Artifact 9f9946fdf86740c42911b27e277e07f47aaf1a04
#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class CollectingBonuses { public:
double expectedBuy(string n, string k)
{
LL N; {stringstream ss; ss<<n; ss>>N;}
LL K; {stringstream ss; ss<<k; ss>>K;}
return N * sigma(K,N);
}
double f(LL b)
{
return 0.5772156649015313 + log(b+0.5);
}
double sigma(LL k, LL n)
{
// compute (1/n-k+1 + ... + 1/n)
if(k<=10000000) {
double p=0.0;
for(LL i=0; i<k; ++i)
p += 1.0 / (n-i);
return p;
}
else if(n-k<=10000000) {
double p=0.0;
for(LL i=1; i<=n-k; ++i)
p += 1.0 / i;
return f(n) - p;
}
LL x = 2*n+1;
LL y = 2*n-2*k+1;
if( x<y*2 )
return log1p(double(x-y)/y);
else
return log( double(x)/y );
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const double& Expected, const double& Received) {
bool ok = (abs(Expected - Received) < 1e-9);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, CollectingBonuses().expectedBuy(n, k));}
int main(){
CASE(0)
string n = "1";
string k = "1";
double _ = 1.0;
END
CASE(1)
string n = "2";
string k = "1";
double _ = 1.0;
END
CASE(2)
string n = "2";
string k = "2";
double _ = 3.0;
END
CASE(3)
string n = "4";
string k = "3";
double _ = 4.333333333333333;
END
CASE(4)
string n = "999999999999999999";
string k = "999999999999999999";
double _ = 4.202374733879435E19;
END
/*
CASE(5)
string n = ;
string k = ;
double _ = ;
END
*/
}
// END CUT HERE