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[2005][2005];
int n,t;
int read(){
    int t=0,f=1;char ch=getchar();
    while (ch<'0'||ch>'9'){if (ch=='-') f=-1;ch=getchar();}
    while ('0'<=ch&&ch<='9'){t=t*10+ch-'0';ch=getchar();}
    return t*f;
}
int main(){
    double p;
    n=read();scanf("%lf",&p);t=read();
    f[0][0]=1;
    for (int i=1;i<=t;i++){
     for (int j=0;j<n;j++)
      f[i][j]=f[i-1][j]*(1-p)+f[i-1][j-1]*p;
     f[i][n]=f[i-1][n]+f[i-1][n-1]*p; 
    }
    double ans=0;
    for (int i=1;i<=n;i++)
     ans+=f[t][i]*i;
    printf("%.6f
",ans);   
    return 0;
}