hdu-2509-反nim博弈

Be the Winner

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4699    Accepted Submission(s): 2576

Problem Description

Let's consider m apples divided into n groups. Each group contains no more than 100 apples, arranged in a line. You can take any number of consecutive apples at one time.
For example "@@@" can be turned into "@@" or "@" or "@ @"(two piles). two people get apples one after another and the one who takes the last is 
the loser. Fra wants to know in which situations he can win by playing strategies (that is, no matter what action the rival takes, fra will win).

 

Input

You will be given several cases. Each test case begins with a single number n (1 <= n <= 100), followed by a line with n numbers, the number of apples in each pile. There is a blank line between cases.

 

Output

If a winning strategies can be found, print a single line with "Yes", otherwise print "No".

 

Sample Input

2 2 2 1 3

 

Sample Output

No Yes

 

Source

ECJTU 2008 Autumn Contest

 

   一开始没注意到0态是胜态这个条件，想成sg来做了，结果WA。

   这个题目参考1709的证明过程，不同的地方在于这个可以将一堆取走一部分之后再把剩下的分成两堆，有趣啊，

但是按照上述证明即使有这个条件依然不影响结论的正确性，所以可以直接套用。

　　

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 int main(){
 4     int t,n,m;
 5     while(cin>>n){
 6         int a,sg=0,tot=0;
 7         for(int i=1;i<=n;++i){
 8             cin>>a;
 9             sg^=a;
10             if(a==1) tot++;
11         }
12         if( (tot==n&&sg==0) || (tot!=n&&sg!=0)) puts("Yes");
13         else puts("No");
14     }
15     return 0;
16 }