Artifact d2075b0ec6259c1aeea8046205094c7ab54630b4
#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
template<typename T>
struct DP2
{
const int N1, N2;
vector<T> data;
DP2(int N1, int N2, const T& t = T())
: N1(N1), N2(N2), data(N1*N2, t) { assert(data.size()*sizeof(T)<(1<<26)); }
T& operator()(int i1, int i2)
{ return data[ (i1*N2)+i2 ]; }
void swap(DP2& rhs)
{ data.swap(rhs.data); }
};
class PerfectMemory { public:
double getExpectation(int N, int M)
{
const int C = N*M;
DP2<double> dp(C+1, C+1);
for(int u=0; u<=C; ++u)
for(int k=0; k<=C; ++k) if( (u+k)%2==0 && k+u<=C )
{
if( k > u )
{
dp(k,u) = 1 + dp(k-2,u);
}
else if( k == u )
{
if( k==0 && u==0 )
dp(k,u) = 0;
else
dp(k,u) = 1 + dp(k-1, u-1);
}
else // k < u
{
dp(k,u) = 1;
double pFirstIsKnown = double(k) / u;
double pSecondIsIt = double(1) / (u-1);
if(k)
dp(k,u) += pFirstIsKnown * dp(k-1, u-1);
double pSecondIsThat = double(k) / (u-1);
dp(k,u) += (1-pFirstIsKnown) * pSecondIsIt * dp(k, u-2);
dp(k,u) += (1-pFirstIsKnown) * (1-pSecondIsIt-pSecondIsThat) * dp(k+2, u-2);
dp(k,u) += (1-pFirstIsKnown) * pSecondIsThat * (1 + dp(k, u-2));
}
// cerr << k << " " << u << " " << dp(k,u) << endl;
}
return dp(0,C);
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const double& Expected, const double& Received) {
bool ok = (abs(Expected - Received) < 1e-9);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, PerfectMemory().getExpectation(N, M));}
int main(){
CASE(0)
int N = 1;
int M = 2;
double _ = 1.0;
END
CASE(1)
int N = 2;
int M = 2;
double _ = 2.6666666666666665;
END
CASE(2)
int N = 2;
int M = 3;
double _ = 4.333333333333334;
END
CASE(3)
int N = 4;
int M = 4;
double _ = 12.392984792984793;
END
/*
CASE(4)
int N = 50;
int M = 50;
double _ = -1;
END
CASE(5)
int N = 2;
int M = 1;
double _ = 1.0;
END
*/
}
// END CUT HERE