[HDU 4336] Card Collector (状态压缩概率dp)

 1 ///#pragma comment(linker, "/STACK:102400000,102400000")
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <algorithm>
 5 #include <vector>
 6 #include <map>
 7 #include <set>
 8 #include <bitset>
 9 #include <cmath>
10 #include <numeric>
11 #include <iterator>
12 #include <iostream>
13 #include <cstdlib>
14 #include <functional>
15 #include <queue>
16 #include <stack>
17 #include <string>
18 #include <cctype>
19 using namespace std;
20 #define PB push_back
21 #define MP make_pair
22 #define SZ size()
23 #define ST begin()
24 #define ED end()
25 #define CLR clear()
26 #define ZERO(x) memset((x),0,sizeof(x))
27 typedef long long LL;
28 typedef unsigned long long ULL;
29 typedef pair<int,int> PII;
30 const double EPS = 1e-8;
31 
32 const int MAX_N = 20;
33 int N;
34 double p[MAX_N+1],f[1<<MAX_N];
35 
36 
37 int main(){
38     
39     while( ~scanf("%d",&N) ) {
40         ZERO(f);
41         double sum = 0.0;
42         for(int i=1;i<=N;i++){
43             scanf("%lf",&p[i]);
44             sum += p[i];
45         }
46         f[(1<<N)-1] = 0;
47         for( int mask=(1<<N)-2;mask>=0;mask-- ){
48             double p1 = 0;
49             for(int i=0;i<N;i++){
50                 if( (mask>>i)&1 ) {
51                     p1 += p[i+1];
52                 }
53             }
54 //            printf("p1 = %f\n",p1);
55             double p2 = 0;
56             for(int i=0;i<N;i++){
57                 if( !((mask>>i)&1) ) {
58                     p2 += f[mask|(1<<i)]*p[i+1];
59 //                    printf("f[mask|(1<<i)]=%f\n",f[mask|(1<<i)]);
60                 }
61             }
62 //            printf("p2 = %f\n",p2);
63             f[mask] = (p2+1.0)/(sum-p1);
64         }
65         printf("%.10f\n",f[0]);
66     }
67     
68     return 0;
69 }