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 FlightScheduler { public:
4fd800b3a8 2011-02-23        kinaba: 	double f(double n, int distance, int K, int emptyMass, int takeoffFuel)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		return n * (exp(distance/n / K) * emptyMass - emptyMass + takeoffFuel);
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 	double minimizeFuel(int distance, int K, int emptyMass, int takeoffFuel)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		LL x = 1;
4fd800b3a8 2011-02-23        kinaba: 		LL w = (1LL<<60);
4fd800b3a8 2011-02-23        kinaba: 		while( w-x > 10 )
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			LL y = 2*x/3 + w/3;
4fd800b3a8 2011-02-23        kinaba: 			LL z = x/3 + 2*w/3;
4fd800b3a8 2011-02-23        kinaba: 			double fx = f(x, distance, K, emptyMass, takeoffFuel);
4fd800b3a8 2011-02-23        kinaba: 			double fy = f(y, distance, K, emptyMass, takeoffFuel);
4fd800b3a8 2011-02-23        kinaba: 			double fz = f(z, distance, K, emptyMass, takeoffFuel);
4fd800b3a8 2011-02-23        kinaba: 			double fw = f(w, distance, K, emptyMass, takeoffFuel);
4fd800b3a8 2011-02-23        kinaba: 			if( fx < fy )      w = y;
4fd800b3a8 2011-02-23        kinaba: 			else if( fz > fw ) x = z;
4fd800b3a8 2011-02-23        kinaba: 			else if( fy < fz ) w = z;
4fd800b3a8 2011-02-23        kinaba: 			else               x = y;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		double fuMin = 1e+300;
4fd800b3a8 2011-02-23        kinaba: 		for(LL n=x; n<=w; ++n)
4fd800b3a8 2011-02-23        kinaba: 			fuMin = min(fuMin, f(n, distance, K, emptyMass, takeoffFuel));
4fd800b3a8 2011-02-23        kinaba: 		return fuMin;
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:  double diff = Expected - Received; if (diff < 0) diff = -diff; bool ok = (diff < 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(_, FlightScheduler().minimizeFuel(distance, K, emptyMass, takeoffFuel));}
4fd800b3a8 2011-02-23        kinaba: int main(){
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: CASE(0)
4fd800b3a8 2011-02-23        kinaba: 	int distance = 40000;
4fd800b3a8 2011-02-23        kinaba: 	int K = 100000;
4fd800b3a8 2011-02-23        kinaba: 	int emptyMass = 150000;
4fd800b3a8 2011-02-23        kinaba: 	int takeoffFuel = 5000;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 76420.82744805096;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int distance = 40000;
4fd800b3a8 2011-02-23        kinaba: 	int K = 55000;
4fd800b3a8 2011-02-23        kinaba: 	int emptyMass = 150000;
4fd800b3a8 2011-02-23        kinaba: 	int takeoffFuel = 5000;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 138450.61724934017;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int distance = 1000;
4fd800b3a8 2011-02-23        kinaba: 	int K = 500;
4fd800b3a8 2011-02-23        kinaba: 	int emptyMass = 1000;
4fd800b3a8 2011-02-23        kinaba: 	int takeoffFuel = 50;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 2664.9853821314487;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int distance = 10000;
4fd800b3a8 2011-02-23        kinaba: 	int K = 100;
4fd800b3a8 2011-02-23        kinaba: 	int emptyMass = 200;
4fd800b3a8 2011-02-23        kinaba: 	int takeoffFuel = 5;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 24635.869665316768;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int distance = 140000;
4fd800b3a8 2011-02-23        kinaba: 	int K = 4;
4fd800b3a8 2011-02-23        kinaba: 	int emptyMass = 10000;
4fd800b3a8 2011-02-23        kinaba: 	int takeoffFuel = 10;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 3.6576871282155204E8;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE