HDU-4336 Card Collector 概率DP

　　题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4336

　　题意：买食品收集n个卡片，每个卡片的概率分别是pi，且Σp[i]<=1，求收集n个卡片需要买的食品数的期望。

　　压缩DP：把每个食品用二进制表示，0和1分别表示没有卡片和已经收集到此卡片的期望，则

　　　　 f[s]=(1-Σp[i])*f[s]+Σp[j]*f[s]+Σp[k]*f[s|(1<<k)]

　　　　　　s表示状态，i表示所有卡片编号，j表示s状态中已经有的卡片编号，k表示s状态中没有的卡片编号

　　-> Σp[i]*f[s]=Σp[i]*f[s|(1<<i)]

　　或者容斥原理做：

　　压缩DP:

 //STATUS:C++_AC_281MS_7128KB

 #include <functional>

 #include <algorithm>

 #include <iostream>

 //#include <ext/rope>

 #include <fstream>

 #include <sstream>

 #include <iomanip>

 #include <numeric>

 #include <cstring>

 #include <cassert>

 #include <cstdio>

 #include <string>

 #include <vector>

 #include <bitset>

 #include <queue>

 #include <stack>

 #include <cmath>

 #include <ctime>

 #include <list>

 #include <set>

 #include <map>

 using namespace std;

 //#pragma comment(linker,"/STACK:102400000,102400000")

 //using namespace __gnu_cxx;

 //define

 #define pii pair<int,int>

 #define mem(a,b) memset(a,b,sizeof(a))

 #define lson l,mid,rt<<1

 #define rson mid+1,r,rt<<1|1

 #define PI acos(-1.0)

 //typedef

 typedef __int64 LL;

 typedef unsigned __int64 ULL;

 //const

 const int N=(<<)+;

 const int INF=0x3f3f3f3f;

 const int MOD= ,STA=;

 const LL LNF=1LL<<;

 const double EPS=1e-;

 const double OO=1e30;

 const int dx[]={-,,,};

 const int dy[]={,,,-};

 const int day[]={,,,,,,,,,,,,};

 //Daily Use ...

 inline int sign(double x){return (x>EPS)-(x<-EPS);}

 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}

 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}

 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}

 template<class T> inline T Min(T a,T b){return a<b?a:b;}

 template<class T> inline T Max(T a,T b){return a>b?a:b;}

 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}

 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}

 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}

 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}

 //End

 double p[],f[N];

 int n;

 int main(){

  //   freopen("in.txt","r",stdin);

     int i,j,up;

     double s;

     while(~scanf("%d",&n))

     {

         for(i=;i<n;i++){

             scanf("%lf",&p[i]);

         }

         up=(<<n)-;

         f[up]=;

         for(i=up-;i>=;i--){

             f[i]=;s=;

             for(j=;j<n;j++){

                 if(i&(<<j))continue;

                 f[i]+=p[j]*f[i|(<<j)];

                 s+=p[j];

             }

             f[i]/=s;

         }

         printf("%lf\n",f[]);

     }

     return ;

 }

　　容斥原理：

 //STATUS:C++_AC_203MS_244KB

 #include <functional>

 #include <algorithm>

 #include <iostream>

 //#include <ext/rope>

 #include <fstream>

 #include <sstream>

 #include <iomanip>

 #include <numeric>

 #include <cstring>

 #include <cassert>

 #include <cstdio>

 #include <string>

 #include <vector>

 #include <bitset>

 #include <queue>

 #include <stack>

 #include <cmath>

 #include <ctime>

 #include <list>

 #include <set>

 #include <map>

 using namespace std;

 //#pragma comment(linker,"/STACK:102400000,102400000")

 //using namespace __gnu_cxx;

 //define

 #define pii pair<int,int>

 #define mem(a,b) memset(a,b,sizeof(a))

 #define lson l,mid,rt<<1

 #define rson mid+1,r,rt<<1|1

 #define PI acos(-1.0)

 //typedef

 typedef __int64 LL;

 typedef unsigned __int64 ULL;

 //const

 const int N=(<<)+;

 const int INF=0x3f3f3f3f;

 const int MOD= ,STA=;

 const LL LNF=1LL<<;

 const double EPS=1e-;

 const double OO=1e30;

 const int dx[]={-,,,};

 const int dy[]={,,,-};

 const int day[]={,,,,,,,,,,,,};

 //Daily Use ...

 inline int sign(double x){return (x>EPS)-(x<-EPS);}

 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}

 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}

 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}

 template<class T> inline T Min(T a,T b){return a<b?a:b;}

 template<class T> inline T Max(T a,T b){return a>b?a:b;}

 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}

 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}

 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}

 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}

 //End

 double p[];

 int n;

 int main(){

  //   freopen("in.txt","r",stdin);

     int i,j,up,cnt;

     double ans,s;

     while(~scanf("%d",&n))

     {

         for(i=;i<n;i++){

             scanf("%lf",&p[i]);

         }

         up=(<<n)-;ans=;

         for(i=;i<=up;i++){

             s=;

             for(j=cnt=;j<n;j++){

                 if(i&(<<j)){

                     cnt++;

                     s+=p[j];

                 }

             }

             if(cnt&)ans+=/s;

             else ans-=/s;

         }

         printf("%lf\n",ans);

     }

     return ;

 }

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HDU-4336 Card Collector 概率DP

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