HDU 2147-kiki's game(博弈/找规律)

墨蓝 2022-08-22 00:27 173阅读 0赞

# kiki's game #

**Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 40000/10000 K (Java/Others)  
Total Submission(s): 9174 Accepted Submission(s): 5485**

Problem Description

Recently kiki has nothing to do. While she is bored, an idea appears in his mind, she just playes the checkerboard game.The size of the chesserboard is n\*m.First of all, a coin is placed in the top right corner(1,m). Each time one people can move the coin into the left, the underneath or the left-underneath blank space.The person who can't make a move will lose the game. kiki plays it with ZZ.The game always starts with kiki. If both play perfectly, who will win the game?

Input

Input contains multiple test cases. Each line contains two integer n, m (0<n,m<=2000). The input is terminated when n=0 and m=0.

Output

If kiki wins the game printf "Wonderful!", else "What a pity!".

Sample Input

5 3
    5 4
    6 6
    0 0

Sample Output

What a pity!
    Wonderful!
    Wonderful!

Author

月野兔

Source

[HDU 2007-11 Programming Contest][]

Recommend

威士忌

## 题目意思： ##

有一个n\*m的棋盘，从右上角的位置走到左下角的位置，每次只能向左、下和左下三个方向移动。

最后不能再移动的人输掉比赛，如果kiki赢，输出"Wonderful!"；反之，输出"What a pity!"

就这道题而言，最后走到左下角位置的人为输掉比赛。

## 解题思路： ##

刚刚看了这个文件→[传送门][Link 1]

学了一点：

必败点(P点)  : 前一个选手(Previous player)将取胜的位置称为必败点。

必胜点(N点)  : 下一个选手(Next player)将取胜的位置称为必胜点。

**步骤1:将所有终结位置标记为必败点（P点）；**

**步骤2: 将所有一步操作能进入必败点（P点）的位置标记为必胜点（N点）**

**步骤3:如果从某个点开始的所有一步操作都只能进入必胜点（N点） ，则将该点标记为必败点（P点） ；**

**步骤4: 如果在步骤3未能找到新的必败（P点），则算法终止；否则，返回到步骤2。**

如图：![Center][]![Center 1][]

通过观察对角线和其他m或n为偶数时，N的位置，可以发现：如果n或m中有一个是偶数，那么必胜；反之，必败。

#include<iostream>
    using namespace std;
    
    int main()
    {
        int n,m;
        while(cin>>n>>m&&(m||n))
        {
            if(n%2==0||m%2==0)cout<<"Wonderful!"<<endl;
            else cout<<"What a pity!"<<endl;
        }
        return 0;
    }

[HDU 2007-11 Programming Contest]: http://acm.hdu.edu.cn/search.php?field=problem&key=HDU+2007-11++Programming+Contest&source=1&searchmode=source
[Link 1]: http://acm.hdu.edu.cn/forum/read.php?tid=6875
[Center]: https://img-blog.csdn.net/20160509171031951?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQv/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center
[Center 1]: /images/20220724/79a23404c171458e80ff9097c490487e.png