【HDOJ】4336 Card Collector

概率DP的题目，一直就不会做这类题目。
dp[s]表示状态为s的时候再买多少张牌可以买全，表示的是一个期望值。
dp[s] = 1 + P(empty) * dp[s] + P(had) * dp[s] + P(new) * dp[nst]。
从而可以解dp[s]。

 1 /* 4336 */
 2 #include <iostream>
 3 #include <sstream>
 4 #include <string>
 5 #include <map>
 6 #include <queue>
 7 #include <set>
 8 #include <stack>
 9 #include <vector>
10 #include <deque>
11 #include <algorithm>
12 #include <cstdio>
13 #include <cmath>
14 #include <ctime>
15 #include <cstring>
16 #include <climits>
17 #include <cctype>
18 #include <cassert>
19 #include <functional>
20 #include <iterator>
21 #include <iomanip>
22 using namespace std;
23 //#pragma comment(linker,"/STACK:102400000,1024000")
24 
25 #define sti                set<int>
26 #define stpii            set<pair<int, int> >
27 #define mpii            map<int,int>
28 #define vi                vector<int>
29 #define pii                pair<int,int>
30 #define vpii            vector<pair<int,int> >
31 #define rep(i, a, n)     for (int i=a;i<n;++i)
32 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
33 #define clr                clear
34 #define pb                 push_back
35 #define mp                 make_pair
36 #define fir                first
37 #define sec                second
38 #define all(x)             (x).begin(),(x).end()
39 #define SZ(x)             ((int)(x).size())
40 #define lson            l, mid, rt<<1
41 #define rson            mid+1, r, rt<<1|1
42 
43 const int maxn = 20;
44 double p[maxn];
45 double dp[1<<maxn];
46 int n;
47 
48 void solve() {
49     int mst = 1 << n;
50     int mask = mst - 1;
51     dp[mask] = 0;
52     
53     per(i, 0, mask) {
54         double tmp = 0.0;
55         
56         dp[i] = 1.0;
57         rep(j, 0, n) {
58             if (i & (1<<j))
59                 continue;
60             dp[i] += p[j] * dp[i|(1<<j)];
61             tmp += p[j];
62         }
63         dp[i] /= tmp;
64     }
65     
66     double ans = dp[0];
67     printf("%.06lf\n", ans);
68 }
69     
70 int main() {
71     ios::sync_with_stdio(false);
72     #ifndef ONLINE_JUDGE
73         freopen("data.in", "r", stdin);
74         freopen("data.out", "w", stdout);
75     #endif
76         
77     while (scanf("%d", &n)!=EOF) {
78         rep(i, 0, n)
79             scanf("%lf", &p[i]);
80         solve();
81     }
82     
83     #ifndef ONLINE_JUDGE
84         printf("time = %d.\n", (int)clock());
85     #endif
86     
87     return 0;
88 }