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 TheBoredomDivOne { public:
4fd800b3a8 2011-02-23        kinaba: 	double find(int n, int m)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		double total = (n+m)*(n+m-1);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		vector<double> e(n+m+1);
4fd800b3a8 2011-02-23        kinaba: 		e[n+m] = 0;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=n+m-1; i>=n; --i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			double p2 = (n+m-i)*(n+m-i-1) / total;
4fd800b3a8 2011-02-23        kinaba: 			double p1 = 2*i*(n+m-i) / total;
4fd800b3a8 2011-02-23        kinaba: 			double p0 = 1-p2-p1;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 			// e[i] = 1 + p0*e[i] + p1*e[i+1] + p2*e[i+2];
4fd800b3a8 2011-02-23        kinaba: 			e[i] = 1/(1-p0) + p1/(1-p0)*e[i+1] + (i==n+m-1 ? 0 : p2/(1-p0)*e[i+2]);
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return e[n];
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(_, TheBoredomDivOne().find(n, m));}
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 = 1;
4fd800b3a8 2011-02-23        kinaba: 	int m = 1;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int n = 2;
4fd800b3a8 2011-02-23        kinaba: 	int m = 1;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.5;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int n = 1;
4fd800b3a8 2011-02-23        kinaba: 	int m = 2;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 2.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int n = 4;
4fd800b3a8 2011-02-23        kinaba: 	int m = 7;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 13.831068977298521;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: 	/*
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int n = ;
4fd800b3a8 2011-02-23        kinaba: 	int m = ;
4fd800b3a8 2011-02-23        kinaba: 	double _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int n = ;
4fd800b3a8 2011-02-23        kinaba: 	int m = ;
4fd800b3a8 2011-02-23        kinaba: 	double _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: */
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE