POJ 1704 Georgia and Bob

最新推荐文章于 2021-03-04 06:48:44 发布

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最新推荐文章于 2021-03-04 06:48:44 发布

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分类专栏：博弈论

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Description

Georgia and Bob decide to play a self-invented game. They draw a row of grids on paper, number the grids from left to right by 1, 2, 3, ..., and place N chessmen on different grids, as shown in the following figure for example:

Georgia and Bob move the chessmen in turn. Every time a player will choose a chessman, and move it to the left without going over any other chessmen or across the left edge. The player can freely choose number of steps the chessman moves, with the constraint that the chessman must be moved at least ONE step and one grid can at most contains ONE single chessman. The player who cannot make a move loses the game.

Georgia always plays first since "Lady first". Suppose that Georgia and Bob both do their best in the game, i.e., if one of them knows a way to win the game, he or she will be able to carry it out.

Given the initial positions of the n chessmen, can you predict who will finally win the game?

Input

The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Each test case contains two lines. The first line consists of one integer N (1 <= N <= 1000), indicating the number of chessmen. The second line contains N different integers P1, P2 ... Pn (1 <= Pi <= 10000), which are the initial positions of the n chessmen.

Output

For each test case, prints a single line, "Georgia will win", if Georgia will win the game; "Bob will win", if Bob will win the game; otherwise 'Not sure'.

Sample Input

2
3
1 2 3
8
1 5 6 7 9 12 14 17

Sample Output

Bob will win
Georgia will win

从恐惧到入门

博弈论！！！对于棋子，我们对他们进行每两个分一组，把每组之间的首和尾之间的空格作为每一堆石子的个数，可以这么想：每组之间的距离对结果造不成影响，因为如果前面的向前移动，后面的也可以跟上，最后真正起作用的只是首和尾的距离。

#include <stdio.h>
#include <cstring>
#include <algorithm>
const int MAXN = 1005;
int T,n,a[MAXN];


template<typename _t>
inline _t read(){
    _t x=0,f=1;
    char ch=getchar();
    for(;ch>'9'||ch<'0';ch=getchar())if(ch=='-')f=-f;
    for(;ch>='0'&&ch<='9';ch=getchar())x=x*10+(ch^48);
    return x*f;
}

int main(){
    T=read<int>();
    while(T--){
        n=read<int>();
        for(int i=1;i<=n;i++)a[i]=read<int>();
        std :: sort(&a[1],&a[n+1]);
        int xor_sum=0;
        for(int i=n;i>=1;i-=2){
            if(i==1)xor_sum^=a[i]-1;
            else xor_sum^=a[i]-a[i-1]-1;
        }
        if(xor_sum==0)printf("Bob will win\n");
        else printf("Georgia will win\n");
    }
}