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 IncredibleMachine {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	double gravitationalAcceleration(vector <int> x, vector <int> y, int T)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		double gL = 0.0, gR = 1e+9;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<100; ++i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			double gC = (gL + gR) / 2;
4fd800b3a8 2011-02-23        kinaba: 			double tC = est(x, y, gC);
4fd800b3a8 2011-02-23        kinaba: 			(tC < T ? gR : gL) = gC;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return gL;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	double est(const vector<int>& x, const vector<int>& y, double g)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		double v = 0.0;
4fd800b3a8 2011-02-23        kinaba: 		double tot_t = 0.0;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i+1<x.size(); ++i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			double v0 = v;
4fd800b3a8 2011-02-23        kinaba: 			double len = sqrt(double((x[i+1]-x[i])*(x[i+1]-x[i]) + (y[i+1]-y[i])*(y[i+1]-y[i])));
4fd800b3a8 2011-02-23        kinaba: 			double sin_alpha = (y[i]-y[i+1]) / len;
4fd800b3a8 2011-02-23        kinaba: 			double a = g * sin_alpha;
4fd800b3a8 2011-02-23        kinaba: 			// len = v0*t + 0.5a t^2
4fd800b3a8 2011-02-23        kinaba: 			// 0.5a t^2 + v0 t - len = 0
4fd800b3a8 2011-02-23        kinaba: 			double t = (-v0 + sqrt(v0*v0 + 2*a*len)) / a;
4fd800b3a8 2011-02-23        kinaba: 			v = v0 + a*t;
4fd800b3a8 2011-02-23        kinaba: 			tot_t += t;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return tot_t;
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() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: int verify_case(const double &Expected, const double &Received) { double diff = Expected - Received; if (diff < 0) diff = -diff; if (diff < 1e-9) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> struct Case_ { Case_(){start_time=clock();} };
4fd800b3a8 2011-02-23        kinaba: char Test_(...);
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<0>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,6};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {100,22};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int T = 4;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 9.807692307692307;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, IncredibleMachine().gravitationalAcceleration(x, y, T)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<1>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,26,100};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {50,26,24};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int T = 4;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 26.743031720603582;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, IncredibleMachine().gravitationalAcceleration(x, y, T)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<2>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,7,8};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {10,6,0};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int T = 7;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 1.1076837407708007;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, IncredibleMachine().gravitationalAcceleration(x, y, T)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<3>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,100};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {1,0};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int T = 1;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 20002;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, IncredibleMachine().gravitationalAcceleration(x, y, T)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<4>) {
4fd800b3a8 2011-02-23        kinaba: 	int x_[] = {0,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
4fd800b3a8 2011-02-23        kinaba: 	int y_[] = {100,0};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> y(y_, y_+sizeof(y_)/sizeof(*y_));
4fd800b3a8 2011-02-23        kinaba: 	int T = 100;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 0.020002;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, IncredibleMachine().gravitationalAcceleration(x, y, T)); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
4fd800b3a8 2011-02-23        kinaba: template<>      void Run_<-1>() {}
4fd800b3a8 2011-02-23        kinaba: int main() { Run_<0>(); }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE
4fd800b3a8 2011-02-23        kinaba: