Triangulation

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 96    Accepted Submission(s): 29

Problem Description There are n points in a plane, and they form a convex set.

No, you are wrong. This is not a computational geometry problem.

Carol and Dave are playing a game with this points. (Why not Alice and Bob? Well, perhaps they are bored. ) Starting from no edges, the two players play in turn by drawing one edge in each move. Carol plays first. An edge means a line segment connecting two different points. The edges they draw cannot have common points.

To make this problem a bit easier for some of you, they are simutaneously playing on N planes. In each turn, the player select a plane and makes move in it. If a player cannot move in any of the planes, s/he loses.

Given N and all n’s, determine which player will win.  

Input First line, number of test cases, T.

Following are 2*T lines. For every two lines, the first line is N; the second line contains N numbers, n
₁, …, n
_N.

Sum of all N <= 10
⁶.

1<=n
_i<=10
⁹.  

Output T lines. If Carol wins the corresponding game, print ‘Carol’ (without quotes;) otherwise, print ‘Dave’ (without quotes.)  

Sample Input 2 1 2 2 2 2  

Sample Output Carol Dave  

Source
2013 Multi-University Training Contest 6  

Recommend zhuyuanchen520         这题一开始看错题目意思了。   导致连SG函数转移都写不出来。   其实这题看懂了就很好搞了。   每次加边，不能形成三角形，所以肯定不加共点的边，否则就是自杀。   x个点，转移后相当于 i    ,    x-i-2 .加的那两个点去掉了。     SG函数打表以后，很明显是要找规律。 发现周期是34. 而且周期要到后面才有周期。   所以前面打表，后面利用周期。   可以参考下oeis,发现这个是经典的问题。Sprague-Grundy values for Dawson’s Chess
http://oeis.org/search?q=0%2C1%2C1%2C2%2C0%2C3%2C1%2C1%2C0%2C3%2C3%2C2%2C2%2C4%2C0%2C5%2C2%2C2%2C3%2C3%2C0&sort=&language=english&go=Search   Has period 34 with the only exceptions at n=0, 14, 16, 17, 31, 34 and 51.     然后胡搞下就过了    

 1 /*
 2  * Author:  kuangbin
 3  * Created Time:  2013/8/8 11:54:23
 4  * File Name: 1010.cpp
 5  */
 6 #include <iostream>
 7 #include <cstdio>
 8 #include <cstdlib>
 9 #include <cstring>
10 #include <cmath>
11 #include <algorithm>
12 #include <string>
13 #include <vector>
14 #include <stack>
15 #include <queue>
16 #include <set>
17 #include <time.h>
18 using namespace std;
19 const int MAXN = 100010;
20 int sg[MAXN];
21 bool vis[MAXN];
22 int mex(int x)
23 {
24 
25     if(sg[x]!=-1)return sg[x];
26     if(x == 0)return sg[x] = 0;
27     if(x == 1)return sg[x] = 0;
28     if(x == 2)return sg[x] = 1;
29     if(x == 3)return sg[x] = 1;
30     memset(vis,false,sizeof(vis));
31     for(int i = 0;i < x-1;i++)
32         vis[mex(i)^mex(x-i-2)] = true;
33     for(int i = 0;;i++)
34         if(!vis[i])
35             return sg[x] = i;
36 }
37 
38 int SG(int x)
39 {
40     if(x <= 200)return sg[x];
41     else
42     {
43         x %= 34;
44         x += 4*34;
45         return sg[x];
46     }
47 }
48 
49 int main()
50 {
51     //freopen("in.txt","r",stdin);
52     //freopen("out.txt","w",stdout);
53     memset(sg,-1,sizeof(sg));
54     for(int i = 0;i <= 1000;i++)
55     {
56         sg[i] = mex(i);
57     }
58     int T;
59     int n;
60     int a;
61     scanf("%d",&T);
62     while(T--)
63     {
64         scanf("%d",&n);
65         int sum = 0;
66         for(int i = 0;i < n;i++)
67         {
68             scanf("%d",&a);
69             sum ^= SG(a);
70         }
71         if(sum)printf("Carol\n");
72         else printf("Dave\n");
73     }
74     return 0;
75 }