bzoj1867: [Noi1999]钉子和小球（DP）

#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio> 
#include<algorithm>
#define ll long long 
using namespace std;
const int maxn=60,inf=1e9;
struct fra{ll u,d;fra(ll a=0,ll b=1){u=a,d=b;}}f[maxn][maxn];
int n,m;
bool mp[maxn][maxn];
int readch()
{
    char ch=getchar();
    while(ch==‘ ‘||ch==‘\n‘||ch==‘\t‘||ch==‘\r‘)ch=getchar();
    return ch==‘*‘;
}
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
void sim(fra &x){ll t=gcd(x.u,x.d);x.u/=t;x.d/=t;}
fra operator+(fra x,fra y)
{
    ll t=gcd(x.d,y.d);
    fra c=fra(y.d/t*x.u+x.d/t*y.u,x.d/t*y.d);
    return sim(c),c;
}
fra operator*(fra x,fra y)
{
    fra c=fra(x.u*y.u,x.d*y.d);
    return sim(c),c;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
    for(int j=1;j<=i;j++)
    mp[i][j]=readch();
    f[1][1]=fra(1,1);
    for(int i=1;i<=n;i++)
    for(int j=1;j<=i;j++)
    if(mp[i][j])f[i+1][j]=f[i+1][j]+f[i][j]*fra(1,2),f[i+1][j+1]=f[i+1][j+1]+f[i][j]*fra(1,2);
    else f[i+2][j+1]=f[i+2][j+1]+f[i][j];
    printf("%lld/%lld",f[n+1][m+1].u,f[n+1][m+1].d);
    return 0;
}