[經典演算法]海盜分金問題sql求解

問題：

經濟學上有個“海盜分金”模型：是說5個海盜搶得100枚金幣，他們按抽簽的順序依次提方案：首先由1號提出分配方案，然後5人表決，超過半數同意方案才被通過，否則他將被扔入大海喂鯊魚，依此類推,假設海盜是足夠聰明的，最後方案是怎樣的？

網上百度來的的代碼：

with a as 
(select 101 - rownum  n from dual connect by rownum <102),
max_one as 
(select max(n) max1 from a),
max_two as 
(select /*+leading(p2,p1) use_nl(p1) */ p2.n max2,p1.n max1 
 from a p1,a p2
 where p1.n+p2.n=100
 and p1.n=(select max1 from max_one)
 and rownum=1),
max_three as 
(select /*+leading(p3,p2,p1) use_nl(p2) use_nl(p1)*/ p3.n max3,p2.n max2,p1.n max1
 from a p1,a p2,a p3,max_two
 where p1.n+p2.n+p3.n=100
 and sign(p2.n-max2)+sign(p1.n-max1)>=0
 and rownum=1),
max_four as 
(select /*+leading(p4,p3,p2,p1) use_nl(p3) use_nl(p2) use_nl(p1)*/ p4.n max4,p3.n max3,p2.n max2,p1.n max1
 from a p1,a p2,a p3,a p4,max_three
 where p1.n+p2.n+p3.n+p4.n=100
 and sign(p3.n-max3)+sign(p2.n-max2)+sign(p1.n-max1)>0
 and rownum=1),
five as 
(select /*+leading(p5,p4,p3,p2,p1) use_nl(p4) use_nl(p3) use_nl(p2) use_nl(p1)*/ p5.n n5, p4.n n4,p3.n n3,p2.n n2,p1.n n1
 from a p1,a p2,a p3,a p4,a p5,max_four
 where p1.n+p2.n+p3.n+p4.n+p5.n=100
 and sign(p4.n-max4)+sign(p3.n-max3)+sign(p2.n-max2)+sign(p1.n-max1)>=0
 and rownum=1)
select * from five;

嚴格篩選數據，優化後

with a as 
(select 101 - rownum  n from dual connect by rownum <102),
max_one as 
(select max(n) max1 from a),
max_two as 
(select /*+leading(max_one,p2,p1) use_nl(p2) use_nl(p1) */ p2.n max2,p1.n max1 
 from a p1,a p2,max_one
 where p1.n+p2.n=100
 and p1.n>=max1
 and rownum=1),
max_three as 
(select /*+leading(max_two,p3,p2,p1) use_nl(max_two) use_nl(p2) use_nl(p1)*/ p3.n max3,p2.n max2,p1.n max1
 from a p1,a p2,a p3,max_two
 where p1.n+p2.n+p3.n=100
 AND p3.n+p2.n<=100
 and CASE WHEN p2.n > max2 THEN 1 ELSE -1 END +
     CASE WHEN p1.n > max1 THEN 1 ELSE -1 END >= 0
 and rownum=1),
max_four as 
(select /*+leading(max_three,p4,p3,p2,p1) use_nl(max_three) use_nl(p3) use_nl(p2) use_nl(p1)*/ p4.n max4,p3.n max3,p2.n max2,p1.n max1
 from a p1,a p2,a p3,a p4,max_three
 where p1.n+p2.n+p3.n+p4.n=100
 AND p4.n+p3.n <= 100
 AND p4.n+p3.n+p2.n <= 100
 and CASE WHEN p3.n > max3 THEN 1 ELSE -1 END +
     CASE WHEN p2.n > max2 THEN 1 ELSE -1 END +
     CASE WHEN p1.n > max1 THEN 1 ELSE -1 END >= 0
 and rownum=1),
five as 
(select /*+leading(max_four,p5,p4,p3,p2,p1) use_nl(p5) use_nl(p4) use_nl(p3) use_nl(p2) use_nl(p1)*/ p5.n n5, p4.n n4,p3.n n3,p2.n n2,p1.n n1
 from a p1,a p2,a p3,a p4,a p5,max_four
 where p1.n+p2.n+p3.n+p4.n+p5.n=100
 AND p5.n+p4.n <= 100
 AND p5.n+p4.n+p3.n <= 100
 AND p5.n+p4.n+p3.n+p2.n <= 100
 AND CASE WHEN p4.n > max4 THEN 1 ELSE -1 END + 
     CASE WHEN p3.n > max3 THEN 1 ELSE -1 END +
     CASE WHEN p2.n > max2 THEN 1 ELSE -1 END +
     CASE WHEN p1.n > max1 THEN 1 ELSE -1 END >= 0
 and rownum=1)
select * from five;