Task: For each article, find the dealer or dealers with the most expensive price.

In standard SQL (and as of MySQL 4.1), the problem can be solved with a subquery like this:

SELECT article, dealer, price
FROM   shop s1
WHERE  price=(SELECT MAX(s2.price)
              FROM shop s2
              WHERE s1.article = s2.article);

The preceding example uses a correlated subquery, which can be inefficient (see Section 12.2.8.7, “Correlated Subqueries”). Other possibilities for solving the problem are to use an uncorrelated subquery in the FROM clause or a LEFT JOIN:

SELECT s1.article, dealer, s1.price
FROM shop s1
JOIN (
  SELECT article, MAX(price) AS price
  FROM shop
  GROUP BY article) AS s2
  ON s1.article = s2.article AND s1.price = s2.price;

SELECT s1.article, s1.dealer, s1.price
FROM shop s1
LEFT JOIN shop s2 ON s1.article = s2.article AND s1.price < s2.price
WHERE s2.article IS NULL;

The LEFT JOIN works on the basis that when s1.price is at its maximum value, there is no s2.price with a greater value and the s2 rows values will be NULL. See Section 12.2.7.1, “JOIN Syntax”.

Before MySQL 4.1, subqueries are unavailable. Another approach is to solve the problem in several steps:

This can easily be done with a temporary table and a join:

CREATE TEMPORARY TABLE tmp (
        article INT(4) UNSIGNED ZEROFILL DEFAULT '0000' NOT NULL,
        price   DOUBLE(16,2)             DEFAULT '0.00' NOT NULL);

LOCK TABLES shop READ;

INSERT INTO tmp SELECT article, MAX(price) FROM shop GROUP BY article;

SELECT shop.article, dealer, shop.price FROM shop, tmp
WHERE shop.article=tmp.article AND shop.price=tmp.price;

UNLOCK TABLES;

DROP TABLE tmp;

If you don't use a TEMPORARY table, you must also lock the tmp table.

“Can it be done with a single query?”

Yes, but only by using a quite inefficient trick called the “MAX-CONCAT trick”:

SELECT article,
       SUBSTRING( MAX( CONCAT(LPAD(price,6,'0'),dealer) ), 7) AS dealer,
  0.00+LEFT(      MAX( CONCAT(LPAD(price,6,'0'),dealer) ), 6) AS price
FROM   shop
GROUP BY article;

+---------+--------+-------+
| article | dealer | price |
+---------+--------+-------+
|    0001 | B      |  3.99 |
|    0002 | A      | 10.99 |
|    0003 | C      |  1.69 |
|    0004 | D      | 19.95 |
+---------+--------+-------+

The last example can be made a bit more efficient by doing the splitting of the concatenated column in the client.