HDU 1907:John(尼姆博弈变形)
John
Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 6017 Accepted Submission(s): 3499
Problem Description
Little John is playing very funny game with his younger brother. There is one big box filled with M&Ms of different colors. At first John has to eat several M&Ms of the same color. Then his opponent has to make a turn. And so on. Please note that each player has to eat at least one M&M during his turn. If John (or his brother) will eat the last M&M from the box he will be considered as a looser and he will have to buy a new candy box.
Both of players are using optimal game strategy. John starts first always. You will be given information about M&Ms and your task is to determine a winner of such a beautiful game.
Input
The first line of input will contain a single integer T – the number of test cases. Next T pairs of lines will describe tests in a following format. The first line of each test will contain an integer N – the amount of different M&M colors in a box. Next line will contain N integers Ai, separated by spaces – amount of M&Ms of i-th color.
Constraints:
1 <= T <= 474,
1 <= N <= 47,
1 <= Ai <= 4747
Output
Output T lines each of them containing information about game winner. Print “John” if John will win the game or “Brother” in other case.
Sample Input
2
3
3 5 1
1
1
Sample Output
John
Brother
题意
两个人取n堆石子,每个人至少去一个,最多把一堆石子取完,取到最后一个石子的人失败
思路
先手胜的情况:
- n堆石子全部都只有一个石子,且n堆石子的异或值为0
- n堆石子不全是一个石子,且异或值不为0
证明:
- 若所有堆石子数都为1且SG值为0,则共有偶数堆石子,故先手胜。
- 只有一堆石子数大于1时,我们总可以对该堆石子操作,使操作后石子堆数为奇数且所有堆得石子数均为1
- 有超过一堆石子数大于1时,先手将SG值变为0即可,且总还存在某堆石子数大于1
思路来自:http://hzwer.com/1950.html
AC代码
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <math.h>
#include <limits.h>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#include <set>
#include <string>
#define ll long long
#define ull unsigned long long
#define ms(a) memset(a,0,sizeof(a))
#define pi acos(-1.0)
#define INF 0x7f7f7f7f
#define lson o<<1
#define rson o<<1|1
const double E=exp(1);
const int maxn=1e6+10;
const int mod=1e9+7;
using namespace std;
int main(int argc, char const *argv[])
{
ios::sync_with_stdio(false);
int t;
int n;
int x;
cin>>t;
while(t--)
{
cin>>n;
int sum=0;
int res=0;
while(n--)
{
cin>>x;
sum^=x;
if(x>1)
res++;
}
if(!res)
{
if(!sum)
cout<<"John"<<endl;
else
cout<<"Brother"<<endl;
}
else
{
if(!sum)
cout<<"Brother"<<endl;
else
cout<<"John"<<endl;
}
}
return 0;
}
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