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SQL Server
Tips by Burleson |
Relational Division
Dr. Codd defined a set of eight basic operators for his relational
model. This series of articles looks at those basic operators in
Standard SQL. Some are implemented directly, some require particular
programming tricks and all of them have to be slightly modified to
fit into the SQL language model.
Relational division is one of the eight basic operations in Codd's
relational algebra. The idea is that a divisor table is used to
partition a dividend table and produce a quotient or results table.
The quotient table is made up of those values of one column for
which a second column had all of the values in the divisor.
This is easier to explain with an example. We have a table of pilots
and the planes they can fly (dividend); we have a table of planes in
the hangar (divisor); we want the names of the pilots who can fly
every plane (quotient) in the hangar. To get this result, we divide
the PilotSkills table by the planes in the hangar.
CREATE TABLE PilotSkills
(pilot CHAR(15) NOT NULL,
plane CHAR(15) NOT NULL,
PRIMARY KEY (pilot, plane));
PilotSkills
pilot plane
=========================
'Celko' 'Piper Cub'
'Higgins' 'B-52 Bomber'
'Higgins' 'F-14 Fighter'
'Higgins' 'Piper Cub'
'Jones' 'B-52 Bomber'
'Jones' 'F-14 Fighter'
'Smith' 'B-1 Bomber'
'Smith' 'B-52 Bomber'
'Smith' 'F-14 Fighter'
'Wilson' 'B-1 Bomber'
'Wilson' 'B-52 Bomber'
'Wilson' 'F-14 Fighter'
'Wilson' 'F-17 Fighter'
CREATE TABLE Hangar
(plane CHAR(15) NOT NULL PRIMARY KEY);
Hangar
plane
=============
'B-1 Bomber'
'B-52 Bomber'
'F-14 Fighter'
PilotSkills DIVIDED BY Hangar
pilot
=============================
'Smith'
'Wilson'
In this example, Smith and Wilson are the two pilots who can fly
everything in the hangar. Notice that Higgins and Celko know how to
fly a Piper Cub, but we don't have one right now. In Codd's original
definition of relational division, having more rows than are called
for is not a problem.
The important characteristic of a relational division is that the
CROSS JOIN (Cartesian product) of the divisor and the quotient
produces a valid subset of rows from the dividend. This is where the
name comes from, since the CROSS JOIN acts like a multiplication
operator.
Relational division can be written as a single query, thus:
SELECT DISTINCT pilot
FROM PilotSkills AS PS1
WHERE...
See code depot
This is a book excerpt from:
Advanced SQL Database Programmer Handbook
Donald K. Burleson, Joe Celko, John Paul Cook, Peter Gulutzan
ISBN: 0-9744355-2-X
http://www.rampant-books.com/ebook_dbazine_SQL_prog.htm
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