通过SQL绘制杨辉三角的实现方法介绍

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：
复制代码代码如下:
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：
*/

set @cols=@rows*2-1
;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<=@rows*2
)
,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<@rows*2

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：