df56ee954d 2011-12-29        kinaba: #include <iostream>
df56ee954d 2011-12-29        kinaba: #include <sstream>
df56ee954d 2011-12-29        kinaba: #include <iomanip>
df56ee954d 2011-12-29        kinaba: #include <vector>
df56ee954d 2011-12-29        kinaba: #include <string>
df56ee954d 2011-12-29        kinaba: #include <map>
df56ee954d 2011-12-29        kinaba: #include <set>
df56ee954d 2011-12-29        kinaba: #include <algorithm>
df56ee954d 2011-12-29        kinaba: #include <numeric>
df56ee954d 2011-12-29        kinaba: #include <iterator>
df56ee954d 2011-12-29        kinaba: #include <functional>
df56ee954d 2011-12-29        kinaba: #include <complex>
df56ee954d 2011-12-29        kinaba: #include <queue>
df56ee954d 2011-12-29        kinaba: #include <stack>
df56ee954d 2011-12-29        kinaba: #include <cmath>
df56ee954d 2011-12-29        kinaba: #include <cassert>
df56ee954d 2011-12-29        kinaba: #include <cstring>
df56ee954d 2011-12-29        kinaba: #ifdef __GNUC__
df56ee954d 2011-12-29        kinaba: #include <ext/hash_map>
df56ee954d 2011-12-29        kinaba: #define unordered_map __gnu_cxx::hash_map
df56ee954d 2011-12-29        kinaba: #else
df56ee954d 2011-12-29        kinaba: #include <unordered_map>
df56ee954d 2011-12-29        kinaba: #endif
df56ee954d 2011-12-29        kinaba: using namespace std;
df56ee954d 2011-12-29        kinaba: typedef long long LL;
df56ee954d 2011-12-29        kinaba: typedef complex<double> CMP;
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: class Mosquitoes { public:
df56ee954d 2011-12-29        kinaba: 	int getMaximum(vector <int> xInit, vector <int> v, int R)
df56ee954d 2011-12-29        kinaba: 	{
df56ee954d 2011-12-29        kinaba: 		vector< pair<double,double> > tx;
df56ee954d 2011-12-29        kinaba: 		for (int i = 0; i < xInit.size(); i++)
df56ee954d 2011-12-29        kinaba: 			for (int j = i+1; j < xInit.size(); j++)
df56ee954d 2011-12-29        kinaba: 				critical_points(xInit[i], v[i], xInit[j], v[j], R, &tx);
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: 		int best = 1;
df56ee954d 2011-12-29        kinaba: 		for(int i=0; i<tx.size(); ++i) {
df56ee954d 2011-12-29        kinaba: 			double t = tx[i].first;
df56ee954d 2011-12-29        kinaba: 			double x = tx[i].second;
df56ee954d 2011-12-29        kinaba: 			if( t >= 0 ) {
df56ee954d 2011-12-29        kinaba: 				int cnt = 0;
df56ee954d 2011-12-29        kinaba: 				for (int k = 0; k < xInit.size(); k++)
df56ee954d 2011-12-29        kinaba: 					if( is_in(xInit[k], v[k], t, x, R) )
df56ee954d 2011-12-29        kinaba: 						++cnt;
df56ee954d 2011-12-29        kinaba: 				best = max(best, cnt);
df56ee954d 2011-12-29        kinaba: 			}
df56ee954d 2011-12-29        kinaba: 		}
df56ee954d 2011-12-29        kinaba: 		return best;
df56ee954d 2011-12-29        kinaba: 	}
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: 	void critical_points(double x1, double v1, double x2, double v2, double R,
df56ee954d 2011-12-29        kinaba: 		vector< pair<double,double> >* tx)
df56ee954d 2011-12-29        kinaba: 	{
df56ee954d 2011-12-29        kinaba: 		// Compute t such that | (x1 + t v1) - (x2 - t v2) | = 2R
df56ee954d 2011-12-29        kinaba: 		double x = x1 - x2;
df56ee954d 2011-12-29        kinaba: 		double v = v1 - v2;
df56ee954d 2011-12-29        kinaba: 		if( v == 0 ) {
df56ee954d 2011-12-29        kinaba: 			if( abs(x) <= 2*R )
df56ee954d 2011-12-29        kinaba: 				tx->push_back( make_pair(0, (x1+x2)/2) );
df56ee954d 2011-12-29        kinaba: 		} else {
df56ee954d 2011-12-29        kinaba: 			double t1 = (2*R - x) / v;
df56ee954d 2011-12-29        kinaba: 			double t2 = (2*R + x) / (-v);
df56ee954d 2011-12-29        kinaba: 			tx->push_back( make_pair(t1, (func(x1,v1,t1)+func(x2,v2,t1))/2) );
df56ee954d 2011-12-29        kinaba: 			tx->push_back( make_pair(t2, (func(x1,v1,t2)+func(x2,v2,t2))/2) );
df56ee954d 2011-12-29        kinaba: 		}
df56ee954d 2011-12-29        kinaba: 	}
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: 	double func(double x, double v, double t)
df56ee954d 2011-12-29        kinaba: 	{
