4fd800b3a8 2011-02-23        kinaba: #include <iostream>
4fd800b3a8 2011-02-23        kinaba: #include <sstream>
4fd800b3a8 2011-02-23        kinaba: #include <iomanip>
4fd800b3a8 2011-02-23        kinaba: #include <vector>
4fd800b3a8 2011-02-23        kinaba: #include <string>
4fd800b3a8 2011-02-23        kinaba: #include <map>
4fd800b3a8 2011-02-23        kinaba: #include <set>
4fd800b3a8 2011-02-23        kinaba: #include <algorithm>
4fd800b3a8 2011-02-23        kinaba: #include <numeric>
4fd800b3a8 2011-02-23        kinaba: #include <iterator>
4fd800b3a8 2011-02-23        kinaba: #include <functional>
4fd800b3a8 2011-02-23        kinaba: #include <complex>
4fd800b3a8 2011-02-23        kinaba: #include <queue>
4fd800b3a8 2011-02-23        kinaba: #include <stack>
4fd800b3a8 2011-02-23        kinaba: #include <cmath>
4fd800b3a8 2011-02-23        kinaba: #include <cassert>
4fd800b3a8 2011-02-23        kinaba: #include <cstring>
4fd800b3a8 2011-02-23        kinaba: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: typedef complex<double> CMP;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class CollectingBonuses { public:
4fd800b3a8 2011-02-23        kinaba: 	double expectedBuy(string n, string k)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		LL N; {stringstream ss; ss<<n; ss>>N;}
4fd800b3a8 2011-02-23        kinaba: 		LL K; {stringstream ss; ss<<k; ss>>K;}
4fd800b3a8 2011-02-23        kinaba: 		return N * sigma(K,N);
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 	double f(LL b)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		return 0.5772156649015313 + log(b+0.5);
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 	double sigma(LL k, LL n)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		// compute (1/n-k+1 + ... + 1/n)
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		if(k<=10000000) {
4fd800b3a8 2011-02-23        kinaba: 			double p=0.0;
4fd800b3a8 2011-02-23        kinaba: 			for(LL i=0; i<k; ++i)
4fd800b3a8 2011-02-23        kinaba: 				p += 1.0 / (n-i);
4fd800b3a8 2011-02-23        kinaba: 			return p;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		else if(n-k<=10000000) {
4fd800b3a8 2011-02-23        kinaba: 			double p=0.0;
4fd800b3a8 2011-02-23        kinaba: 			for(LL i=1; i<=n-k; ++i)
4fd800b3a8 2011-02-23        kinaba: 				p += 1.0 / i;
4fd800b3a8 2011-02-23        kinaba: 			return f(n) - p;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		LL x = 2*n+1;
4fd800b3a8 2011-02-23        kinaba: 		LL y = 2*n-2*k+1;
4fd800b3a8 2011-02-23        kinaba: 		if( x<y*2 )
4fd800b3a8 2011-02-23        kinaba: 			return log1p(double(x-y)/y);
4fd800b3a8 2011-02-23        kinaba: 		else
4fd800b3a8 2011-02-23        kinaba: 			return log( double(x)/y );
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: #include <ctime>
4fd800b3a8 2011-02-23        kinaba: double start_time; string timer()
4fd800b3a8 2011-02-23        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
4fd800b3a8 2011-02-23        kinaba:  { os << "{ ";
4fd800b3a8 2011-02-23        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
4fd800b3a8 2011-02-23        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
4fd800b3a8 2011-02-23        kinaba: void verify_case(const double& Expected, const double& Received) {
4fd800b3a8 2011-02-23        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
4fd800b3a8 2011-02-23        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
4fd800b3a8 2011-02-23        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
4fd800b3a8 2011-02-23        kinaba: #define END	 verify_case(_, CollectingBonuses().expectedBuy(n, k));}
4fd800b3a8 2011-02-23        kinaba: int main(){
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: CASE(0)
4fd800b3a8 2011-02-23        kinaba: 	string n = "1";
4fd800b3a8 2011-02-23        kinaba: 	string k = "1";
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	string n = "2";
4fd800b3a8 2011-02-23        kinaba: 	string k = "1";
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	string n = "2";
4fd800b3a8 2011-02-23        kinaba: 	string k = "2";
4fd800b3a8 2011-02-23        kinaba: 	double _ = 3.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	string n = "4";
4fd800b3a8 2011-02-23        kinaba: 	string k = "3";
4fd800b3a8 2011-02-23        kinaba: 	double _ = 4.333333333333333;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	string n = "999999999999999999";
4fd800b3a8 2011-02-23        kinaba: 	string k = "999999999999999999";
4fd800b3a8 2011-02-23        kinaba: 	double _ = 4.202374733879435E19;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: /*
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	string n = ;
4fd800b3a8 2011-02-23        kinaba: 	string k = ;
4fd800b3a8 2011-02-23        kinaba: 	double _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: */
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE