【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]。

 /* 4336 */
 #include <iostream>
 #include <sstream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 const int maxn = ;
 double p[maxn];
 double dp[<<maxn];
 int n;

 void solve() {
     int mst =  << n;
     int mask = mst - ;
     dp[mask] = ;

     per(i, , mask) {
         double tmp = 0.0;

         dp[i] = 1.0;
         rep(j, , n) {
             if (i & (<<j))
                 continue;
             dp[i] += p[j] * dp[i|(<<j)];
             tmp += p[j];
         }
         dp[i] /= tmp;
     }

     double ans = dp[];
     printf("%.06lf\n", ans);
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     while (scanf("%d", &n)!=EOF) {
         rep(i, , n)
             scanf("%lf", &p[i]);
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }