設f[i][j]為掉到f[i][j]時的概率然後分情況隨便轉移一下就好
主要是要手寫分數比較麻煩

#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
*
*.
***
*.**
*****
*/
 

bzoj 1867: [Noi1999]釘子和小球【dp】