loading..
Русский    English
18:26

About generation of number sequences in SQL Server page 1

Author: Bezhaev A.Yu.

In the next realization of MS  Cистема управления реляционными базами данных (СУБД), разработанная корпорацией Microsoft. SQL(Structured Query Language) is a database computer language designed for the retrieval and management of data in relational database management systems (RDBMS), database schema creation and modification, and database object access control management.SQL Server 2005 the new possibility to use recursive CTE-constructions had appeared. The  CTE (common table expression) allows to determine a table in framework of a query for multiple referencings.CTE allows to realize cycles for generation of number sequences and iterative calculations.

The introduction to recursion in MS SQL Server may be founded in Microsoft`s corresponding manuals, this book and in the Internet. In this paragraph we`ll consider only new examples, useful in the practical mastering. The simplest example of using recursive CTE is generation limited number of natural sequence: 1,2,3, ... N.

Console
Execute
  1. WITH Series(a) AS
  2. (
  3.  SELECT 1
  4.  UNION ALL
  5.  SELECT a+1 FROM Series WHERE a < 100
  6. )
  7. SELECT * FROM Series;

This construction is meant for generation of natural sequences as one-column table with values from 1 to 100.

A. Iteration calculations

In the elementary and the high mathematics there are more interesting sequences with notable features. Some sequences converge and may be used for realization of calculate algorithms or for calculation of algebraic and transcendent numbers, values of trigonometric functions, for finding equation`s roots, solving linear equation systems and others. Other sequences, such as factorial, Binomial theorem and Fibonacci numbers are divergent sequences which have wide application in the probability theory and the mathematical statistics.

These sequences are made by iterations (recursions in SQL Server), for instance:
A1, A2, A3, A4 = fun(A1, A2, A3).

Here, A1, A2, A3 — start values for iteration process, fun — is a function for calculation 4th, 5th numbers etc, it always uses three previous numbers. Let`s suppose process starts with three equal numbers A1 = A2 = A3 = 1. Then the realization`s schema with using recursive CTE assumes such view:

  1. WITH TABLE(iter, A1, A2, A3, A4) AS
  2. (
  3.  SELECT iter = 1, A1 = 1, A2 = 1, A3 = 1, A4 = fun(1, 1, 1)
  4.  UNION ALL
  5.  SELECT iter + 1, A1 = A2, A2 = A3, A3 = A4, A4=fun(A2, A3, A4)
  6.  FROM TABLE WHERE iter < 50
  7. )
  8. SELECT * FROM TABLE;

Here [iter] column is using for iteration`s number output, [A1] column contains first fifty members of sequence and [A2], [A3], [A4] columns are auxiliary and contain intermediate results.

The generalization of this method is in this example. Let n >= 1, m >= 1. Then sequent calculations

A[n+1] = fun(A[1], A[2], …, A[n])
A[n+2] = fun(A[2], A[3], …, A[n+1])
A[n+m] = fun(A[m], A[m+1], …, A[m+n-1])

lead to generation of m new members of sequence A[n+1],…,A[n+m].

We aren`t going to make an example of using recursion in general, because it`s possible only in pseudocode perhaps. You can try to make it for your own. Note that the resulting table has such look:

A[1]    A[2]    …    A[n]      A[n+1]
A[2]    A[3]    …    A[n+1]  A[n+2]

A[m+1]  A[m+2]  …    A[m+n-1] A[m+n]

Bookmark and Share
Pages 1 2 3
Tags
aggregate functions Airport ALL AND AS keyword ASCII AVG Battles Bezhaev Bismarck C.J.Date calculated columns Cartesian product CASE cast CHAR CHARINDEX Chebykin check constraint classes COALESCE common table expressions comparison predicates Computer firm CONVERT correlated subqueries COUNT CROSS APPLY CTE data type conversion data types database schema date/time functions DATEADD DATEDIFF DATENAME DATEPART DATETIME DDL DEFAULT DEFAULT VALUES DELETE DISTINCT DML duplicates EXCEPT exercise (-2) exercise 19 exercise 23 exercise 32 More tags
The book was updated
month ago
©SQL-EX,2008 [Evolution] [Feedback] [About] [Links] [Team]
All right reserved.
Rambler's Top100