（poj 2484）A Funny Game（博弈，对称）

Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 5992 Accepted: 3740
Description

Alice and Bob decide to play a funny game. At the beginning of the game they pick n(1 <= n <= 106) coins in a circle, as Figure 1 shows. A move consists in removing one or two adjacent coins, leaving all other coins untouched. At least one coin must be removed. Players alternate moves with Alice starting. The player that removes the last coin wins. (The last player to move wins. If you can’t move, you lose.)

Figure 1

Note: For n > 3, we use c1, c2, …, cn to denote the coins clockwise and if Alice remove c2, then c1 and c3 are NOT adjacent! (Because there is an empty place between c1 and c3.)

Suppose that both Alice and Bob do their best in the game.
You are to write a program to determine who will finally win the game.
Input

There are several test cases. Each test case has only one line, which contains a positive integer n (1 <= n <= 106). There are no blank lines between cases. A line with a single 0 terminates the input.
Output

For each test case, if Alice win the game,output “Alice”, otherwise output “Bob”.
Sample Input

1
2
3
0
Sample Output

Alice
Alice
Bob
Source

POJ Contest,Author:Mathematica@ZSU

题意：n个硬币排成一圈，A和B轮流从中取一枚或者两枚硬币（取两枚时必须是连续的），硬币取走后留下的空位当成不连续。每次都是A先取，双方都采取最优策略，问谁获胜？

分析：这里要 考虑对称的状态，再完全模仿对方的策略

#include<cstdio>int main(){    int n;    while(~scanf("%d",&n)&&n)    {        if(n<=2) puts("Alice");        else puts("Bob");    }    return 0;}