid <> 0 AND f.id = r.fid
      WHERE f.cid = 421563
UNION SELECT r.* FROM r_table r
        LEFT JOIN f_table ff ON r.fid = 0 AND r.obj_type = 'f' AND r.obj_id = ff.id
      WHERE ff.cid = 421563;

And explain output

'2', 'UNION', 'ff', 'ref', 'PRIMARY,cid', 'cid', '4', 'const', '2', 'Using where; Using index'
'2', 'UNION', 'r', 'ref', 'Index1,obj_id_type', 'Index1', '13', 'const,const,ff.id', '1', 'Using where'
'1', 'PRIMARY', 'f', 'ref', 'PRIMARY,cid', 'cid', '4', 'const', '2', 'Using where; Using index'
'1', 'PRIMARY', 'r', 'ref', 'Index1', 'Index1', '4', 'f.id', '1', ''
NULL, 'UNION RESULT', '<union1,2>', 'ALL', NULL, NULL, NULL, NULL, NULL, ''

But once again, I would rather not do a UNION for this

Answer 1

Just move the filters on ff.cid and f.cid from the where clause to the join. In fact, since you are doing a left join, you have to do this anyway.