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 GreatExpectations {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	double expectedTime(vector <string> doors)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		const int Y = doors.size()/2  +1;
4fd800b3a8 2011-02-23        kinaba: 		const int X = doors[0].size() +1;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		vector< vector<double> > e(Y, vector<double>(X, -1.0));
4fd800b3a8 2011-02-23        kinaba: 		e[Y-1][X-1] = 0.0;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		for(int k=0; k<X*Y; ++k)
4fd800b3a8 2011-02-23        kinaba: 			for(int y=0; y<Y; ++y)
4fd800b3a8 2011-02-23        kinaba: 				for(int x=0; x<X; ++x)
4fd800b3a8 2011-02-23        kinaba: 				{
4fd800b3a8 2011-02-23        kinaba: 					// neibours : (expected_time, door_prob)
4fd800b3a8 2011-02-23        kinaba: 					vector< pair<double,double> > ep;
4fd800b3a8 2011-02-23        kinaba: 					if( x+1<X && doors[y*2][x]!='0' && e[y][x+1]>=0 )
4fd800b3a8 2011-02-23        kinaba: 						ep.push_back( make_pair(e[y][x+1], (doors[y*2][x]-'0')/8.0) );
4fd800b3a8 2011-02-23        kinaba: 					if( 0<x && doors[y*2][x-1]!='0' && e[y][x-1]>=0 )
4fd800b3a8 2011-02-23        kinaba: 						ep.push_back( make_pair(e[y][x-1], (doors[y*2][x-1]-'0')/8.0) );
4fd800b3a8 2011-02-23        kinaba: 					if( y+1<Y && doors[y*2+1][x]!='0' && e[y+1][x]>=0 )
4fd800b3a8 2011-02-23        kinaba: 						ep.push_back( make_pair(e[y+1][x], (doors[y*2+1][x]-'0')/8.0) );
4fd800b3a8 2011-02-23        kinaba: 					if( 0<y && doors[y*2-1][x]!='0' && e[y-1][x]>=0 )
4fd800b3a8 2011-02-23        kinaba: 						ep.push_back( make_pair(e[y-1][x], (doors[y*2-1][x]-'0')/8.0) );
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 					if( ep.empty() ) continue;
4fd800b3a8 2011-02-23        kinaba: 					sort( ep.begin(), ep.end() ); // better first
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 					// choose k that minimizes the following E:
4fd800b3a8 2011-02-23        kinaba: 					//   E = (1+e[0])*p[0]
4fd800b3a8 2011-02-23        kinaba: 					//     + (1+e[1])*(1-p[0])*p[1]
4fd800b3a8 2011-02-23        kinaba: 					//     + (1+e[2])*(1-p[0])*(1-p[1])*p[2]
4fd800b3a8 2011-02-23        kinaba: 					//     + ...
4fd800b3a8 2011-02-23        kinaba: 					//     + (1+E)   *(1-p[0])*(1-p[1])*...*(1-p[k])
4fd800b3a8 2011-02-23        kinaba: 					double r=1.0, s=0.0, E=1e+50;
4fd800b3a8 2011-02-23        kinaba: 					for(int i=0; i<ep.size(); ++i) {
4fd800b3a8 2011-02-23        kinaba: 						double s2 = s + r * ep[i].second * (1 + ep[i].first);
4fd800b3a8 2011-02-23        kinaba: 						double r2 = r * (1 - ep[i].second);
4fd800b3a8 2011-02-23        kinaba: 						double E2 = (s2 + r2) / (1-r2);
4fd800b3a8 2011-02-23        kinaba: 						if( E2 > E ) break;
4fd800b3a8 2011-02-23        kinaba: 						r=r2, s=s2, E=E2;
4fd800b3a8 2011-02-23        kinaba: 					}
4fd800b3a8 2011-02-23        kinaba: 					if( e[y][x]<0 || e[y][x]>E )
4fd800b3a8 2011-02-23        kinaba: 						e[y][x]=E;
4fd800b3a8 2011-02-23        kinaba: 				}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		return e[0][0];
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: 	string doors_[] = { "4",
4fd800b3a8 2011-02-23        kinaba:   "44",
4fd800b3a8 2011-02-23        kinaba:   "4" };
4fd800b3a8 2011-02-23        kinaba: 	  vector <string> doors(doors_, doors_+sizeof(doors_)/sizeof(*doors_));
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 3.3333333333333335;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, GreatExpectations().expectedTime(doors)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<1>) {
4fd800b3a8 2011-02-23        kinaba: 	string doors_[] = { "48",
4fd800b3a8 2011-02-23        kinaba:   "440",
4fd800b3a8 2011-02-23        kinaba:   "42",
4fd800b3a8 2011-02-23        kinaba:   "862",
4fd800b3a8 2011-02-23        kinaba:   "06" };
4fd800b3a8 2011-02-23        kinaba: 	  vector <string> doors(doors_, doors_+sizeof(doors_)/sizeof(*doors_));
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 6.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, GreatExpectations().expectedTime(doors)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<2>) {
4fd800b3a8 2011-02-23        kinaba: 	string doors_[] = { "0808",
4fd800b3a8 2011-02-23        kinaba:   "88888",
4fd800b3a8 2011-02-23        kinaba:   "0000",
4fd800b3a8 2011-02-23        kinaba:   "88888",
4fd800b3a8 2011-02-23        kinaba:   "8080" }
4fd800b3a8 2011-02-23        kinaba: ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <string> doors(doors_, doors_+sizeof(doors_)/sizeof(*doors_));
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 14.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, GreatExpectations().expectedTime(doors)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<3>) {
4fd800b3a8 2011-02-23        kinaba: 	string doors_[] = { "2815",
4fd800b3a8 2011-02-23        kinaba:   "67686",
4fd800b3a8 2011-02-23        kinaba:   "1324",
4fd800b3a8 2011-02-23        kinaba:   "75767",
4fd800b3a8 2011-02-23        kinaba:   "6051" }
4fd800b3a8 2011-02-23        kinaba: ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <string> doors(doors_, doors_+sizeof(doors_)/sizeof(*doors_));
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 11.852782338798935;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, GreatExpectations().expectedTime(doors)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<4>) {
4fd800b3a8 2011-02-23        kinaba: 	string doors_[] = { "823",
4fd800b3a8 2011-02-23        kinaba:   "2630",
4fd800b3a8 2011-02-23        kinaba:   "130" }
4fd800b3a8 2011-02-23        kinaba: ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <string> doors(doors_, doors_+sizeof(doors_)/sizeof(*doors_));
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = -1.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, GreatExpectations().expectedTime(doors)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<5>) {
4fd800b3a8 2011-02-23        kinaba: 	string doors_[] = { "0",
4fd800b3a8 2011-02-23        kinaba:   "44",
4fd800b3a8 2011-02-23        kinaba:   "4" }
4fd800b3a8 2011-02-23        kinaba: ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <string> doors(doors_, doors_+sizeof(doors_)/sizeof(*doors_));
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 4.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, GreatExpectations().expectedTime(doors)); }
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: