Codeforces 518D Ilya and Escalator

http://codeforces.com/problemset/problem/518/D

题意:n个人，每秒有p的概率进电梯，求t秒后电梯里人数的期望

考虑dp:f[i][j]代表第i秒有j个人的概率，f[0][0]=1,f[i][j]=f[i-1][j-1]*p+f[i-1][j]*(1-p),特别有:f[i][n]=f[i-1][n]+f[i-1][n-1]*p

 #include<cstdio>
 #include<cmath>
 #include<algorithm>
 #include<cstring>
 #include<iostream>
 double p,f[][];
 int n,t;
 int read(){
     int t=,f=;char ch=getchar();
     while (ch<''||ch>''){if (ch=='-') f=-;ch=getchar();}
     while (''<=ch&&ch<=''){t=t*+ch-'';ch=getchar();}
     return t*f;
 }
 int main(){
     double p;
     n=read();scanf("%lf",&p);t=read();
     f[][]=;
     for (int i=;i<=t;i++){
      for (int j=;j<n;j++)
       f[i][j]=f[i-][j]*(-p)+f[i-][j-]*p;
      f[i][n]=f[i-][n]+f[i-][n-]*p;
     }
     double ans=;
     for (int i=;i<=n;i++)
      ans+=f[t][i]*i;
     printf("%.6f\n",ans);
     return ;
 }