改進的sql計算n王后

原來的版本，不能計算大於11的N，因為那使oracle的bitand溢位了。在newkid的指點下，用同列，同左斜線，同右斜線3個bitmap代替用格子標號的1個bitmap。

with p(p,r,c)
as(select level,ceil(level/:n),mod(level-1,:n)+1 from dual connect by level<=:n*:n)
,w as(select p,power(2,c-1)w,power(2,:N-1+r-c)w1,power(2,r+c-2)w2 from p)
,b(board, n_queens,w,w1,w2)as(
    SELECT lpad('-',p-1,'-')||'*', 1 ,w,w1,w2
      FROM w where  p<=:N
    UNION all
    SELECT
      rpad(board,p-1,'-') || '*' ,N_queens + 1 ,b.w+w.w,b.w1+w.w1,b.w2+w.w2
      FROM b, w
    WHERE n_queens <:N
      and p >n_queens*:N and p<=(n_queens+1)*:N
      and bitand(b.w,w.w)=0 and bitand(b.w1,w.w1)=0 and bitand(b.w2,w.w2)=0 
)
select rpad(board,:N*:N,'-')board from b where n_queens =:N
;

計算n=12大約50秒.

with p(p,r,c)
as(select level,ceil(level/:n),mod(level-1,:n)+1 from dual connect by level<=:n*:n)
,w as(select p,power(2,c-1)w,power(2,:N-1+r-c)w1,power(2,r+c-2)w2 from p)
,b(board, n_queens,w,w1,w2)as(
    SELECT lpad('-',p-1,'-')||'*', 1 ,w,w1,w2
      FROM w where  p<=ceil(:N/2)
    UNION all
    SELECT
      rpad(board,p-1,'-') || '*' ,N_queens + 1 ,b.w+w.w,b.w1+w.w1,b.w2+w.w2
      FROM b, w
    WHERE n_queens <:N
      and p >n_queens*:N and 
    p<=case when mod(:N,2)=1 and b.w=power(2,(:N-1)/2) -- mid of row 1 is set
   then (n_queens+1)*:N-(:N+1)/2 
   else (n_queens+1)*:N end
      and bitand(b.w,w.w)=0 and bitand(b.w1,w.w1)=0 and bitand(b.w2,w.w2)=0 
),
hf as(select rpad(board,:N*:N,'-')board from b where n_queens =:N)
select * from hf
union all
select listagg(reverse(substr(board,(l-1)*:N+1,:N)))
within group(order by l) from hf a,(select level l from dual connect by level<=:N)b
group by board
;

利用對稱,大約26秒。看來對於大的N,基本可以節約1半時間。