bzoj 1867: [Noi1999]钉子和小球【dp】

设f[i][j]为掉到f[i][j]时的概率然后分情况随便转移一下就好
主要是要手写分数比较麻烦

#include<iostream>
#include<cstdio>
using namespace std;
const int N=55;
int n,m;
char a[N][N];
long long gcd(long long a,long long b)
{
	return !b?a:gcd(b,a%b);
}
struct fs
{
	long long x,y;
	fs(long long X=0,long long Y=1)
	{
		x=X,y=Y;
	}
	fs operator + (const fs &a) const
	{
		long long d=gcd(a.y,y),l=a.y/d*y;
		fs b=fs(l/y*x+l/a.y*a.x,l);
		long long g=gcd(b.x,b.y);
		return fs(b.x/g,b.y/g);
	}
	fs operator * (const fs &a) const
	{
		fs b=fs(x*a.x,y*a.y);
		long long g=gcd(b.x,b.y);
		return fs(b.x/g,b.y/g);
	}
}f[N][N];
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=i;j++)
		{
			a[i][j]=getchar();
			while(a[i][j]!='*'&&a[i][j]!='.')
				a[i][j]=getchar();
		}
	f[1][1]=fs(1,1);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=i;j++)
		{
			if(a[i][j]=='*')
			{
				f[i+1][j]=f[i+1][j]+f[i][j]*fs(1,2);
				f[i+1][j+1]=f[i+1][j+1]+f[i][j]*fs(1,2);
			}
			else
				f[i+2][j+1]=f[i+2][j+1]+f[i][j];
		}
	printf("%lld/%lld\n",f[n+1][m+1].x,f[n+1][m+1].y);
	return 0;
}
/*
5 2
*
*.
***
*.**
*****
*/