poj2096 Collecting Bugs---기대 복습

Collecting Bugs
Time Limit: 10000MS
 
Memory Limit: 64000K
Total Submissions: 1245
 
Accepted: 524
Case Time Limit: 2000MS
 
Special Judge
Description
Ivan is fond of collecting. Unlike other people who collect post stamps, coins or other material stuff, he collects software bugs. When Ivan gets a new program, he classifies all possible bugs into n categories. Each day he discovers exactly one bug in the program and adds information about it and its category into a spreadsheet. When he finds bugs in all bug categories, he calls the program disgusting, publishes this spreadsheet on his home page, and forgets completely about the program.
Two companies, Macrosoft and Microhard are in tight competition. Microhard wants to decrease sales of one Macrosoft program. They hire Ivan to prove that the program in question is disgusting. However, Ivan has a complicated problem. This new program has s subcomponents, and finding bugs of all types in each subcomponent would take too long before the target could be reached. So Ivan and Microhard agreed to use a simpler criteria --- Ivan should find at least one bug in each subsystem and at least one bug of each category.
Macrosoft knows about these plans and it wants to estimate the time that is required for Ivan to call its program disgusting. It's important because the company releases a new version soon, so it can correct its plans and release it quicker. Nobody would be interested in Ivan's opinion about the reliability of the obsolete version.
A bug found in the program can be of any category with equal probability. Similarly, the bug can be found in any given subsystem with equal probability. Any particular bug cannot belong to two different categories or happen simultaneously in two different subsystems. The number of bugs in the program is almost infinite, so the probability of finding a new bug of some category in some subsystem does not reduce after finding any number of bugs of that category in that subsystem.
Find an average time (in days of Ivan's work) required to name the program disgusting.
Input
Input file contains two integer numbers, n and s (0 < n, s <= 1 000).
Output
Output the expectation of the Ivan's working days needed to call the program disgusting, accurate to 4 digits after the decimal point.
Sample Input

1 2

Sample Output

3.0000

 
 
한 사람이 어떤 회사에 고용되어 어떤 소프트웨어의bugs와subcomponents를 찾아내려고 한다. 이 소프트웨어는 모두 n개의bugs와s개의subcomponents가 있다. 매번 그는 무작위로 1개의bug와1개의subcomponent를 발견하고 그에게 모든 bugs와subcomponents를 찾는 기대 횟수를 물어볼 수 있다.우리는 E(i, j)로 그가 i개의bugs와 j개의subcomponents를 찾았고, n개의bugs와 s개의subcomponents를 찾을 때까지 필요한 기대 횟수를 표시했다.
임의의 E(i, j)에 대해 한 번에 4가지 상황을 찾았지만 새로운 버그와subcomponents를 발견하지 못했고, 새로운 버그를 발견하였으며, 새로운subcomponent를 발견하였으며, 동시에 새로운 버그와subcomponent를 발견하였다.
e(i,j)=1+(i*j/n/s)e(i,j)+(i*(s-j)/n/s)e(i,j+1)+((n-i)*j/n/s)e(i+1,j)+(n-i)(s-j)/n/s*e(i+1,j+1)

#include<iostream>
#include<cstdlib>
#include<stdio.h>
#include<memory.h>
using namespace std;
double e[1005][1005];
int main()
{
    int n,s;
    while(scanf("%d%d",&n,&s)!=EOF)
    {
        memset(e,0,sizeof(e));
        for(int i=n;i>=0;i--)
        for(int j=s;j>=0;j--)
        {
            if(i==n&&j==s) continue;
            double f=1.0*n*s;
            double p=1+e[i][j+1]*i*(s-j)/f+e[i+1][j]*(n-i)*j/f+e[i+1][j+1]*(n-i)*(s-j)/f;
            //cout<<p<<endl;
            double q=1-i*j/f;
            //cout<<q<<endl;
            e[i][j]=p/q;
        }
        printf("%.4lf
",e[0][0]);
    }
}