poj 2096 概率DP 解题报告
2017-07-30 12:06
323 查看
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 2Sample Output
3.0000思路
概率DP经典,很简单看代码代码
WA#include<cstdio> #include<iostream> #include<cstring> #include<algorithm> using namespace std; double dp[1005][1005]; int n,s; int main() { while(~scanf("%d%d",&n,&s)) { memset(dp,0,sizeof(dp)); dp [s]=0.0; int ns=n*s; for(int i=n;i>=0;i--) for(int j=s;j>=0;j--) { if(n==i&&s==j) continue; dp[i][j]=( ns + (n-i)*j*dp[i+1][j] + i*(s-j)*dp[i][j+1] + (n-i)*(s-j)*dp[i+1][j+1] )/( ns - i*j ); } printf("%lf",dp[0][0]); } return 0; }
AC
#include<cstring> #include<cstdio> #include<algorithm> #include<iostream> #include<cmath> using namespace std; const int N=1010; double dp ; int n,s; int main() { while(scanf("%d%d",&n,&s)!=EOF) { dp [s]=0; 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]+(n-i)*j*dp[i+1][j]+(n-i)*(s-j)*dp[i+1][j+1]+n*s)/(n*s-i*j); } printf("%.4f\n",dp[0][0]); return 0; } }
相关文章推荐
- POJ 2096 概率DP 解题报告
- poj 2096 期望DP 解题报告
- POJ 2096 Collecting Bugs(概率DP)
- POJ - 1260 Pearls(二维dp)解题报告
- poj 2096(概率dp求期望)
- POJ-2096 Collecting Bugs (概率DP求期望)
- POJ 1739 Tony's Tour 解题报告(插头DP)
- poj 2096 概率dp
- POJ 2096 概率dp
- poj 2096 Collecting Bugs (概率dp 天数期望)
- POJ - 1836 Alignment解题报告(dp求至少删除多少个数可以变成递增数列)
- poj 2096 概率dp
- poj 2096 Collecting Bugs 概率dp入门题
- Poj 2096 Collecting Bugs (概率DP求期望)
- POJ 2096 概率dp
- poj 2096 概率dp
- 概率DP求期望入门,HDU 4405,POj 2096,HDU 3853
- 占坑[概率dp] poj 2096 Collecting Bugs
- poj2096 Collecting Bugs(概率dp)
- poj 2096 Collecting Bugs【概率DP】