POJ
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A Funny Game
Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 6198 Accepted: 3873
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.
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
1230
Sample Output
AliceAliceBob
Source
POJ Contest,Author:Mathematica@ZSU
题意：有n个硬币围成一圈，每次只能拿一个硬币或者拿相连的两个硬币，Alice先拿
训练时直接画了几个就瞎猜结论就过了
n>=3时
Alice第一次拿完之后 剩下的硬币可以看成是一条连续的由n-1或n-2个硬币组成的直线
Bob只需将剩下硬币分为均等的两半之后照着Alice 拿便可获胜
所以n<=2时Alice赢，其他情况Bob赢
