1535d63cea 2011-05-28        kinaba: #include <iostream>
1535d63cea 2011-05-28        kinaba: #include <sstream>
1535d63cea 2011-05-28        kinaba: #include <iomanip>
1535d63cea 2011-05-28        kinaba: #include <vector>
1535d63cea 2011-05-28        kinaba: #include <string>
1535d63cea 2011-05-28        kinaba: #include <map>
1535d63cea 2011-05-28        kinaba: #include <set>
1535d63cea 2011-05-28        kinaba: #include <algorithm>
1535d63cea 2011-05-28        kinaba: #include <numeric>
1535d63cea 2011-05-28        kinaba: #include <iterator>
1535d63cea 2011-05-28        kinaba: #include <functional>
1535d63cea 2011-05-28        kinaba: #include <complex>
1535d63cea 2011-05-28        kinaba: #include <queue>
1535d63cea 2011-05-28        kinaba: #include <stack>
1535d63cea 2011-05-28        kinaba: #include <cmath>
1535d63cea 2011-05-28        kinaba: #include <cassert>
1535d63cea 2011-05-28        kinaba: #include <cstring>
1535d63cea 2011-05-28        kinaba: using namespace std;
1535d63cea 2011-05-28        kinaba: typedef long long LL;
1535d63cea 2011-05-28        kinaba: typedef complex<double> CMP;
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: class TheTicketsDivOne { public:
1535d63cea 2011-05-28        kinaba: 	double find(int n, int m)
1535d63cea 2011-05-28        kinaba: 	{
1535d63cea 2011-05-28        kinaba: 		vector<double> p(1, 1.0);
1535d63cea 2011-05-28        kinaba: 		for(int N=2; N<=n; ++N) {
1535d63cea 2011-05-28        kinaba: 			vector<double> q(N, 0.0);
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: 			// q[0] = 1/6 + 1/2 q[N-1]
1535d63cea 2011-05-28        kinaba: 			// q[i] = 1/2 q[i-1] + 1/3 p[i-1]
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: 			double s = 1.0/6;
1535d63cea 2011-05-28        kinaba: 			double f = 1.0/3;
1535d63cea 2011-05-28        kinaba: 			for(int i=N-2; i>=0; --i) {
1535d63cea 2011-05-28        kinaba: 				f = f/2;
1535d63cea 2011-05-28        kinaba: 				s += f*p[i];
1535d63cea 2011-05-28        kinaba: 			}
1535d63cea 2011-05-28        kinaba: 			q[0] = s / (1.0 - pow(0.5, N));
1535d63cea 2011-05-28        kinaba: 			for(int i=1; i<N; ++i)
1535d63cea 2011-05-28        kinaba: 				q[i] = q[i-1]/2.0 + p[i-1]/3.0;
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: 			p.swap(q);
1535d63cea 2011-05-28        kinaba: 		}
1535d63cea 2011-05-28        kinaba: 		return p[m-1];
1535d63cea 2011-05-28        kinaba: 	}
1535d63cea 2011-05-28        kinaba: };
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: // BEGIN CUT HERE
1535d63cea 2011-05-28        kinaba: #include <ctime>
1535d63cea 2011-05-28        kinaba: double start_time; string timer()
1535d63cea 2011-05-28        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
1535d63cea 2011-05-28        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
1535d63cea 2011-05-28        kinaba:  { os << "{ ";
1535d63cea 2011-05-28        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
1535d63cea 2011-05-28        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
1535d63cea 2011-05-28        kinaba: void verify_case(const double& Expected, const double& Received) {
1535d63cea 2011-05-28        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
1535d63cea 2011-05-28        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
1535d63cea 2011-05-28        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
1535d63cea 2011-05-28        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
1535d63cea 2011-05-28        kinaba: #define END	 verify_case(_, TheTicketsDivOne().find(n, m));}
1535d63cea 2011-05-28        kinaba: int main(){
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: CASE(0)
1535d63cea 2011-05-28        kinaba: 	int n = 2;
1535d63cea 2011-05-28        kinaba: 	int m = 1;
1535d63cea 2011-05-28        kinaba: 	double _ = 0.4444444444444444;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(1)
1535d63cea 2011-05-28        kinaba: 	int n = 2;
1535d63cea 2011-05-28        kinaba: 	int m = 2;
1535d63cea 2011-05-28        kinaba: 	double _ = 0.5555555555555556;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(2)
1535d63cea 2011-05-28        kinaba: 	int n = 1;
1535d63cea 2011-05-28        kinaba: 	int m = 1;
1535d63cea 2011-05-28        kinaba: 	double _ = 1.0;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(3)
1535d63cea 2011-05-28        kinaba: 	int n = 3;
1535d63cea 2011-05-28        kinaba: 	int m = 2;
1535d63cea 2011-05-28        kinaba: 	double _ = 0.31746031746031744;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(4)
1535d63cea 2011-05-28        kinaba: 	int n = 1000;
1535d63cea 2011-05-28        kinaba: 	int m = 500;
1535d63cea 2011-05-28        kinaba: 	double _ = -1;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(5)
1535d63cea 2011-05-28        kinaba: 	int n = 1;
1535d63cea 2011-05-28        kinaba: 	int m = 1;
1535d63cea 2011-05-28        kinaba: 	double _ = 1.0;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(6)
1535d63cea 2011-05-28        kinaba: 	int n = 1000;
1535d63cea 2011-05-28        kinaba: 	int m = 1000;
1535d63cea 2011-05-28        kinaba: 	double _ = -1;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: CASE(7)
1535d63cea 2011-05-28        kinaba: 	int n = 1000;
1535d63cea 2011-05-28        kinaba: 	int m = 1;
1535d63cea 2011-05-28        kinaba: 	double _ = -1;
1535d63cea 2011-05-28        kinaba: END
1535d63cea 2011-05-28        kinaba: 
1535d63cea 2011-05-28        kinaba: }
1535d63cea 2011-05-28        kinaba: // END CUT HERE