df56ee954d 2011-12-29        kinaba: 		return x + v*t;
df56ee954d 2011-12-29        kinaba: 	}
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: 	bool is_in(double x, double v, double t, double c, double R)
df56ee954d 2011-12-29        kinaba: 	{
df56ee954d 2011-12-29        kinaba: 		return abs(func(x,v,t) - c) <= R + 1e-8;
df56ee954d 2011-12-29        kinaba: 	}
df56ee954d 2011-12-29        kinaba: };
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: // BEGIN CUT HERE
df56ee954d 2011-12-29        kinaba: #include <ctime>
df56ee954d 2011-12-29        kinaba: double start_time; string timer()
df56ee954d 2011-12-29        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
df56ee954d 2011-12-29        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
df56ee954d 2011-12-29        kinaba:  { os << "{ ";
df56ee954d 2011-12-29        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
df56ee954d 2011-12-29        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
df56ee954d 2011-12-29        kinaba: void verify_case(const int& Expected, const int& Received) {
df56ee954d 2011-12-29        kinaba:  bool ok = (Expected == Received);
df56ee954d 2011-12-29        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
df56ee954d 2011-12-29        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
df56ee954d 2011-12-29        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
df56ee954d 2011-12-29        kinaba: #define END	 verify_case(_, Mosquitoes().getMaximum(xInit, v, R));}
df56ee954d 2011-12-29        kinaba: int main(){
df56ee954d 2011-12-29        kinaba: 
df56ee954d 2011-12-29        kinaba: CASE(0)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = {1, -1};
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = {1, -1};
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = 10;
df56ee954d 2011-12-29        kinaba: 	int _ = 2;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: CASE(1)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = {100, -100};
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = {1, -1};
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = 10;
df56ee954d 2011-12-29        kinaba: 	int _ = 1;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: CASE(2)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = {0, -1, 10, -11, 99, -99};
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = {1, -1, -3, 3, 47, -47};
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = 3;
df56ee954d 2011-12-29        kinaba: 	int _ = 4;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: CASE(3)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = {5};
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = {2};
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = 8;
df56ee954d 2011-12-29        kinaba: 	int _ = 1;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: CASE(4)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = {12,34,56,78,90};
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = {-1,2,-3,4,-5};
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = 6;
df56ee954d 2011-12-29        kinaba: 	int _ = 3;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: CASE(5)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = {-29, -27};
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = {25, 61};
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = 7;
df56ee954d 2011-12-29        kinaba: 	int _ = 2;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: /*
df56ee954d 2011-12-29        kinaba: CASE(6)
df56ee954d 2011-12-29        kinaba: 	int xInit_[] = ;
df56ee954d 2011-12-29        kinaba: 	  vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
df56ee954d 2011-12-29        kinaba: 	int v_[] = ;
df56ee954d 2011-12-29        kinaba: 	  vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
df56ee954d 2011-12-29        kinaba: 	int R = ;
df56ee954d 2011-12-29        kinaba: 	int _ = ;
df56ee954d 2011-12-29        kinaba: END
df56ee954d 2011-12-29        kinaba: */
df56ee954d 2011-12-29        kinaba: }
df56ee954d 2011-12-29        kinaba: // END CUT HERE