[POJ2096] Collecting Bugs (Probabilistic DP)

Title Link: http://poj.org/problem?id=2096

The main problem: There are n kinds of bugs, there is a subsystem of S. A bug is found every day, belongs to a category and belongs to a subsystem. Ask you how many days each bug and each subsystem finds a bug.

Set DP[I][J] For now I have found a bug, within the J sub-system, to the desired number of days to the target State.

Dp[n][s] = 0, because n bugs have been found within the S sub-system, and no additional days are required.

DP[I][J] can be transferred to the following state:

DP[I][J]: Newly discovered bugs within J sub-systems that have been found in I species. Probability is: (i/n) * (J/S)

DP[I+1][J]: Newly discovered bugs are found in the category, but within the J sub-system that has been found. Probability is ((n-i)/N) * (J/S)

DP[I][J+1]: Newly discovered bugs in the discovered species, but not within the J sub-system already found. Probability is (i/n) * ((S-J)/s)

DP[I+1][J+1]: Newly discovered bugs are not found in the categories that have been discovered, and are not within the J sub-systems that have been discovered. Probability is ((n-i)/N) * ((S-J)/s)

State transitions:

DP[I][J] = dp[i][j] * (i/n) * (J/S) + dp[i+1][j] * ((n-i)/N) * (j/s) + dp[i][j+1]* (i/n) * ((S-J)/s) + dp[i+1][j+1] * ((n-i) /N) * ((S-J)/s) + 1

1 ///#pragma COMMENT (linker, "/stack:102400000,102400000")2#include <cstdio>3#include <cstring>4#include <algorithm>5#include <vector>6#include <map>7#include <Set>8#include <bitset>9#include <cmath>Ten#include <numeric> One#include <iterator> A#include <iostream> -#include <cstdlib> -#include <functional> the#include <queue> -#include <stack> -#include <string> -#include <cctype> + using namespacestd; - #definePB push_back + #defineMP Make_pair A #defineSZ size () at #defineST begin () - #defineED End () - #defineCLR Clear () - #defineZERO (x) memset ((x), 0,sizeof (x)) -typedefLong LongLL; -typedef unsignedLong LongULL; intypedef pair<int,int>PII; - Const DoubleEPS = 1e-8; to  + Const intMax_n =1111; - intn,s; the DoubleF[max_n][max_n]; *  $ intMain () {Panax Notoginseng      while(~SCANF ("%d%d",&n,&s)) { -F[n][s] =0.0; the          for(inti=n;i>=0; i--){ +              for(intj=s;j>=0; j--){ A                 if(N*S==I*J)Continue; theF[I][J] =1.0* (f[i+1][j]* (n-i) *j+f[i][j+1]*i* (S-J) +f[i+1][j+1]* (n-i) * (S-J) +n*s)/(n*s-i*j); +             } -         } $printf"%.4f\n", f[0][0]); $     } -      -     return 0; the}

[POJ2096] Collecting Bugs (Probabilistic DP)