Artifact 4ab9d94a2abea13a2c7703a4bbc4ba9430731547
#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 BouncingDiceGame { public:
double winProbability(int n, int d, int x, int y)
{
int B = n-d;
x = min(B,x);
y = min(B,y);
int Z = min(x,y);
vector< vector<double> > p(B+1, vector<double>(B+1, 0));
// solve:
// p[B][k] = 1 - p[k][B]
// p[i][k] = 1/d \Sigma_{b=1..d} (1 - p[k][min(B,i+b)])
// return p[x][y];
for(int ik=B*2; ik>=Z*2; --ik)
for(int i=Z; i<=B; ++i)
{
int k = ik-i;
if( Z<=k && k<=B ) {
if(i==B && k==B) p[B][B] = d / (2*d-1);
else if( i==B ) p[B][k] = 1 - p[k][B]*(d-1)/d;
else {
double q = 0;
for(int b=1; b<=d; ++b)
q += 1 - p[k][min(B,i+b)];
p[i][k] = q/d;
}
}
}
return p[x][y];
}
};
// 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(_, BouncingDiceGame().winProbability(n, d, x, y));}
int main(){
CASE(0)
int n = 10;
int d = 6;
int x = 1;
int y = 1;
double _ = 0.5417251215862328;
END
CASE(1)
int n = 10;
int d = 2;
int x = 1;
int y = 1;
double _ = 0.6090494791666666;
END
CASE(2)
int n = 100;
int d = 20;
int x = 1;
int y = 10;
double _ = 0.49158887163174947;
END
CASE(3)
int n = 10;
int d = 5;
int x = 9;
int y = 1;
double _ = 0.6943018666666667;
END
/*
CASE(4)
int n = ;
int d = ;
int x = ;
int y = ;
double _ = ;
END
CASE(5)
int n = ;
int d = ;
int x = ;
int y = ;
double _ = ;
END
*/
}
// END CUT HERE