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Multiplication means producing a Cartesian product of grouping sets. You perform multiplication by separating GROUPING SETS subclauses (or the abbreviated CUBE and ROLLUP subclauses) by commas. For example, if A represents a set of attributes a1, a2, . . ., an, and B represents a set of attributes b1, b2, . . ., bn, and so on, the product GROUPING SETS( (A), (B), (C) ), GROUPING SETS( (D), (E) ) is equal to GROUPING SETS ( (A, D), (A, E), (B, D), (B, E), (C, D), (C, E) ). Consider the following query and try to gure out which grouping sets it de nes:
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SELECT custid, empid, YEAR(orderdate) AS orderyear, MONTH(orderdate) AS ordermonth, DAY(orderdate) AS orderday, SUM(qty) AS qty FROM dbo.Orders GROUP BY CUBE(custid, empid), ROLLUP(YEAR(orderdate), MONTH(orderdate), DAY(orderdate));
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First, expand the CUBE and ROLLUP subclauses to the corresponding GROUPING SETS subclauses, and you get the following query:
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SELECT custid, empid, YEAR(orderdate) AS orderyear, MONTH(orderdate) AS ordermonth, SUM(qty) AS qty
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FROM dbo.Orders GROUP BY GROUPING SETS ( ( custid, empid ), ( custid ), ( empid ), () ), GROUPING SETS ( ( YEAR(orderdate), MONTH(orderdate), DAY(orderdate) ), ( YEAR(orderdate), MONTH(orderdate) ), ( YEAR(orderdate) ), () );
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Now apply the multiplication between the GROUPING SETS subclauses, and you get the following query:
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SELECT custid, empid, YEAR(orderdate) AS orderyear, MONTH(orderdate) AS ordermonth, SUM(qty) AS qty FROM dbo.Orders GROUP BY GROUPING SETS ( ( custid, empid, YEAR(orderdate), MONTH(orderdate), DAY(orderdate) ( custid, empid, YEAR(orderdate), MONTH(orderdate) ( custid, empid, YEAR(orderdate) ( custid, empid ( custid, YEAR(orderdate), MONTH(orderdate), DAY(orderdate) ( custid, YEAR(orderdate), MONTH(orderdate) ( custid, YEAR(orderdate) ( custid ( empid, YEAR(orderdate), MONTH(orderdate), DAY(orderdate) ( empid, YEAR(orderdate), MONTH(orderdate) ( empid, YEAR(orderdate) ( empid ( YEAR(orderdate), MONTH(orderdate), DAY(orderdate) ( YEAR(orderdate), MONTH(orderdate) ( YEAR(orderdate) () );
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), ), ), ), ), ), ), ), ), ), ), ), ), ), ),
Division
When multiple grouping sets in an existing GROUPING SETS subclause share common elements, you can separate the common elements to another GROUPING SETS subclause and multiply the two. The concept is similar to arithmetic division, where you divide operands of an expression by a common element and pull it outside the parentheses. For example, (5 3 + 5 7) can be expressed as (5) (3 + 7). Based on this logic, you can sometimes reduce
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the amount of code needed to de ne multiple grouping sets. For example, see if you can reduce the code in the following query while preserving the same grouping sets:
SELECT custid, empid, YEAR(orderdate) AS orderyear, MONTH(orderdate) AS ordermonth, SUM(qty) AS qty FROM dbo.Orders GROUP BY GROUPING SETS ( ( custid, empid, YEAR(orderdate), MONTH(orderdate) ), ( custid, empid, YEAR(orderdate) ), ( custid, YEAR(orderdate), MONTH(orderdate) ), ( custid, YEAR(orderdate) ), ( empid, YEAR(orderdate), MONTH(orderdate) ), ( empid, YEAR(orderdate) ) );
Because YEAR(orderdate) is a common element to all grouping sets, you can move it to another GROUPING SETS subclause and multiply the two, like so:
SELECT custid, empid, YEAR(orderdate) AS orderyear, MONTH(orderdate) AS ordermonth, SUM(qty) AS qty FROM dbo.Orders GROUP BY GROUPING SETS ( ( YEAR(orderdate) ), GROUPING SETS ( ( custid, empid, MONTH(orderdate) ( custid, empid ( custid, MONTH(orderdate) ( custid ( empid, MONTH(orderdate) ( empid );
), ), ), ), ), )
Note that when a GROUPING SETS subclause contains only one grouping set, it is equivalent to listing the grouping set s elements directly in the GROUP BY clause. Hence, the previous query is logically equivalent to the following:
SELECT custid, empid, YEAR(orderdate) AS orderyear,
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MONTH(orderdate) AS ordermonth, SUM(qty) AS qty FROM dbo.Orders GROUP BY YEAR(orderdate), GROUPING SETS ( ( custid, empid, MONTH(orderdate) ( custid, empid ( custid, MONTH(orderdate) ( custid ( empid, MONTH(orderdate) ( empid );
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), ), ), ), ), )
You can reduce this form even further. Notice in the remaining GROUPING SETS subclause that three subsets of elements appear once with MONTH(orderdate) and once without. Hence, you can reduce this form to a multiplication between a GROUPING SETS subclause containing those three and another containing two grouping sets, (MONTH(orderdate)) and the empty grouping set, like so:
SELECT custid, empid, YEAR(orderdate) AS orderyear, MONTH(orderdate) AS ordermonth, SUM(qty) AS qty FROM dbo.Orders GROUP BY YEAR(orderdate), GROUPING SETS ( ( custid, empid ), ( custid ), ( empid ) ), GROUPING SETS ( ( MONTH(orderdate) ), () );
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