fca716a31c 2011-07-26        kinaba: #include <iostream>
fca716a31c 2011-07-26        kinaba: #include <sstream>
fca716a31c 2011-07-26        kinaba: #include <iomanip>
fca716a31c 2011-07-26        kinaba: #include <vector>
fca716a31c 2011-07-26        kinaba: #include <string>
fca716a31c 2011-07-26        kinaba: #include <map>
fca716a31c 2011-07-26        kinaba: #include <set>
fca716a31c 2011-07-26        kinaba: #include <algorithm>
fca716a31c 2011-07-26        kinaba: #include <numeric>
fca716a31c 2011-07-26        kinaba: #include <iterator>
fca716a31c 2011-07-26        kinaba: #include <functional>
fca716a31c 2011-07-26        kinaba: #include <complex>
fca716a31c 2011-07-26        kinaba: #include <queue>
fca716a31c 2011-07-26        kinaba: #include <stack>
fca716a31c 2011-07-26        kinaba: #include <cmath>
fca716a31c 2011-07-26        kinaba: #include <cassert>
fca716a31c 2011-07-26        kinaba: #include <cstring>
fca716a31c 2011-07-26        kinaba: using namespace std;
fca716a31c 2011-07-26        kinaba: typedef long long LL;
fca716a31c 2011-07-26        kinaba: typedef complex<double> CMP;
fca716a31c 2011-07-26        kinaba: 
fca716a31c 2011-07-26        kinaba: template<typename T>
fca716a31c 2011-07-26        kinaba: struct DP2
fca716a31c 2011-07-26        kinaba: {
fca716a31c 2011-07-26        kinaba: 	const int N1, N2;
fca716a31c 2011-07-26        kinaba: 	vector<T> data;
fca716a31c 2011-07-26        kinaba: 	DP2(int N1, int N2, const T& t = T())
fca716a31c 2011-07-26        kinaba: 		: N1(N1), N2(N2), data(N1*N2, t) { assert(data.size()*sizeof(T)<(1<<26)); }
fca716a31c 2011-07-26        kinaba: 	T& operator()(int i1, int i2)
fca716a31c 2011-07-26        kinaba: 		{ return data[ (i1*N2)+i2 ]; }
fca716a31c 2011-07-26        kinaba: 	void swap(DP2& rhs)
fca716a31c 2011-07-26        kinaba: 		{ data.swap(rhs.data); }
fca716a31c 2011-07-26        kinaba: };
fca716a31c 2011-07-26        kinaba: 
fca716a31c 2011-07-26        kinaba: class PerfectMemory { public:
fca716a31c 2011-07-26        kinaba: 	double getExpectation(int N, int M)
fca716a31c 2011-07-26        kinaba: 	{
fca716a31c 2011-07-26        kinaba: 		const int C = N*M;
fca716a31c 2011-07-26        kinaba: 		DP2<double> dp(C+1, C+1);
fca716a31c 2011-07-26        kinaba: 		for(int u=0; u<=C; ++u)
fca716a31c 2011-07-26        kinaba: 			for(int k=0; k<=C; ++k) if( (u+k)%2==0 && k+u<=C )
fca716a31c 2011-07-26        kinaba: 			{
fca716a31c 2011-07-26        kinaba: 				if( k > u )
fca716a31c 2011-07-26        kinaba: 				{
fca716a31c 2011-07-26        kinaba: 					dp(k,u) = 1 + dp(k-2,u);
fca716a31c 2011-07-26        kinaba: 				}
fca716a31c 2011-07-26        kinaba: 				else if( k == u )
fca716a31c 2011-07-26        kinaba: 				{
fca716a31c 2011-07-26        kinaba: 					if( k==0 && u==0 )
fca716a31c 2011-07-26        kinaba: 						dp(k,u) = 0;
fca716a31c 2011-07-26        kinaba: 					else
fca716a31c 2011-07-26        kinaba: 						dp(k,u) = 1 + dp(k-1, u-1);
fca716a31c 2011-07-26        kinaba: 				}
fca716a31c 2011-07-26        kinaba: 				else // k < u
fca716a31c 2011-07-26        kinaba: 				{
fca716a31c 2011-07-26        kinaba: 					dp(k,u) = 1;
fca716a31c 2011-07-26        kinaba: 
fca716a31c 2011-07-26        kinaba: 					double pFirstIsKnown = double(k) / u;
fca716a31c 2011-07-26        kinaba: 					double pSecondIsIt = double(1) / (u-1);
fca716a31c 2011-07-26        kinaba: 					if(k)
fca716a31c 2011-07-26        kinaba: 						dp(k,u) += pFirstIsKnown * dp(k-1, u-1);
