ZOJ 3329 Problem Set (期望dp)

Posted HWIM

tags:

篇首语:本文由小常识网(cha138.com)小编为大家整理,主要介绍了ZOJ 3329 Problem Set (期望dp)相关的知识,希望对你有一定的参考价值。

One Person Game

There is a very simple and interesting one-person game. You have 3 dice, namely Die1Die2 and Die3Die1 has K1 faces. Die2 has K2 faces. Die3 has K3 faces. All the dice are fair dice, so the probability of rolling each value, 1 to K1K2K3 is exactly 1 / K1, 1 / K2 and 1 / K3. You have a counter, and the game is played as follow:

  1. Set the counter to 0 at first.
  2. Roll the 3 dice simultaneously. If the up-facing number of Die1 is a, the up-facing number of Die2 is b and the up-facing number of Die3 is c, set the counter to 0. Otherwise, add the counter by the total value of the 3 up-facing numbers.
  3. If the counter\'s number is still not greater than n, go to step 2. Otherwise the game is ended.

Calculate the expectation of the number of times that you cast dice before the end of the game.

Input

There are multiple test cases. The first line of input is an integer T (0 < T <= 300) indicating the number of test cases. Then T test cases follow. Each test case is a line contains 7 non-negative integers nK1K2K3abc (0 <= n <= 500, 1 < K1K2K3 <= 6, 1 <= a <= K1, 1 <= b <= K2, 1 <= c <= K3).

Output

For each test case, output the answer in a single line. A relative error of 1e-8 will be accepted.

Sample Input

2
0 2 2 2 1 1 1
0 6 6 6 1 1 1

Sample Output

1.142857142857143
1.004651162790698

 

code

大米饼的博客

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 
 5 using namespace std;
 6 const int N = 1010;
 7 double p[N],x[N],y[N],t;
 8 
 9 int main() {
10     
11     int T,n,k1,k2,k3,a,b,c,sum;
12     scanf("%d",&T);
13     while (T--) {
14         scanf("%d%d%d%d%d%d%d",&n,&k1,&k2,&k3,&a,&b,&c);
15         memset(p,0,sizeof(p));
16         memset(x,0,sizeof(x));
17         memset(y,0,sizeof(y));
18         
19         t = 1.0/(double(k1*k2*k3));
20         sum = k1+k2+k3;
21         
22         for (int i=1; i<=k1; ++i) 
23             for (int j=1; j<=k2; ++j)
24                 for (int k=1; k<=k3; ++k)
25                     if (i!=a || j!=b || k!=c) p[i+j+k] += t;
26         
27         for (int i=n; i>=0; --i) {
28             x[i] = t;y[i] = 1.0;
29             for (int k=3; k<=sum; ++k) 
30                 x[i] += p[k]*x[i+k],y[i] += p[k]*y[i+k];  
31         }
32         
33         printf("%.15lf\\n",y[0]/(1.0-x[0]));
34         
35     }
36     return 0;    
37 }

 

以上是关于ZOJ 3329 Problem Set (期望dp)的主要内容,如果未能解决你的问题,请参考以下文章

[ZOJ 3329] One Person Game

概率dp——逆推期望+循环迭代zoj3329

ZOJ-3329 One Person Game (有环期望问题)

ZOJ 3329:One Person Game 概率DP求期望(有环)

ZOJ3329One Person Game(循环型 数学期望)

ZOJ 3329 One Person Game——期望DP