HDU - 2869 - Paper Cutting Game【 博弈 】题解

1.题目

Lily and Lucy are playing a new paper cutting game.
The game uses a rectangular paper that consists of WH grids.At first,there is only a sheet of WH paper. In each turn,One player picks up cut one piece of paper and cut it into several pieces of equal rectangular sections,and puts them back. Lily can only cut horizontally and Lucy can only cut vertically,keeping every grids unbroken.The one who can’t cut the paper loses.
Now given you a sheet of WH paper.We know Lily always plays first.We can assume that both player are clever enough to make the right move.Could you help Lily to make sure if she can win the game?
Input
Input contains multiple cases.
Each test case starts with two integerW(1<=N<=1000) ,H(1<=H<=1000) ,says that there is a sheet of WH paper at firsst.
Output
For each test case, if Lily can win the game output “Win”,otherwise output “Lose”.
Sample Input
1 1
2 2
4 2
6 4
Sample Output
Lose
Lose
Win
Lose

Hint
Hint
In sample 3,we have a sheet of 42 paper.Lily may cut the paper into 22,22 or 12,12,12,12.
Obviously Lily would choose the first kind of move.Lucy then can only pick up one 22 paper and cut it into 21,21.We know that Lily is sure to win.

2 .代码

#include<iostream>
#include<cstdio>
using namespace std;
int cut(int n)
{
	for(int i=2;i<=n;i++)
	{
		if(n%i==0)
		 return n/i;
	}
}
int main()
{
   int w,h;
   while(cin>>w>>h)
   {
   	  int flag;
      while(1)
	  {
	     w=cut(w);
		 if(w==1)
		 {
		 	flag=0;
		 	break;
	     }	
	     h=cut(h);
	     if(h==1)
	     {
	     	flag=1;
	     	break;
		 }
	  }	
	  if(flag)
	   cout<<"Win"<<endl;
	  else 
	   cout<<"Lose"<<endl;
   }	
   return 0;
}