[ACM] poj 2484 A Funny Game（对称博弈）

A Funny Game

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 3795		Accepted: 2268

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

Alice
Alice
Bob

Source

POJ Contest,Author:Mathematica@ZSU

解题思路：

对于n<=2，先手ALICE必胜。n>3时，无论Alice怎么取，BOB都可以取一定的数目来构造出中心对称，这样BOB一定是最后一次取光的。

代码：