UVa 10404. Bachet's Game

题意为给出总石子数n，和m堆石子，两个人轮着取石子，每次只能从总石子中取m堆中的一堆的个数的石子，取走最后一个石子的胜。S先取，O后取。

用博弈的输赢观念+dp就可以了，由于记忆化搜索会爆栈，那就递推了，索性还好推……

不然就不会了……

#include<iostream>#include<map>#include<string>#include<cstring>#include<cstdio>#include<cstdlib>#include<cmath>#include<queue>#include<vector>#include<algorithm>using namespace std;int dp[1000010];int a[20];int n,m;int main(){int i,j;while(cin>>n>>m){for(i=0;i<m;i++)cin>>a[i];for(i=0;i<=n;i++){dp[i]=0;for(j=0;j<m;j++)if(i-a[j]>-1&&dp[i-a[j]]==0){dp[i]=1;continue;}}if(dp[n]==1)cout<<"Stan wins"<<endl;elsecout<<"Ollie wins"<<endl;}}

Bachet's Game

Time Limit:6666MS Memory Limit:Unknown 64bit IO Format:%lld & %llu

SubmitStatus

Description

Problem B: Bachet's Game

Bachet's game is probably known to all but probably not by this name. Initially there aren 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 thank 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 ofm 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 isn <= 1000000 the number of stones on the table; the second number ism <= 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

---

Problem Setter: Piotr Rudnicki

Source

Root :: Competitive Programming 3: The New Lower Bound of Programming Contests (Steven & Felix Halim) :: Mathematics :: Game Theory ::Standard
Root :: AOAPC I: Beginning Algorithm Contests (Rujia Liu) :: Volume 5. Dynamic Programming
Root :: Competitive Programming 2: This increases the lower bound of Programming Contests. Again (Steven & Felix Halim) :: Mathematics ::Game Theory - Standard

Root :: Prominent Problemsetters :: Piotr Rudnicki