Josephina and RPG

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 929    Accepted Submission(s):
265
Special Judge

Problem Description

A role-playing game (RPG and sometimes roleplaying
game) is a game in which players assume the roles of characters in a fictional
setting. Players take responsibility for acting out these roles within a
narrative, either through literal acting or through a process of structured
decision-making or character development.
Recently, Josephina is busy playing
a RPG named TX3. In this game, M characters are available to by selected by
players. In the whole game, Josephina is most interested in the "Challenge Game"
part.
The Challenge Game is a team play game. A challenger team is made up of
three players, and the three characters used by players in the team are required
to be different. At the beginning of the Challenge Game, the players can choose
any characters combination as the start team. Then, they will fight with N AI
teams one after another. There is a special rule in the Challenge Game: once the
challenger team beat an AI team, they have a chance to change the current
characters combination with the AI team. Anyway, the challenger team can insist
on using the current team and ignore the exchange opportunity. Note that the
players can only change the characters combination to the latest defeated AI
team. The challenger team gets victory only if they beat all the AI
teams.
Josephina is good at statistics, and she writes a table to record the
winning rate between all different character combinations. She wants to know the
maximum winning probability if she always chooses best strategy in the game. Can
you help her?

Input

There are multiple test cases. The first line of each
test case is an integer M (3 ≤ M ≤ 10), which indicates the number of
characters. The following is a matrix T whose size is R × R. R equals to C(M,
3). T(i, j) indicates the winning rate of team i when it is faced with team j.
We guarantee that T(i, j) + T(j, i) = 1.0. All winning rates will retain two
decimal places. An integer N (1 ≤ N ≤ 10000) is given next, which indicates the
number of AI teams. The following line contains N integers which are the IDs
(0-based) of the AI teams. The IDs can be duplicated.

Output

For each test case, please output the maximum winning
probability if Josephina uses the best strategy in the game. For each answer, an
absolute error not more than 1e-6 is acceptable.

Sample Input

4

0.50 0.50 0.20 0.30

0.50 0.50 0.90 0.40

0.80 0.10 0.50 0.60

0.70 0.60 0.40 0.50

3

0 1 2

Sample Output

0.378000

 1 /*                    dp[i+1][j]
 2         dp[i][j]=
 3                     dp[i+1][num[i]]
 4 */
 5 #include<iostream>
 6 #include<cstdio>
 7 #include<cstring>
 8 #include<algorithm>
 9 #include<string>
10 #include<set>
11 #include<map>
12 #include<vector>
13 #include<stack>
14 #include<queue>
15 using namespace std;
16 const int ms=12;
17 const int cms=122;
18 const int MAXN=10002;
19 double dp[MAXN][cms];
20 double p[cms][cms];
21 int num[MAXN];
22 int main()
23 {
24     int i,j,k,t,n,m,cnt;
25     while(scanf("%d",&n)!=EOF)
26     {
27         for(cnt=1,i=n;i>=(n-3+1);i--)
28             cnt*=i;
29         cnt/=6;
30         for(i=0;i<cnt;i++)
31             for(j=0;j<cnt;j++)
32                 scanf("%lf",&p[i][j]);
33         scanf("%d",&m);
34         for(i=1;i<=m;i++)
35             scanf("%d",&num[i]);
36         for(i=0;i<=cnt;i++)
37             dp[m+1][i]=1.0;
38         for(i=m;i>0;i--)
39         {
40             for(j=0;j<cnt;j++)
41             {
42                 dp[i][j]=p[j][num[i]]*max(dp[i+1][j],dp[i+1][num[i]]);
43             }
44         }
45         double ans=-1.0;
46         for(j=0;j<cnt;j++)
47             if(ans<dp[1][j])
48                 ans=dp[1][j];
49         printf("%.6lf\n",ans);
50     }
51     return 0;
52 }