#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;
class CarrotBoxes { public:
double theProbability(vector <string> info)
{
info = warshall_floyd(info);
double answer=0.0, p=1.0;
set<int> boxes;
for(int v=0; v<info.size(); ++v)
boxes.insert(v);
while( !boxes.empty() )
{
for(set<int>::iterator it=boxes.begin(); it!=boxes.end(); ++it)
if( isRoot(*it, info, boxes) && !isSingleton(*it, info, boxes) )
{
int N = boxes.size();
int nr = 0;
for(int u=0; u<info.size(); ++u)
if( info[*it][u]=='Y' && boxes.count(u) )
{++nr; boxes.erase(u);}
answer += p * (nr-1) / N;
p *= double(N-nr) / N;
goto nextIter;
}
// ‘S•”‚ª stand alone
answer += p / boxes.size();
break;
nextIter:;
}
return answer;
}
bool isRoot(int v, const vector<string>& info, const set<int>& boxes)
{
for(set<int>::const_iterator jt=boxes.begin(); jt!=boxes.end(); ++jt)
if( info[v][*jt]=='N' && info[*jt][v]=='Y' )
return false;
return true;
}
bool isSingleton(int v, const vector<string>& info, const set<int>& boxes)
{
for(set<int>::const_iterator jt=boxes.begin(); jt!=boxes.end(); ++jt)
if( v!=*jt && info[v][*jt]=='Y' )
return false;
return true;
}
vector<string> warshall_floyd(const vector<string>& gg)
{
vector<string> g = gg;
for(int k=0; k<g.size(); ++k)
for(int i=0; i<g.size(); ++i)
for(int j=0; j<g.size(); ++j)
if( g[i][k]=='Y' && g[k][j]=='Y' )
g[i][j] = 'Y';
return g;
}
};
// 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(_, CarrotBoxes().theProbability(information));}
int main(){
CASE(0)
string information_[] = {"YYYYY",
"NYNNN",
"NNYNN",
"NNNYN",
"NNNNY"}
;
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = 0.8;
END
CASE(1)
string information_[] = {"YNNNN",
"NYNNN",
"NNYNN",
"NNNYN",
"NNNNY"};
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = 0.2;
END
CASE(2)
string information_[] = {"Y"};
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = 1.0;
END
CASE(3)
string information_[] = {"YNNNN",
"YYNNN",
"YNYNN",
"NNNYY",
"NNNYY"}
;
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = 0.6;
END
CASE(4)
string information_[] = {"YYYNNNYN",
"NYNNNNYN",
"NNYNNNNN",
"NYNYNNNN",
"YNNNYNNY",
"NNYNNYNN",
"NNNNYNYN",
"NNYNNNNY"}
;
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = 0.875;
END
CASE(5)
string information_[] = {"YNNNNNNNNYNNNNNNNNNN",
"NYNNNNNNNNNNNNNNNNNN",
"NNYNNNNNNNYNNNNNYNNN",
"NNNYNYNNNNNNNNYNNNNN",
"NNNNYNNNNNNNNNYNNNNY",
"NNNNNYNNNNNNNNNNNNNY",
"NNNNYNYNYNNNNNNNNNNN",
"NNNNNNNYNNNYYNNNNNNN",
"NNNNNNNNYNNNNNNNNNNN",
"YNNNNNNNNYNNNNNYNNNN",
"NNNNNNNNNNYNNNNNNNNN",
"NYNNNNNNNNNYNNNNNNNN",
"NNNNNNNYNNNNYNNNNNNN",
"NNNNNNNNNNNNNYNNNYNN",
"NNNNNNNNNNNYNNYNNNYN",
"NYNNNNNNNNNNNNNYNNNN",
"NNYNNNNNNNNNNNNNYNNN",
"NNNNNNNNNNNNNYNYNYNN",
"NNNNNNNNYNYNNNNNNNYY",
"NNNYNNNNNNNNNNNNNNNY"};
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = 0.75;
END
/*
CASE(6)
string information_[] = ;
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = ;
END
CASE(7)
string information_[] = ;
vector <string> information(information_, information_+sizeof(information_)/sizeof(*information_));
double _ = ;
END
*/
}
// END CUT HERE