Poj2096 -- collecting bugs (probability DP second play)

Collecting bugs Time limit:10000 ms   Memory limit:64000 K Total submissions:2678   Accepted:1302 Case time limit:2000 ms   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 callthe 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 wocould take too long before the target cocould be reached. so Ivan and microhard agreed to use a simpler criteria --- Ivan shocould 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 wocould 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 particle 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 Source Northeastern Europe 2004, northern subregion

Given s subprograms and N bugs, you can find a bug every day. This bug is a random bug. In a random program, you can ask when n bugs are found, in addition, bug expectations are found in every program.

DP [I] [J] indicates the expectation that J bugs have been found in I subprograms. The obtained DP [0] [0] is the result.

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;double dp[1200][1200] ;int main(){    int i , j , s , n ;    scanf("%d %d", &s, &n);    memset(dp,0,sizeof(dp));    for(i = s ; i >= 0 ; i--)    {        for(j = n ; j >= 0 ; j--)        {            if( i == s && j == n ) continue ;            else if( i == s )                dp[i][j] = ( (n-j)*1.0/n*dp[i][j+1] + 1.0 ) * n / (n-j) ;            else if( j == n )                dp[i][j] = ( (s-i)*1.0/s*dp[i+1][j] + 1.0 ) * s / (s-i) ;            else                dp[i][j] = ( (s-i)*1.0*j/(s*n)*dp[i+1][j] + i*(n-j)*1.0/(s*n)*dp[i][j+1] + (s-i)*(n-j)*1.0/(s*n)*dp[i+1][j+1] + 1.0 )*s*n/(s*n-i*j);        }    }    printf("%.4lf\n", dp[0][0]);    return 0;}

 

Poj2096 -- collecting bugs (probability DP second play)