一个很有用的自定义函数(判断自然数是否包含2的指定次幂)

王朝mssql·作者佚名 2006-12-17

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一个很有用的自定义函数(判断自然数是否包含2的指定次幂) /*

Name : Fun_WheIncluded

Function : 判断选定的数字是否在给定的整数中

可以知道任何一个自然数都可以拆分成若干个2的幂的和，如：

1 = 2^0

2 = 2^1

3 = 2^0 + 2^1

4 = 2^2

5 = 2^0 + 2^2

6 = 2^1 + 2^4

7 = 2^0 + 2^1 + 2^2

8 = 2^3

9 = 2^0 + 2^3

10 = 2^1 + 2^3

11 = 2^0 + 2^1 + 2^3

12 = 2^2 + 2^3

13 = 2^0 + 2^2 + 2^3

14 = 2^1 + 2^2 + 2^3

15 = 2^0 + 2^1 + 2^2 + 2^3

16 = 2^4

17 = 2^0 + 2^4

将任意一个数解析为2的幂的和的方法——递归

规律：

如给定 14

∵ 2^3 < 14 < 2^4

∴ 14中必有8——2^3

14 - 8 = 6

∵ 2^2 < 6 < 2^3

∴ 6中必有4——2^2

6 - 4 = 2

∵ 2 = 2

∴ 14 = 2^3 + 2^2 + 2^1

Parameters : @TotalNum

Type: INT

@SpecifiedNum

Type: INT

Steps :

Author : Waxdoll Cheung

Date : 2005-03-21

CREATE FUNCTION

dbo.Fun_WheIncluded

(

@TotalNum INT,

@SpecifiedNum INT

)

RETURNS BIT AS

BEGIN

DECLARE @varRet BIT

DECLARE @varLoop INT

SET @varLoop = 0

WHILE (@TotalNum >= CAST(POWER(2, @VarLoop) AS INT))

SET @varLoop = @varLoop + 1

SET @TotalNum = @TotalNum - CAST(POWER(2, @varLoop - 1) AS INT)

IF (@varLoop = @SpecifiedNum + 1)

SET @varRet = 1

ELSE

BEGIN

IF (@TotalNum >= 1)

RETURN dbo.Fun_WheIncluded(@TotalNum, @SpecifiedNum)

ELSE

SET @varRet = 0

END

RETURN @varRet

END