HDU 5159 Card( 计数 期望 )
Card
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 191 Accepted Submission(s): 52
Special Judge
In the next T lines, every line contain x,b separated by exactly one space.
[Technique specification]
All numbers are integers.
1<=T<=500000
1<=x<=100000
1<=b<=5
See the sample for more details.
For the first case, all possible combinations BieBie can pick are (1, 1, 1),(1,1,2),(1,2,1),(1,2,2),(2,1,1),(2,1,2),(2,2,1),(2,2,2)
For (1,1,1),there is only one kind number i.e. 1, so the sum of different score is 1.
However, for (1,2,1), there are two kind numbers i.e. 1 and 2, so the sum of different score is 1+2=3.
So the sums of different score to corresponding combination are 1,3,3,3,3,3,3,2
So the expectation is (1+3+3+3+3+3+3+2)/8=2.625
设Xi代表分数为i的牌在b次操作中是否被选到,Xi=1为选到,Xi=0为未选到
那么期望EX=1*X1+2*X2+3*X3+…+x*Xx
Xi在b次中被选到的概率是1-(1-1/x)^b
那么E(Xi)= 1-(1-1/x)^b
那么EX=1*E(X1)+2*E(X2)+3*E(X3)+…+x*E(Xx)=(1+x)*x/2*(1-(1-1/x)^b)
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <cmath>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <stack>
#include <algorithm>
using namespace std;
#define root 1,n,1
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
#define lr rt<<1
#define rr rt<<1|1
typedef long long LL;
typedef pair<int,int>pii;
#define X first
#define Y second
const int oo = 1e9+;
const double PI = acos(-1.0);
const double eps = 1e- ;
const int N = ;
double n ;int m ;
void Run() {
scanf("%lf%d",&n,&m);
double avg = ( 1.0 + n ) * n / 2.0 * pow( 1.0 / n , (double) m ) , res = ;
for( int i = ; i < m ; ++i ) {
res += avg * pow( n - 1.0 , (double)i )*pow( (double)n, m-i-1.0 );
}
printf("%.3lf\n",res);
}
int main()
{
#ifdef LOCAL
freopen("in.txt","r",stdin);
#endif // LOCAL
ios::sync_with_stdio(false);
int _ , cas = ; scanf("%d",&_);
while( _-- ){
printf("Case #%d: ",cas++); Run();
}
}
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