Cartesian Products and Outer Joins

Answer

Cartesian Product

• Definition: The Cartesian product, also known as a cross join, is a mathematical operation that combines every row from one table with every row from another table.

• Resulting Rows: If Table A has $m$ rows and Table B has $n$ rows, the Cartesian product will result in a new table with $m \times n$ rows.

• Use Case: It is generally used when you want to generate all possible combinations of rows from two tables.

• Example:

  Consider two tables:

  Table A (Employees):

  EmployeeID	Name
  1	Alice
  2	Bob

  Table B (Departments):

  DepartmentID	DepartmentName
  1	HR
  2	IT

  Cartesian Product (A × B):

  EmployeeID	Name	DepartmentID	DepartmentName
  1	Alice	1	HR
  1	Alice	2	IT
  2	Bob	1	HR
  2	Bob	2	IT

Outer Join

• Definition: An outer join is a type of join that returns all rows from one table and the matched rows from the other table. If no match is found, NULL values are returned for the columns of the table that has no matching rows.

• Types of Outer Joins:

  • Left Outer Join: Includes all rows from the left table and matched rows from the right table. Unmatched rows from the right table will show NULL.
  • Right Outer Join: Includes all rows from the right table and matched rows from the left table. Unmatched rows from the left table will show NULL.
  • Full Outer Join: Includes all rows from both tables, with NULLs in places where there are no matches.

• Use Case: Useful for retrieving all records from both tables, including those that do not have a corresponding match.

• Example:

  Using the same tables:

  Table A (Employees):

  EmployeeID	Name
  1	Alice
  2	Bob

  Table B (Departments):

  DepartmentID	DepartmentName	EmployeeID
  1	HR	1
  2	IT	NULL

  Left Outer Join (A LEFT JOIN B ON A.EmployeeID = B.EmployeeID):

  EmployeeID	Name	DepartmentID	DepartmentName
  1	Alice	1	HR
  2	Bob	NULL	NULL

Summary

• Cartesian Product: Generates all possible combinations of rows from two tables without any relation.
• Outer Join: Combines rows based on a relationship, including unmatched rows from one or both tables, filling in NULLs where appropriate. This makes outer joins more useful for querying related data, while the Cartesian product can lead to a combinatorial explosion of results if the tables are large.