Bachet's Game - UVa 10404 dp博弈论
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Problem B: Bachet's Game
Bachet's game is probably known to all but probably not by this name. Initially there are n stones 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 k stones 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 3 821 3 1 3 822 3 1 3 823 3 1 3 81000000 10 1 23 38 11 7 5 4 8 3 13999996 10 1 23 38 11 7 5 4 8 3 13
Output for sample input
Stan winsStan winsOllie winsStan winsStan winsOllie wins
题意:一共有n个石子,每人每次可以取规定中的一种数量的石子,问先手的胜负。
思路:对于i个石子,如果i-num[j]都是必胜的情况,那么i是必败的,如果其中有一种是必败的,那么i是必胜的,然后从小到大递推。
AC代码如下:
#include<cstdio>#include<cstring>using namespace std;int dp[1000010],num[15];int main(){ int n,m,i,j,k; while(~scanf("%d%d",&n,&m)) { for(i=1;i<=m;i++) scanf("%d",&num[i]); dp[0]=1; for(i=1;i<=n;i++) { k=0; for(j=1;j<=m;j++) if(num[j]<=i) k+=dp[i-num[j]]; if(k==0) dp[i]=1; else dp[i]=0; } if(dp[n]==0) printf("Stan wins\n"); else printf("Ollie wins\n"); }}
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