Collecint Bugs

Subject:
http://poj.org/problem?id=2096

A software has $s$ subsystems will produce$n$种$bug$ . Someone can find abug ina day$bug$ , thisbug bugThe probability that$b$$u$$g$ belongs to a subsystem is$\frac{1}{s}$, Belonging to a certain type of bug bugThe probability of$b$$u$$g$ is$\frac{1}{n}$. Ask to discover $n$种$bug$ , andbugshave been found in every subsystemExpectation of$b$$u$$g$ days.

Thinking:
$dp\left[i\right]\left[j\right]$ means thatiihas been found$i$种$bug$ , and these$bug$ belongs to$j$个系统，达到目标状态的天数的期望。有
$$\begin{array}{rl}dp[i][j]& =1+\frac{i}{n}\ast \frac{j}{s}dp\left[i\right]\left[j\right]+\frac{i}{n}\ast \frac{s-j}{s}dp[i][j+1]\\ & +\frac{n-i}{n}\ast \frac{j}{s}dp[i+1][j]+\frac{n-i}{n}\ast \frac{s-j}{s}dp[i+1][j+1]\\ (1-\frac{i\ast j}{s\ast n})\ast dp[i][j]& =1+\frac{i}{n}\ast \frac{s-j}{s}dp\left[i\right][j+1]+\frac{n-i}{n}\ast \frac{j}{s}dp[i+1]\left[j\right]\\ & +\frac{n-i}{n}\ast \frac{s-j}{s}dp[i+1][j+1]\end{array}$$
$dp[n][s]=0$

#include"cstdlib"
#include"cstdio"
#include"cstring"
#include"cmath"
#include"queue"
#include"algorithm"
#include"iostream"
#define eps 1e-5
using namespace std;
double dp[1020][1020];
int main()
{
    
    
    int n,s;
    while(cin>>n>>s)
    {
    
    
        memset(dp,0,sizeof(dp));
        for(int i=n; i>=0; i--)
        {
    
    
            for(int j=s; j>=0; j--)
            {
    
    
                if(i==n&&j==s) continue;
                double tep=1.0;
                if(i<n) tep+=(n*1.0-i)*j/(n*s)*dp[i+1][j];
                if(j<s) tep+=(s*1.0-j)*i/(n*s)*dp[i][j+1];
                if(i<n&&j<s) tep+=(n*1.0-i)*(s*1.0-j)/(n*s)*dp[i+1][j+1];
                dp[i][j]=tep/(1-(i*j*1.0)/(s*n));
            }
        }
        printf("%.4f\n",dp[0][0]);
    }
    return 0;
}