【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 = 20;
double p[maxn];
double dp[1<<maxn];
int n;

void solve() {
    int mst = 1 << n;
    int mask = mst - 1;
    dp[mask] = 0;
    
    per(i, 0, mask) {
        double tmp = 0.0;
        
        dp[i] = 1.0;
        rep(j, 0, n) {
            if (i & (1<<j))
                continue;
            dp[i] += p[j] * dp[i|(1<<j)];
            tmp += p[j];
        }
        dp[i] /= tmp;
    }
    
    double ans = dp[0];
    printf("%.06lf
", 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, 0, n)
            scanf("%lf", &p[i]);
        solve();
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}