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 DrawingLines { public:
4fd800b3a8 2011-02-23        kinaba: 	double countLineCrossings(int n, vector <int> startDot, vector <int> endDot)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		int m = n-startDot.size();
4fd800b3a8 2011-02-23        kinaba: 		double news = c(m);
4fd800b3a8 2011-02-23        kinaba: 		double ooolds = 0.0;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<startDot.size(); ++i)
4fd800b3a8 2011-02-23        kinaba: 			for(int j=i+1; j<startDot.size(); ++j)
4fd800b3a8 2011-02-23        kinaba: 				if( startDot[i]<startDot[j] && endDot[i]>endDot[j]
4fd800b3a8 2011-02-23        kinaba: 				||  startDot[i]>startDot[j] && endDot[i]<endDot[j] )
4fd800b3a8 2011-02-23        kinaba: 					ooolds += 1;
4fd800b3a8 2011-02-23        kinaba: 		double olds = 0.0;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		vector<int> sTaken, eTaken;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<startDot.size(); ++i) {
4fd800b3a8 2011-02-23        kinaba: 			sTaken.push_back(startDot[i]);
4fd800b3a8 2011-02-23        kinaba: 			eTaken.push_back(endDot[i]);
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		sort(sTaken.begin(), sTaken.end());
4fd800b3a8 2011-02-23        kinaba: 		sort(eTaken.begin(), eTaken.end());
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		if( n > startDot.size() )
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<startDot.size(); ++i) {
4fd800b3a8 2011-02-23        kinaba: 			vector<int>::iterator si = lower_bound(sTaken.begin(), sTaken.end(), startDot[i]);
4fd800b3a8 2011-02-23        kinaba: 			vector<int>::iterator ei = lower_bound(eTaken.begin(), eTaken.end(),   endDot[i]);
4fd800b3a8 2011-02-23        kinaba: 			olds += f( (startDot[i]-1) - (si-sTaken.begin()),
4fd800b3a8 2011-02-23        kinaba: 			           (n-startDot[i]) - (sTaken.end()-si-1),
4fd800b3a8 2011-02-23        kinaba: 					   (endDot[i]-1) - (ei-eTaken.begin()),
4fd800b3a8 2011-02-23        kinaba: 					   (n-endDot[i]) - (eTaken.end()-ei-1)
4fd800b3a8 2011-02-23        kinaba: 					   );
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return news + ooolds + olds;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	double c(int m)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		return m*(m-1) / 4.0;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	double f(double a, double b, double c, double d)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		return a * d/(c+d) + b*c/(c+d);
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(_, DrawingLines().countLineCrossings(n, startDot, endDot));}
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 n = 3;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {2};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {3};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int n = 5;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1,4};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {3,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 5.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int n = 4;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {4,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {4,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int n = 8;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1,4,3,6,7};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {1,3,2,4,5};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 7.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int n = 2;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1,2} ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {1,2};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int n = 2;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1,2} ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {2,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(6)
4fd800b3a8 2011-02-23        kinaba: 	int n = 3;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1} ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(7)
4fd800b3a8 2011-02-23        kinaba: 	int n = 3;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1} ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	int endDot_[] = {3};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 2.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(8)
4fd800b3a8 2011-02-23        kinaba: 	int n = 10000;
4fd800b3a8 2011-02-23        kinaba: 	int startDot_[] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> startDot(startDot_, startDot_+sizeof(startDot_)/sizeof(*startDot_));
4fd800b3a8 2011-02-23        kinaba: 	  int endDot_[] = {20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> endDot(endDot_, endDot_+sizeof(endDot_)/sizeof(*endDot_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE