POJ2096------Collecting Bugs

Collecting Bugs
Time Limit: 10000MS
 
Memory Limit: 64000K
Total Submissions: 2824
 
Accepted: 1394
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.
확률 dp, dp[i][j]를 설정하면 분류에 속하는 i개, 하위 시스템에 속하는 j개를 찾았음을 나타낸다.
dp[i][j] = (dp[i][j] + 1)  * (i/n) * (j/s)  + (dp[i +1][j] + 1) * (1 - i/n) * (j/s) + (dp[i][j + 1] + 1) * (i/n) * (1 - j/s) + (dp[i + 1][j + 1] + 1) * (1 - i/n) * (1 - j/s) 
4가지 상황이 있기 때문에 현재 찾은 버그는 이미 찾은 i개 분류, j 서브시스템에 속한다.찾은 i개 분류에 속하고 j 서브시스템에 속하지 않습니다.찾은 i개 분류에 속하지 않고 j 서브시스템에 속한다.i개 분류도 아니고 j 서브시스템도 아니다
그리고 코드를 조금 줄이면 쓸 수 있어요.

/*************************************************************************
    > File Name: POJ2096.cpp
    > Author: ALex
    > Mail: [email protected] 
    > Created Time: 2014 12 20      17 04 15 
 ************************************************************************/

#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

const int N = 1010;
int n, s;
double dp[N][N];

int main()
{
	while (~scanf("%d%d", &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;
				}
				dp[i][j] += i* (s - j) * dp[i][j + 1];
				dp[i][j] += j * (n - i) * dp[i + 1][j];
				dp[i][j] += (n - i) * (s - j) * dp[i + 1][j + 1];
				dp[i][j] += n * s;
				dp[i][j] /= (n * s - i * j);
			}
		}
		printf("%.4f
", dp[0][0]);
	}
	return 0;
}