通过SQL绘制杨辉三角的实现方法介绍

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本篇文章长沙网络推广为大家介绍,通过SQL绘制杨辉三角的实现方法介绍。需要的朋友参考下

无意中在csdn上看到一帖有关绘制杨辉三角的sql表达式,感觉很有意思。后来自己想下不借助临时表,根据杨辉三角的组合数计算方法C(n,m)=n!/[m!(n-m)!],进行绘制。

以下是完整的SQL代码

代码如下:

use tempdb
go
set nocount on
declare @rows int=10, --行数,根据实际来控制
        @x int=1,@y int=1,@sql nvarchar(max),@cols int

/
根据杨辉三角的组合数计算方法C(n,m)=n!/[m!(n-m)!]进行绘制
参照http://baike.baidu./view/7804.htm
/

set @cols=@rows2-1
;with cte_n as
(
    select r from (select row_number() over(order by a.object_id) as r from sys.all_columns a ) x where r<=@rows2
)
,cte_1 as(select n.r,b.data_lse
            from cte_n n
                cross apply(select 'select '+stuff((select ',rtrim('+isnull(F1.v+'/(('+F2.v+')'+F3.v+')','''''') +') as '+quotename(isnull(nullif((m.r +(@rows-n.r)+(m.r-1)1)%@cols,0),@cols))
                                from cte_n m
                                    outer apply(select stuff((select ''+rtrim(i.r) from cte_n i where i.r<=isnull((nullif(n.r-1,0)),1) for xml path('')),1,1,'') as v
                                        ) F1
                                    outer apply(select stuff((select ''+rtrim(i.r) from cte_n i where i.r<=isnull((nullif(m.r-1,0)),1) for xml path('')),1,1,'') as v
                                        ) F2
                                    outer apply(select stuff((select ''+rtrim(i.r) from cte_n i where i.r<=isnull((nullif(n.r-m.r,0)),1) for xml path('')),1,1,'') as v
                                        ) F3
                                where m.r<@rows2
                                order by isnull(nullif((m.r +(@rows-n.r)+(m.r-1)1)%@cols,0),@cols) asc
                                for xml path('')                                   
                                ),1,1,'') as data_lse
                            )b
                where n.r <=@rows
            )

    select @sql=isnull(@sql+' union all ','')+data_lse from  cte_1
exec(@sql)


(【注】当前脚本在SQL Server 2012上测试通过)

效果图



这方法虽然没有借助临时表,也有一个最大的不足就是不能设置太多行,因为在公式(C(n,m)=n!/[m!(n-m)!])中有n! 和m! 算式,设置行数太多会导致阶乘数据太大,发生数据类型转换溢出。有时间再想办法看能否从表示式中"/"除位置进行优化

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