[NOI赛前训练]——专项测试3·数学

 1 #include "bits/stdc++.h"
 2 
 3 using namespace std;
 4 
 5 const int N=4e2+10;
 6 
 7 double f[N][N],p[N][N],C[N][N],mi[N][N];
 8 
 9 int n,num[N][N];
10 char s[N];
11 
12 inline void init(){
13     int i,j,k;
14     for (C[0][0]=i=1;i<N;++i)
15         for (C[i][0]=j=1;j<=i;++j)
16             C[i][j]=C[i-1][j]+C[i-1][j-1];
17     for (i=1;i<=n;++i)
18         for (j=i,k=0;j<=n;++j){
19             if (s[j]==‘.‘) ++k;
20             num[i][j]=k;
21         }
22 }
23 
24 inline void dp(){
25     if (!num[1][n]){
26         puts("0.000000");return ;
27     }
28     register int i,j,k,l;
29     for (i=1;i<=n;++i) if(s[i]==‘.‘)
30         p[i][i]=1.0;
31     for (l=2;l<=(n>>1);++l) {
32         for (i=1;i<=l;++i)
33             for (mi[i][0]=1,k=1;k<=l;++k) 
34                  mi[i][k]=mi[i][k-1]*i/l;
35         for (i=1,j=l;i<=n;++i,++j) {
36             f[i][j]=p[i][j]=0.0;
37             if(s[j]==‘.‘){
38                 for (k=i;k<j;++k) if(s[k]==‘.‘){
39                     int lk=num[i][k-1],rk=num[k+1][j-1];
40                     double now=C[lk+rk][lk]*
41                                mi[(k-i+1)][lk+1]*
42                                mi[(j-k)][rk]*
43                                p[i][k]*p[k+1][j];
44                     p[i][j]+=now;
45                     f[i][j]+=now*(f[i][k]+f[k+1][j]+(k-i)/2.0);
46                 }
47                 if (num[i][j-1]==0)p[i][j]=1.0;
48                 f[i][j]/=p[i][j];              
49             }
50         }
51     }
52     double ans=0.0;
53     for (i=1;i<=n/2;++i)
54         ans+=f[i][i+n/2-1]*p[i][i+n/2-1];
55     ans+=(n/2-1)/2.0;
56     printf("%.6f\n",ans);
57 }
58 
59 int main(){
60     int T;
61     scanf("%d",&T);      
62     while (T--) {
63         scanf("%s",s+1);
64         n=strlen(s+1);
65         for (int i=n+1;i<=(n<<1);++i)
66             s[i]=s[i-n];
67         n<<=1;
68         init();
69         dp();
70     }
71 }