A Funny Game(POJ-2484)

题面

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.

输入

There are several test cases. Each test case has only one line, which contains a positive integer n (1 <= n <= 10^6). There are no blank lines between cases. A line with a single 0 terminates the input.

输出

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

样例输入

11
22
33
40

样例输出

1Alice
2Alice
3Bob

提示

无

思路

当n < 3时，先手可以直接取完；n = 3时，无论先手如何取，后手都能取走剩下的；n > 3时，无论先手如何取，后手都能取走对应的，使得局面变为相等的两部分，随之后手模仿先手操作即可获得胜利。

代码

 1using namespace std;
 2
 3int main()
 4{
 5    int n;
 6    while(~scanf("%d", &n) && n)
 7    {
 8        if(n<3){
 9            printf("Alice\n");
10        }else{
11            printf("Bob\n");
12        }
13    }
14    return 0;
15}