【叶子函数分享四十】将一个正整数分解为m个2的n次方的和

-- =============================================

-- Author:      <maco_wang>

-- Create date: <2011-01-21>

-- Description: <将一个正整数分解为m个2的n次方的和>

-- =============================================

go

--创建函数

CREATE function GetSumSequence(@num INT)

returns nvarchar(200)

AS

    BEGIN

        DECLARE @numc INT

        SET @numc = @num

        DECLARE @numstr VARCHAR(50)

        SET @numstr = ''

        WHILE ( @num <> 0 )

            BEGIN

                SET @numstr = @numstr + CONVERT(CHAR(1), @num % 2)

                SET @num = @num / 2

            END

        --SELECT REVERSE(@numstr)

        DECLARE @i INT

        SET @i = LEN(@numstr)

        DECLARE @j VARCHAR(MAX)

        SET @j = ''

        WHILE ( @i > 0 )

            BEGIN

                IF ( SUBSTRING(REVERSE(@numstr), LEN(@numstr) - @i + 1, 1) = '1' )

                    SELECT  @j = @j + '+2^' + CAST (@i-1 AS VARCHAR(10))

                SET @i = @i - 1

            END

        return (CAST(@numc AS VARCHAR(100)) + '=' + STUFF(@j, 1, 1, ''))

    END

 

go

--测试示例

select dbo.GetSumSequence(12)

select dbo.GetSumSequence(65)

select dbo.GetSumSequence(892)

select dbo.GetSumSequence(1919191)

 

--运行结果

/*

12=2^3+2^2

65=2^6+2^0

892=2^9+2^8+2^6+2^5+2^4+2^3+2^2

1919191=2^20+2^19+2^18+2^16+2^14+2^11+2^7+2^6+2^4+2^2+2^1+2^0

*/