MySQL Query (or Doctrine 1.2 query) - get most rec

I am having trouble constructing a query to do the following:

Filter contacts by activity_type_id, only displaying contacts where the most recent activity has the desired activity_type_id or is NULL (no activity)

Tables are structured as follows:

A contact can have many activities of varying types

activity:
id
contact_id
activity_type_id
date

contact:
id
first_name
last_name

I have this so far:

SELECT * FROM (
    SELECT c.first_name, c.last_name, a.activity_type_id, MAX(a.date) AS maxdate 
    FROM contact AS c
    LEFT JOIN activity AS a ON a.contact_id = c.id
    GROUP BY c.id
    ORDER BY c.first_name  ASC
) AS act

then adding this to filter:

WHERE activity_type_id = 3 /* <- I would like to filter using this */

However I am getting the wrong activity_type_id for contacts that have multiple activities.

I ultimately would like to use this as a Doctrine 1.2 query but I like to get things working in MySQL first.

Thankyou.

The Final Solution

SELECT c.first_name, c.last_name, a.activity_type_id FROM contact c
  LEFT JOIN
    (SELECT a1.contact_id, a1.date, a1.activity_type_id FROM activity a1
      JOIN (SELECT contact_id, MAX(DATE) DATE FROM activity GROUP BY contact_id) a2
        ON a1.contact_id = a2.contact_id AND a1.date = a2.date
     ) a
  ON c.id = a.contact_id  
WHERE a.activity_type_id = 2;

The final where cause can be adjusted to return various activity type or set to IS NULL.

DQL 1.2 Compatible version

SELECT * FROM contact c
LEFT JOIN activity ON c.id = contact_id
WHERE ROW (c.id,DATE) IN (SELECT contact_id, MAX(date) date FROM activity  GROUP BY contact_id)
AND activity_type_id = 2

Try this query -

edit: a1.activity_type_id is added

SELECT c.first_name, c.last_name FROM contacts c
  LEFT JOIN
    (SELECT a1.contact_id, a1.date, a1.activity_type_id FROM activity a1
      JOIN (SELECT contact_id, MAX(date) date FROM activity GROUP BY contact_id) a2
        ON a1.contact_id = a2.contact_id AND a1.date = a2.date
     ) a
  ON c.contact_id = a.contact_id
WHERE a.contact_id IS NULL OR a.activity_type_id = 3;