Artifact 1f5d9f15dbb3d7e23f8fe13f06862147397a196a
#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 TheTicketsDivOne { public:
double find(int n, int m)
{
vector<double> p(1, 1.0);
for(int N=2; N<=n; ++N) {
vector<double> q(N, 0.0);
// q[0] = 1/6 + 1/2 q[N-1]
// q[i] = 1/2 q[i-1] + 1/3 p[i-1]
double s = 1.0/6;
double f = 1.0/3;
for(int i=N-2; i>=0; --i) {
f = f/2;
s += f*p[i];
}
q[0] = s / (1.0 - pow(0.5, N));
for(int i=1; i<N; ++i)
q[i] = q[i-1]/2.0 + p[i-1]/3.0;
p.swap(q);
}
return p[m-1];
}
};
// 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(_, TheTicketsDivOne().find(n, m));}
int main(){
CASE(0)
int n = 2;
int m = 1;
double _ = 0.4444444444444444;
END
CASE(1)
int n = 2;
int m = 2;
double _ = 0.5555555555555556;
END
CASE(2)
int n = 1;
int m = 1;
double _ = 1.0;
END
CASE(3)
int n = 3;
int m = 2;
double _ = 0.31746031746031744;
END
CASE(4)
int n = 1000;
int m = 500;
double _ = -1;
END
CASE(5)
int n = 1;
int m = 1;
double _ = 1.0;
END
CASE(6)
int n = 1000;
int m = 1000;
double _ = -1;
END
CASE(7)
int n = 1000;
int m = 1;
double _ = -1;
END
}
// END CUT HERE