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poj 2151 Check the difficulty of problems(概率DP)
Check the difficulty of problems
Time Limit: 2000MS | Memory Limit: 65536K | |
Total Submissions: 4680 | Accepted: 2049 |
Description
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?
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
ans = (1-第1队做出0题)*(1-第2队做出0题)...(1-第n队做出0题)-(第1队做1-N题)*(第2队做1-N题)...(第n队做1-N题)。
蓝色部分为条件1,红色部分为条件2.
dp[t][m][i]表示第t队在前m题中做出i题:
dp[t][m][i] =dp[t][m-1][i-1]*P[m][i]+dp[t][m-1][i]*(1-P[m][i]),i>0
dp[t][m][i] = dp[t][m-1][i]*(1-P[m][i]),i==0.
#include <iostream> #include <cstdio> #include <cmath> #include <string> #include <cstring> #include <cstdlib> using namespace std; const int maxt = 1010; const int maxm = 35; double dp[maxt][maxm][maxm] , P[maxt][maxm]; int N , M , T; void initial(){ for(int i = 0; i < maxt; i++){ for(int j = 0; j < maxm; j++){ P[i][j] = 0; for(int k = 0; k < maxm; k++) dp[i][j][k] = 0; } } } void readcase(){ for(int i = 1; i <= T; i++){ for(int j = 1; j <= M; j++) scanf("%lf" , &P[i][j]); } } void computing(){ for(int i = 0; i <= T; i++) dp[i][0][0] = 1.0; for(int t = 1; t <= T; t++){ for(int m = 1; m <= M; m++){ for(int i = 0; i <= min(m , N); i++){ if(i)dp[t][m][i] = dp[t][m-1][i-1]*P[t][m]+dp[t][m-1][i]*(1.0-P[t][m]); else dp[t][m][i] = dp[t][m-1][i]*(1.0-P[t][m]); } } } double ans = 1.0; for(int i = 1; i <= T; i++) ans = ans*(1.0-dp[i][M][0]); //cout << ans << endl; double tem = 1.0; for(int t = 1; t <= T; t++){ double ttem = 0.0; for(int i = 1; i < N; i++) ttem += dp[t][M][i]; tem *= ttem; } printf("%.3lf\n" , ans-tem); } int main(){ while(scanf("%d%d%d", &M , &T , &N) && (N!=0 || M!=0 || T!=0)){ initial(); readcase(); computing(); } return 0; }
poj 2151 Check the difficulty of problems(概率DP)
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