PUZZLEUP 2014

〇〇 · 发表于 2014-9-25 18:56

newkid 发表于 2014-9-24 21:43
#9 Knights and Rooks

In how many different ways can two knights and two rooks be placed on a stan ...

是一种颜色的棋，还是2种颜色的棋？
同种颜色的棋能否互相攻击？
马是否必须放在马位上？

newkid · 发表于 2014-9-25 22:12

〇〇发表于 2014-9-25 18:56
是一种颜色的棋，还是2种颜色的棋？
同种颜色的棋能否互相攻击？
马是否必须放在马位上？

自己想想嘛。八皇后问题可曾提到颜色？题目的例子4X4哪里有什么“马位”?

〇〇 · 发表于 2014-9-25 22:15

newkid 发表于 2014-9-25 22:12
自己想想嘛。八皇后问题可曾提到颜色？题目的例子4X4哪里有什么“马位”?

那就是放了1个车，它同行同列都不能放，放了一个马，它周围最多8个点不能放。。。

lastwinner · 发表于 2014-9-26 09:47

newkid 发表于 2014-9-24 21:43
#9 Knights and Rooks

In how many different ways can two knights and two rooks be placed on a stan ...

马和车互不攻击，还是四个子儿都互不攻击？
看原文好像是后者

〇〇 · 发表于 2014-9-26 18:33

newkid 发表于 2014-9-24 21:43
#9 Knights and Rooks

In how many different ways can two knights and two rooks be placed on a stan ...

一气呵成
var n number
exec :n:=4
with t as (select level p,trunc((level-1)/:n)+1 r,mod(level-1,:n)+1 c from dual connect by level<=:n*:n)
select count(*) from t c,t e,t m,t a
where c.p<e.p and m.p<a.p
and c.r<>e.r and c.r<>m.r and c.r<>a.r and e.r<>m.r and e.r<>a.r
and c.c<>e.c and c.c<>m.c and c.c<>a.c and e.c<>m.c and e.c<>a.c
and 5 not in (
(m.r-c.r)*(m.r-c.r)+(m.c-c.c)*(m.c-c.c),
(m.r-e.r)*(m.r-e.r)+(m.c-e.c)*(m.c-e.c),
(m.r-a.r)*(m.r-a.r)+(m.c-a.c)*(m.c-a.c),
(a.r-c.r)*(a.r-c.r)+(a.c-c.c)*(a.c-c.c),
(a.r-e.r)*(a.r-e.r)+(a.c-e.c)*(a.c-e.c)
);

newkid · 发表于 2014-9-26 23:39

你这方法比我的快点：

WITH b AS (
SELECT POWER(2,LEVEL-1) id
   ,CEIL(LEVEL/:N) X
   ,MOD(LEVEL-1,:N) Y
  FROM DUAL
CONNECT BY LEVEL<=:N*:N
)
,c AS (
SELECT b1.id
   ,SUM(CASE WHEN b1.x=b2.x OR b1.y=b2.y THEN b2.id END)+b1.id r_attack
   ,SUM(CASE WHEN (ABS(b1.x-b2.x),ABS(b1.y-b2.y)) IN ((1,2),(2,1)) THEN b2.id END)+b1.id k_attack
  FROM b b1,b b2
WHERE b1.id<>b2.id
GROUP BY b1.id
)
SELECT COUNT(*)
  FROM c r1,c r2,c k1,c k2
WHERE r1.id<r2.id
   AND k1.id<k2.id
   AND BITAND(r1.r_attack,r2.id)=0
   AND BITAND(r1.r_attack,k1.id)=0
   AND BITAND(r1.r_attack,k2.id)=0
   AND BITAND(r2.r_attack,k1.id)=0
   AND BITAND(r2.r_attack,k2.id)=0
   AND BITAND(k1.k_attack,k2.id)=0
   AND BITAND(k1.k_attack,r1.id)=0
   AND BITAND(k1.k_attack,r2.id)=0
   AND BITAND(k2.k_attack,r1.id)=0
   AND BITAND(k2.k_attack,r2.id)=0
   ;

含泪劝OO放弃这个章，我的章只发给非版主的PUBER