元宵快乐：看SQL大师们用SQL绘制的团圆

题记：在多年以前，论坛活跃的时代，在ITPUB上你能看到各种新奇有趣的知识，及时新鲜的信息，出类拔萃的技巧，有很多让人多年以后还记忆犹新。

这个帖子让我忍不住在这个日子，再次发送出来，让大家一起再次体会SQL的强大和神奇能力。而写好SQL，仍然是我们持续不断的追求。

话团圆，画团圆，元宵佳节倍思亲，可是大家知道吗，万能的SQL可以帮助大家绘制团圆。

在ITPUB论坛里，一群SQL爱好者们会用SQL来描摹一切可能。请看如下这段SQL，为大家绘制了团团圆圆的五连环：

with a as (select distinct round(a.x + b.x) x,round(a.y + b.y) y from

(select (sum(x) over(order by n)) x,

                            round(sum(y) over(order by n)) y

              from (select n, cos(n/30 * 3.1415926)*2  x,

                           sin(n/30 * 3.1415926) y

                           from (select rownum - 1 n from all_objects where rownum <= 30 +30))) a,

            (select n, (sum(x) over(order by n)) x,

                            round(sum(y) over(order by n)) y

              from (select n,

                           cos( m /3 * 3.1415926) * 2 * 15 x,

                           sin( m /3 * 3.1415926)* 15 y

                      from (select case when rownum <= 2 then 3 

                      when rownum = 3 then -2 else -6 end m, rownum - 1 n

                              from all_objects where rownum <= 5))) b

          )

select replace(sys_connect_by_path(point, '/'), '/', null) star

  from (select b.y, b.x, decode(a.x, null, ' ', '*') point

          from a,

               (select *

                  from (select rownum - 1 + (select min(x) from a) x

                          from all_objects

                         where rownum <= (select max(x) - min(x) + 1 from a)),

                       (select rownum - 1 + (select min(y) from a) y

                          from all_objects

                         where rownum <= (select max(y) - min(y) + 1 from a))) b

         where a.x(+) = b.x

           and a.y(+) = b.y)

where x = (select max(x) from a)

start with x = (select min(x) from a)

connect by y = prior y

       and x = prior x + 1;

这段SQL在Oracle中输出了下图，请用SQL执行：

好吧，这是五个连环，事实上是奥运会的五环旗，在庆祝奥运期间，网友 nyfor 的随手创作。

再看如下一段SQL，则是输出了一个五角星：

with a as (

            select distinct round(sum(x) over(order by n)) x,

                            round(sum(y) over(order by n)) y

              from (select n,

                           cos(trunc(n / 20) * (1-1/5) * 3.1415926) * 2 x,

                           sin(trunc(n / 20) * (1-1/5) * 3.1415926) y

                      from (select rownum - 1 n from all_objects where rownum <= 20 * 5))

          )

select replace(sys_connect_by_path(point, '/'), '/', null) star

  from (select b.y, b.x, decode(a.x, null, ' ', '*') point

          from a,

               (select *

                  from (select rownum - 1 + (select min(x) from a) x

                          from all_objects

                         where rownum <= (select max(x) - min(x) + 1 from a)),

                       (select rownum - 1 + (select min(y) from a) y

                          from all_objects

                         where rownum <= (select max(y) - min(y) + 1 from a))) b

         where a.x(+) = b.x

           and a.y(+) = b.y)

where x = (select max(x) from a)

start with x = (select min(x) from a)

connect by y = prior y

       and x = prior x + 1;

这个SQL的解释如下：

其中数字20表示五角星每一条边上的点的个数(你也可以设置的大一些或小一些), 其中的数字5表示五角星的边数, 其中的数字2是为了调整横向字符间距与纵向行距之间的差异而设置的, 你也可以不乘以这个2, 这里只是为了输出稍微好看一些.

调整期中数字5, 你还可以输出7角星, 9角星.... 注意我的SQL不能输出6角星,8角星，因为我的SQL算法中是以一笔画能够画成的星为基础设计的算法的.

比如，以下是7角形输出：

在一轮讨论之后，newkid 大神给出了一个系列的SQL改写，小编就列举如下。

SQL一：

with a as ( select distinct round(sum(x) over(order by n)) x,

                            round(sum(y) over(order by n)) y

              from (select n,

                           cos(trunc(n / 20) * (1-1/5) * 3.1415926) * 2 x,

                           sin(trunc(n / 20) * (1-1/5) * 3.1415926) y

                      from (select rownum - 1 n from DUAL CONNECT BY rownum <= 20 * 5))

          )

SELECT LPAD(REPLACE(SUM(POWER(10,x-1)),'0',' '),(SELECT MAX(x) FROM a)) AS star

  FROM a

GROUP BY y

ORDER BY y;

SQL二：

with a as ( select distinct round(sum(x) over(order by n)) x,

                            round(sum(y) over(order by n)) y

              from (select n,

                           cos(trunc(n / 20) * (1-1/5) * 3.1415926) x,

                           sin(trunc(n / 20) * (1-1/5) * 3.1415926) y

                      from (select rownum - 1 n from DUAL CONNECT BY rownum <= 20 * 5))

          )

SELECT LPAD(REPLACE(SUM(POWER(10,x)),'0',' '),(SELECT MAX(x)+1 FROM a)) AS star

  FROM a

GROUP BY y

ORDER BY y;

SQL三：

with a as ( select distinct round(sum(x) over(order by n)) x,

                            round(sum(y) over(order by n)) y

              from (select n,

                           cos(trunc(n / 20) * (1-1/5) * 3.1415926) * 2 x,

                           sin(trunc(n / 20) * (1-1/5) * 3.1415926) y

                      from (select rownum - 1 n from DUAL CONNECT BY rownum <= 20 * 5))

          )

SELECT TRANSLATE(LPAD(NVL(SUM(POWER(10,CASE WHEN x>=40 THEN x-40 END)),0),(SELECT MAX(x)-39 FROM a WHERE x>=40))

                 ||LPAD(SUM(POWER(10,CASE WHEN x<40 THEN x END)),40) 

                ,'01',' *'

                )

        AS star

  FROM a

GROUP BY y

ORDER BY y;

SQL四：

with a as (SELECT x,y

                 ,ROW_NUMBER() OVER(PARTITION BY y ORDER BY x) rn

                 ,MAX(x) OVER(PARTITION BY y) maxx

             FROM (select distinct round(sum(x) over(order by n)) x,

                                  round(sum(y) over(order by n)) y

                    from (select n,

                                 cos(trunc(n / 20) * (1-1/5) * 3.1415926) * 2 x,

                                 sin(trunc(n / 20) * (1-1/5) * 3.1415926) y

                            from (select rownum - 1 n from DUAL CONNECT BY rownum <= 20 * 5)

                          )

                   )

          )

,t(rn,x,y,str,maxx) AS (

SELECT 1,x,y,LPAD('*',x+1),maxx FROM a WHERE rn=1

UNION ALL

SELECT a.rn,a.x,t.y,str||RPAD(' ',a.x-t.x-1)||'*',t.maxx

  FROM t,a 

WHERE t.rn=a.rn-1 AND t.y=a.y

) CYCLE x,y SET cycle_flag TO 'Y' DEFAULT 'N'

SELECT str FROM t WHERE x=maxx ORDER BY y;

SQL五：

VAR SCALE NUMBER;

EXEC :SCALE :=3;

with a as (SELECT x,y

                 ,ROW_NUMBER() OVER(PARTITION BY y ORDER BY x) rn

                 ,MAX(x) OVER(PARTITION BY y) maxx

             FROM (select distinct round(sum(x) over(order by n)) x,

                                  round(sum(y) over(order by n)) y

                    from (select n,

                                 cos(trunc(n / (10*:SCALE)) * (1-1/5) * 3.1415926) * 2 x,

                                 sin(trunc(n / (10*:SCALE)) * (1-1/5) * 3.1415926) y

                            from (select rownum - 1 n from DUAL CONNECT BY rownum <= 10*:SCALE * 5)

                          )

                   )

          )

,t(rn,x,y,str,maxx) AS (

SELECT 1,x,y,LPAD('*',x+1),maxx FROM a WHERE rn=1

UNION ALL

SELECT a.rn,a.x,t.y,str||RPAD(' ',a.x-t.x-1)||'*',t.maxx

  FROM t,a 

WHERE t.rn=a.rn-1 AND t.y=a.y

) CYCLE x,y SET cycle_flag TO 'Y' DEFAULT 'N'

SELECT str FROM t WHERE x=maxx ORDER BY y;

SQL六 - 利用wmsys.wm_concat的写法其实更简单：

with a as (SELECT x,y

                 ,LAG(x,1,0) OVER(PARTITION BY y ORDER BY x) last_x

             FROM (select distinct round(sum(x) over(order by n)) x,

                                  round(sum(y) over(order by n)) y

                    from (select n,

                                 cos(trunc(n / (10*:SCALE)) * (1-1/5) * 3.1415926) * 2 x,

                                 sin(trunc(n / (10*:SCALE)) * (1-1/5) * 3.1415926) y

                            from (select rownum - 1 n from DUAL CONNECT BY rownum <= 10*:SCALE * 5)

                          )

                   )

          )

SELECT REPLACE(MAX(str),',') STR

  FROM (SELECT y,wmsys.wm_concat(LPAD('*',x-last_x)) OVER(PARTITION BY y ORDER BY x) str

          FROM a

        )

GROUP BY y

ORDER BY y;

SQL之七 - wmsys.wm_concat的connect by替代写法：

with a as (SELECT x,y

                 ,LAG(x,1,0) OVER(PARTITION BY y ORDER BY x) last_x

                 ,ROW_NUMBER() OVER(PARTITION BY y ORDER BY x) rn

             FROM (select distinct round(sum(x) over(order by n)) x,

                                  round(sum(y) over(order by n)) y

                    from (select n,

                                 cos(trunc(n / (10*:SCALE)) * (1-1/5) * 3.1415926) * 2 x,

                                 sin(trunc(n / (10*:SCALE)) * (1-1/5) * 3.1415926) y

                            from (select rownum - 1 n from DUAL CONNECT BY rownum <= 10*:SCALE * 5)

                          )

                   )

          )

SELECT REPLACE(MAX(str),',') STR

  FROM (SELECT y,SYS_CONNECT_BY_PATH(LPAD('*',x-last_x),',') str

          FROM a

         START WITH rn=1

        CONNECT BY y=PRIOR y AND rn=PRIOR rn+1

        )

GROUP BY y

ORDER BY y;

SQL如神，学习入化，动手为王，祝愿大家元宵节快乐！

还有一些神奇的文章：

无往不利：用SQL解海盗分金的利益最大化问题

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