fca716a31c 2011-07-26        kinaba: 					double pSecondIsThat = double(k) / (u-1);
fca716a31c 2011-07-26        kinaba: 					dp(k,u) += (1-pFirstIsKnown) * pSecondIsIt * dp(k, u-2);
fca716a31c 2011-07-26        kinaba: 					dp(k,u) += (1-pFirstIsKnown) * (1-pSecondIsIt-pSecondIsThat) * dp(k+2, u-2);
fca716a31c 2011-07-26        kinaba: 					dp(k,u) += (1-pFirstIsKnown) * pSecondIsThat * (1 + dp(k, u-2));
fca716a31c 2011-07-26        kinaba: 				}
fca716a31c 2011-07-26        kinaba: //				cerr << k << " " << u << " " << dp(k,u) << endl;
fca716a31c 2011-07-26        kinaba: 			}
fca716a31c 2011-07-26        kinaba: 		return dp(0,C);
fca716a31c 2011-07-26        kinaba: 	}
fca716a31c 2011-07-26        kinaba: };
fca716a31c 2011-07-26        kinaba: 
fca716a31c 2011-07-26        kinaba: // BEGIN CUT HERE
fca716a31c 2011-07-26        kinaba: #include <ctime>
fca716a31c 2011-07-26        kinaba: double start_time; string timer()
fca716a31c 2011-07-26        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
fca716a31c 2011-07-26        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
fca716a31c 2011-07-26        kinaba:  { os << "{ ";
fca716a31c 2011-07-26        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
fca716a31c 2011-07-26        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
fca716a31c 2011-07-26        kinaba: void verify_case(const double& Expected, const double& Received) {
fca716a31c 2011-07-26        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
fca716a31c 2011-07-26        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
fca716a31c 2011-07-26        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
fca716a31c 2011-07-26        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
fca716a31c 2011-07-26        kinaba: #define END	 verify_case(_, PerfectMemory().getExpectation(N, M));}
fca716a31c 2011-07-26        kinaba: int main(){
fca716a31c 2011-07-26        kinaba: 
fca716a31c 2011-07-26        kinaba: CASE(0)
fca716a31c 2011-07-26        kinaba: 	int N = 1;
fca716a31c 2011-07-26        kinaba: 	int M = 2;
fca716a31c 2011-07-26        kinaba: 	double _ = 1.0;
fca716a31c 2011-07-26        kinaba: END
fca716a31c 2011-07-26        kinaba: CASE(1)
fca716a31c 2011-07-26        kinaba: 	int N = 2;
fca716a31c 2011-07-26        kinaba: 	int M = 2;
fca716a31c 2011-07-26        kinaba: 	double _ = 2.6666666666666665;
fca716a31c 2011-07-26        kinaba: END
fca716a31c 2011-07-26        kinaba: CASE(2)
fca716a31c 2011-07-26        kinaba: 	int N = 2;
fca716a31c 2011-07-26        kinaba: 	int M = 3;
fca716a31c 2011-07-26        kinaba: 	double _ = 4.333333333333334;
fca716a31c 2011-07-26        kinaba: END
fca716a31c 2011-07-26        kinaba: CASE(3)
fca716a31c 2011-07-26        kinaba: 	int N = 4;
fca716a31c 2011-07-26        kinaba: 	int M = 4;
fca716a31c 2011-07-26        kinaba: 	double _ = 12.392984792984793;
fca716a31c 2011-07-26        kinaba: END
fca716a31c 2011-07-26        kinaba: /*
fca716a31c 2011-07-26        kinaba: CASE(4)
fca716a31c 2011-07-26        kinaba: 	int N = 50;
fca716a31c 2011-07-26        kinaba: 	int M = 50;
fca716a31c 2011-07-26        kinaba: 	double _ = -1;
fca716a31c 2011-07-26        kinaba: END
fca716a31c 2011-07-26        kinaba: CASE(5)
fca716a31c 2011-07-26        kinaba: 	int N = 2;
fca716a31c 2011-07-26        kinaba: 	int M = 1;
fca716a31c 2011-07-26        kinaba: 	double _ = 1.0;
fca716a31c 2011-07-26        kinaba: END
fca716a31c 2011-07-26        kinaba: */
fca716a31c 2011-07-26        kinaba: }
fca716a31c 2011-07-26        kinaba: // END CUT HERE