POJ 1704 Georgia and Bob 阶梯尼姆博弈

最新推荐文章于 2021-06-18 01:32:07 发布

Southan97

最新推荐文章于 2021-06-18 01:32:07 发布

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分类专栏： Gaming 文章标签：阶梯尼姆博弈

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本文介绍了一个关于Georgia和Bob之间的棋盘游戏策略问题。玩家轮流移动棋子，目标是在对手无法移动时获胜。文章详细解释了游戏规则，并提供了一段C++代码实现，通过计算初始位置来预测胜利者。

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Georgia and Bob

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 10221		Accepted: 3350

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

阶梯尼姆博弈，将石头两两分组，只要将距离差值抑或即为答案，因为无论前一个石头怎么动，后一个石头总能相应地移动，奇数时将第一个和第零个组合即可。

#include <iostream>
#include <algorithm>
#define endl "\n"
using namespace std;
const int MAXN = 10000 + 7;
int p[MAXN];
int main()
{
        ios::sync_with_stdio(false);
        int T, n, ans = 0;
        cin >> T;
        p[0] = 0;
        while(T--) {
                ans = 0;
                cin >> n;
                for(int i = 1; i <= n; ++i) {
                        cin >> p[i];
                }
                sort(p, p+n+1);
                if(n & 1) {
                        for(int i = 1; i <= n; i += 2) {
                                ans ^= p[i] - p[i-1] - 1;
                        }
                }       
                else {
                        for(int i = 1; i+1 <= n; i += 2) {
                                ans ^= p[i+1] - p[i];
                        }
                }
                if(ans) {
                        cout << "Georgia will win" << endl;
                }
                else {
                        cout << "Bob will win" << endl;
                }
        }
        return 0;
}