HDU 1907 nim博弈变形

John

Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 4479    Accepted Submission(s): 2567

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

 

Source

Southeastern Europe 2007

 题意：n堆石子 两个人轮流拿某一堆的石子 最少拿一个  拿走最后一个的输

 题解：nim博弈的分析 重在分析 贴Fsss的分析 链接

经典的Nim博弈的一点变形。设糖果数为1的叫孤独堆，糖果数大于1的叫充裕堆，设状态S0：a1^a2^..an!=0&&充裕堆=0，则先手必败（奇数个为1的堆，先手必败）。S1：充裕堆=1，则先手必胜（若剩下的n-1个孤独堆个数为奇数个，那么将那个充裕堆全部拿掉，否则将那个充裕堆拿得只剩一个，这样的话先手必胜）。T0：a1^a2^..an=0&&充裕堆=0，先手必胜（只有偶数个孤独堆，先手必胜）。S2：a1^a2^..an!=0&&充裕堆>=2。T2：a1^a2^..an=0&&充裕堆>=2。这样的话我们用S0,S1,S2,T0,T2将所有状态全部表示出来了，并且S0先手必败，S1、T0先手必胜，那么我们只需要对S2和T2的状态进行分析就行了。（a）S2可以取一次变为T2。（b）T2取一次可变为S2或者S1。因为S1是先手必胜态，那么根据a,b这两个转换规则，我们就能得知S2也是先手必胜，T2是先手必败。

/******************************
code by drizzle
blog: www.cnblogs.com/hsd-/
^ ^    ^ ^
 O      O
******************************/
#include<bits/stdc++.h>
#include<map>
#include<set>
#include<cmath>
#include<queue>
#include<bitset>
#include<math.h>
#include<vector>
#include<string>
#include<stdio.h>
#include<cstring>
#include<iostream>
#include<algorithm>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
#define  A first
#define B second
const int mod=1000000007;
const int MOD1=1000000007;
const int MOD2=1000000009;
const double EPS=0.00000001;
typedef __int64 ll;
const ll MOD=1000000007;
const int INF=1000000010;
const ll MAX=1ll<<55;
const double eps=1e-14;
const double inf=~0u>>1;
const double pi=acos(-1.0);
typedef double db;
typedef unsigned int uint;
typedef unsigned long long ull;
int t;
int n;
int ans,cou;
int main()
{
    while(scanf("%d",&t)!=EOF)
    {
        for(int i=1;i<=t;i++)
        {
            scanf("%d",&n);
            ans=cou=0;
            int exm;
            for(int j=1;j<=n;j++)
            {
              scanf("%d",&exm);
              ans^=exm;
              if(exm>1)
                cou++;
            }
            if((ans==0&&cou>=2)||(cou==0&&ans%2!=0))
                printf("Brother
");
            else
                printf("John
");
        }
    }

    return 0;
}