【题解】POJ-2505 A multiplication game

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POJ-2505 A multiplication game 类型 博弈论

A multiplication game(POJ-2505)

题面

Stan and Ollie play the game of multiplication by multiplying an integer p by one of the numbers 2 to 9. Stan always starts with p = 1, does his multiplication, then Ollie multiplies the number, then Stan and so on. Before a game starts, they draw an integer 1 < n < 4294967295 and the winner is who first reaches p >= n.

输入

Each line of input contains one integer number n.

输出

For each line of input output one line either Stan wins. or Ollie wins. assuming that both of them play perfectly.

样例输入

1
2
3
162
17
34012226

样例输出

1
2
3
Stan wins.
Ollie wins.
Stan wins.

提示

无

思路

找出先手必败区间(9, 18]，(162, 324]，$ $

规律： 9 = 9 18 = 2 * 9 162 = 9 * 2 * 9 324 = 2 * 9 * 2 * 9 $ $

代码

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using namespace std;
typedef long long LL;

int main()
{
    LL n;
    while(~scanf("%lld", &n) && n)
    {
        while(1){
            if(n<=9){
                printf("Stan wins.\n");
                break;
            }else if(n<=18){
                printf("Ollie wins.\n");
                break;
            }
            n = (LL)ceil(n/18.0);
        }
    }
    return 0;
}