UVa 10404 Bachet's Game(DP)

最新推荐文章于 2020-02-20 19:53:41 发布

原创最新推荐文章于 2020-02-20 19:53:41 发布 · 988 阅读

1 ·

CC 4.0 BY-SA版权

文章标签：

#ACM #UVa #DP #小白

--------- OJ --------- 同时被 3 个专栏收录

239 篇文章

订阅专栏

-------- 专题 --------

239 篇文章

订阅专栏

-UVa

77 篇文章

订阅专栏

本文探讨了Bachet's Game的一种变化形式，详细解释了如何通过动态规划方法确定最优策略，确保玩家能赢得比赛。游戏初始时桌面上有n颗石头，两名玩家Stan和Olive轮流移除石头，直至取走最后一颗石头者获胜。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

题意给你n个小石头和一个数组a[m] 然后两个人轮流取石头 stan先取 olive后取他们都完美发挥谁取完最后一个石头谁就是赢家感觉不是很容易看出来是dp题令d[i]表示只有i个石子时谁赢 1表示stan赢 0表示olive赢

i-a[j]表示从i个石子一次取走a[j]个还剩下的所以有当(i-a[j]>0&&d[i-a[j]]=0)时 d[i]=1;

#include<cstdio>  
#include<cstring>  
using namespace std;  
int d[1000005],a[12],ans,n,m;  
int main()  
{  
    while(scanf("%d",&n)!=EOF)  
    {  
        scanf("%d",&m);  
        for(int i=1;i<=m;++i)  
                scanf("%d",&a[i]);  
        memset(d,0,sizeof(d));  
        for(int i=1;i<=n;++i)  
            for(int j=1;j<=m;++j)  
            {  
                if(i-a[j]>=0&&d[i-a[j]]==0)  
                {  
                    d[i]=1;  
                    break;  
                }  
            }  
        printf(d[n]?"Stan wins\n":"Ollie wins\n");  
    }  
}

Bachet's Game

Bachet's game is probably known to all but probably not by this name. Initially there are nstones on the table. There are two players Stan and Ollie, who move alternately. Stan always starts. The legal moves consist in removing at least one but not more than kstones from the table. The winner is the one to take the last stone.

Here we consider a variation of this game. The number of stones that can be removed in a single move must be a member of a certain set of m numbers. Among the m numbers there is always 1 and thus the game never stalls.

Input

The input consists of a number of lines. Each line describes one game by a sequence of positive numbers. The first number is n <= 1000000 the number of stones on the table; the second number is m <= 10 giving the number of numbers that follow; the last m numbers on the line specify how many stones can be removed from the table in a single move.

Input

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

Sample input

20 3 1 3 8
21 3 1 3 8
22 3 1 3 8
23 3 1 3 8
1000000 10 1 23 38 11 7 5 4 8 3 13
999996 10 1 23 38 11 7 5 4 8 3 13

Output for sample input

Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins