3101: N皇后
3101: N皇后
Time Limit: 10 Sec Memory Limit: 128 MBSec Special Judge
Submit: 88 Solved: 41
Description
n*n的棋盘,在上面摆下n个皇后，使其两两间不能相互攻击…
Input
一个数n
Output
第i行表示在第i行第几列放置皇后
Sample Input
4
Sample Output
2 4 1 3
HINT
100%的数据3<n<1000000。输出任意一种合法解即可
Source
题解：一道神(dou)奇(bi)的题目，传说中貌似有种O(N)构造N皇后解的方法，具体为啥貌似也查不到，求神犇给出证明orzorzorz（引自N皇后的构造解法）
一、当n mod 6 != 2 或 n mod 6 != 3时，有一个解为： 2,4,6,8,...,n,1,3,5,7,...,n-1 (n为偶数) 2,4,6,8,...,n-1,1,3,5,7,...,n (n为奇数) (上面序列第i个数为ai，表示在第i行ai列放一个皇后；... 省略的序列中，相邻两数以2递增。下同) 二、当n mod 6 == 2 或 n mod 6 == 3时， (当n为偶数,k=n/2；当n为奇数,k=(n-1)/2) k,k+2,k+4,...,n,2,4,...,k-2,k+3,k+5,...,n-1,1,3,5,...,k+1 (k为偶数,n为偶数) k,k+2,k+4,...,n-1,2,4,...,k-2,k+3,k+5,...,n-2,1,3,5,...,k+1,n (k为偶数,n为奇数) k,k+2,k+4,...,n-1,1,3,5,...,k-2,k+3,...,n,2,4,...,k+1 (k为奇数,n为偶数) k,k+2,k+4,...,n-2,1,3,5,...,k-2,k+3,...,n-1,2,4,...,k+1,n (k为奇数,n为奇数)
然后就是码代码了= =
1 /**************************************************************
2 Problem: 3101
3 User: HansBug
4 Language: Pascal
5 Result: Accepted
6 Time:1832 ms
7 Memory:224 kb
8 ****************************************************************/
9
10 var
11 i,j,k,l,m,n:longint;
12 begin
13 readln(n);
14 case n mod 6 of
15 2,3:begin
16 k:=n div 2;
17 case (k mod 2)+(n mod 2)*2 of
18 0:begin
19 for i:=0 to (n-k) div 2 do writeln(k+i*2);
20 for i:=0 to (k-4) div 2 do writeln(2+i*2);
21 for i:=0 to (n-k-4) div 2 do writeln(k+3+i*2);
22 for i:=0 to k div 2 do writeln(1+2*i);
23 end;
24 2:begin
25 for i:=0 to (n-k-1) div 2 do writeln(k+i*2);
26 for i:=0 to (k-4) div 2 do writeln(2+i*2);
27 for i:=0 to (n-k-5) div 2 do writeln(k+3+i*2);
28 for i:=0 to k div 2 do writeln(1+2*i);
29 writeln(n);
30 end;
31 1:begin
32 for i:=0 to (n-k-1) div 2 do writeln(k+i*2);
33 for i:=0 to (k-3) div 2 do writeln(1+i*2);
34 for i:=0 to (n-k-3) div 2 do writeln(k+3+i*2);
35 for i:=0 to (k-1) div 2 do writeln(2+2*i);
36 end;
37 3:begin
38 for i:=0 to (n-k-2) div 2 do writeln(k+i*2);
39 for i:=0 to (k-3) div 2 do writeln(1+i*2);
40 for i:=0 to (n-k-4) div 2 do writeln(k+3+i*2);
41 for i:=0 to (k-1) div 2 do writeln(2+2*i);
42 writeln(n);
43 end;
44 end;
45 end;
46 else begin
47 if odd(n) then
48 begin
49 for i:=1 to (n-1) div 2 do writeln(i*2);
50 for i:=1 to (n+1) div 2 do writeln(i*2-1);
51 end
52 else
53 begin
54 for i:=1 to n div 2 do writeln(i*2);
55 for i:=1 to n div 2 do writeln(i*2-1);
56 end;
57 end;
58 end;
59 readln;
60 end.