POJ-2151 Check the difficulty of problems
2016-04-03 20:45
316 查看
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions: 6332 | Accepted: 2756 |
Organizing a programming contest is not an easy job. To avoid making the problems too difficult, the organizer usually expect the contest result satisfy the following two terms:
1. All of the teams solve at least one problem.
2. The champion (One of those teams that solve the most problems) solves at least a certain number of problems.
Now the organizer has studied out the contest problems, and through the result of preliminary contest, the organizer can estimate the probability that a certain team can successfully solve a certain problem.
Given the number of contest problems M, the number of teams T, and the number of problems N that the organizer expect the champion solve at least. We also assume that team i solves problem j with the probability Pij (1 <= i <= T, 1<= j <= M). Well, can you
calculate the probability that all of the teams solve at least one problem, and at the same time the champion team solves at least N problems?
Input
The input consists of several test cases. The first line of each test case contains three integers M (0 < M <= 30), T (1 < T <= 1000) and N (0 < N <= M). Each of the following T lines contains M floating-point numbers in the range
of [0,1]. In these T lines, the j-th number in the i-th line is just Pij. A test case of M = T = N = 0 indicates the end of input, and should not be processed.
Output
For each test case, please output the answer in a separate line. The result should be rounded to three digits after the decimal point.
Sample Input
2 2 2 0.9 0.9 1 0.9 0 0 0
Sample Output
0.972
Source
POJ Monthly,鲁小石
分析:概率DP 待补
#include <cstdio> #include <cstring> #include <iostream> using namespace std; double f[1001][31][31],p[1001][31],s[1001][31]; int m,t,n; int main() { cin.sync_with_stdio(false); while(cin>>m>>t>>n && m && t && n) { for(int i=1;i <= t;i++) for(int j=1;j <= m;j++) cin>>p[i][j]; memset(f,0,sizeof(f)); memset(s,0,sizeof(s)); for(int i=1;i <= t;i++) { f[i][0][0]=1.0; for(int j=1;j <= m;j++) for(int k=0;k <= j;k++) f[i][j][k]=f[i][j-1][k]*(1.0-p[i][j])+f[i][j-1][k-1]*p[i][j]; for(int k=0;k <= m;k++) for(int j=0;j <= k;j++) s[i][k]+=f[i][m][j]; } double p1=1.0,p2=1.0; for(int i=1;i <= t;i++) p1*=(1-s[i][0]); for(int i=1;i <= t;i++) p2*=(s[i][n-1]-s[i][0]); printf("%.3f\n",p1-p2); } }
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