POJ 1189 钉子和小球 (DP)

题意：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <cmath>
#include <stack>
#include <map>

using namespace std;
#define LL long long
int p[59][59];
LL dp[59][59];
int n,m;
LL gcd(LL a,LL b)
{
    if(a==0) return b;
    else return gcd(b%a,a);
}
void solve()
{
    memset(dp,0,sizeof(dp));
    dp[0][0] = 1ll<<n;
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<=i;j++)
        {
            if(p[i][j]==0)
            {
                dp[i+2][j+1] += dp[i][j];
            }else
            {
                dp[i+1][j] += dp[i][j]>>1;
                dp[i+1][j+1] += dp[i][j]>>1;
            }
        }
    }
    cout<<dp[n][m]/gcd(dp[n][m],(1ll<<n))<<"/"<<(1ll<<n)/gcd(dp[n][m],(1ll<<n))<<endl;
}
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    scanf("%d%d",&n,&m);
    {
        char ch[5];
        for(int i=0;i<n;i++)
        for(int j=0;j<=i;j++)
        {
            scanf("%s",ch);
            if(ch[0]=='*')
            p[i][j] = 1;
            else p[i][j] = 0;
        }
        solve();
    }
    return 0;
}