4fd800b3a8 2011-02-23        kinaba: #include <iostream>
4fd800b3a8 2011-02-23        kinaba: #include <sstream>
4fd800b3a8 2011-02-23        kinaba: #include <iomanip>
4fd800b3a8 2011-02-23        kinaba: #include <vector>
4fd800b3a8 2011-02-23        kinaba: #include <string>
4fd800b3a8 2011-02-23        kinaba: #include <map>
4fd800b3a8 2011-02-23        kinaba: #include <set>
4fd800b3a8 2011-02-23        kinaba: #include <algorithm>
4fd800b3a8 2011-02-23        kinaba: #include <numeric>
4fd800b3a8 2011-02-23        kinaba: #include <iterator>
4fd800b3a8 2011-02-23        kinaba: #include <functional>
4fd800b3a8 2011-02-23        kinaba: #include <complex>
4fd800b3a8 2011-02-23        kinaba: #include <queue>
4fd800b3a8 2011-02-23        kinaba: #include <stack>
4fd800b3a8 2011-02-23        kinaba: #include <cmath>
4fd800b3a8 2011-02-23        kinaba: #include <cassert>
4fd800b3a8 2011-02-23        kinaba: #include <cstring>
4fd800b3a8 2011-02-23        kinaba: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: typedef complex<double> CMP;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class BouncingDiceGame { public:
4fd800b3a8 2011-02-23        kinaba: 	double winProbability(int n, int d, int x, int y)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		int B = n-d;
4fd800b3a8 2011-02-23        kinaba: 		x = min(B,x);
4fd800b3a8 2011-02-23        kinaba: 		y = min(B,y);
4fd800b3a8 2011-02-23        kinaba: 		int Z = min(x,y);
4fd800b3a8 2011-02-23        kinaba: 		vector< vector<double> > p(B+1, vector<double>(B+1, 0));
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		// solve:
4fd800b3a8 2011-02-23        kinaba: 		//   p[B][k] = 1 - p[k][B]
4fd800b3a8 2011-02-23        kinaba: 		//   p[i][k] = 1/d \Sigma_{b=1..d} (1 - p[k][min(B,i+b)])
4fd800b3a8 2011-02-23        kinaba: 		// return p[x][y];
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		for(int ik=B*2; ik>=Z*2; --ik)
4fd800b3a8 2011-02-23        kinaba: 		for(int i=Z; i<=B; ++i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			int k = ik-i;
4fd800b3a8 2011-02-23        kinaba: 			if( Z<=k && k<=B ) {
4fd800b3a8 2011-02-23        kinaba: 				if(i==B && k==B) p[B][B] = d / (2*d-1);
4fd800b3a8 2011-02-23        kinaba: 				else if( i==B ) p[B][k] = 1 - p[k][B]*(d-1)/d;
4fd800b3a8 2011-02-23        kinaba: 				else {
4fd800b3a8 2011-02-23        kinaba: 					double q = 0;
4fd800b3a8 2011-02-23        kinaba: 					for(int b=1; b<=d; ++b)
4fd800b3a8 2011-02-23        kinaba: 						q += 1 - p[k][min(B,i+b)];
4fd800b3a8 2011-02-23        kinaba: 					p[i][k] = q/d;
4fd800b3a8 2011-02-23        kinaba: 				}
4fd800b3a8 2011-02-23        kinaba: 			}
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return p[x][y];
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: #include <ctime>
4fd800b3a8 2011-02-23        kinaba: double start_time; string timer()
4fd800b3a8 2011-02-23        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
4fd800b3a8 2011-02-23        kinaba:  { os << "{ ";
4fd800b3a8 2011-02-23        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
4fd800b3a8 2011-02-23        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
4fd800b3a8 2011-02-23        kinaba: void verify_case(const double& Expected, const double& Received) {
4fd800b3a8 2011-02-23        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
4fd800b3a8 2011-02-23        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
4fd800b3a8 2011-02-23        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
4fd800b3a8 2011-02-23        kinaba: #define END	 verify_case(_, BouncingDiceGame().winProbability(n, d, x, y));}
4fd800b3a8 2011-02-23        kinaba: int main(){
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: CASE(0)
4fd800b3a8 2011-02-23        kinaba: 	int n = 10;
4fd800b3a8 2011-02-23        kinaba: 	int d = 6;
4fd800b3a8 2011-02-23        kinaba: 	int x = 1;
4fd800b3a8 2011-02-23        kinaba: 	int y = 1;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.5417251215862328;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int n = 10;
4fd800b3a8 2011-02-23        kinaba: 	int d = 2;
4fd800b3a8 2011-02-23        kinaba: 	int x = 1;
4fd800b3a8 2011-02-23        kinaba: 	int y = 1;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.6090494791666666;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int n = 100;
4fd800b3a8 2011-02-23        kinaba: 	int d = 20;
4fd800b3a8 2011-02-23        kinaba: 	int x = 1;
4fd800b3a8 2011-02-23        kinaba: 	int y = 10;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.49158887163174947;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int n = 10;
4fd800b3a8 2011-02-23        kinaba: 	int d = 5;
4fd800b3a8 2011-02-23        kinaba: 	int x = 9;
4fd800b3a8 2011-02-23        kinaba: 	int y = 1;
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.6943018666666667;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: /*
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int n = ;
4fd800b3a8 2011-02-23        kinaba: 	int d = ;
4fd800b3a8 2011-02-23        kinaba: 	int x = ;
4fd800b3a8 2011-02-23        kinaba: 	int y = ;
4fd800b3a8 2011-02-23        kinaba: 	double _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int n = ;
4fd800b3a8 2011-02-23        kinaba: 	int d = ;
4fd800b3a8 2011-02-23        kinaba: 	int x = ;
4fd800b3a8 2011-02-23        kinaba: 	int y = ;
4fd800b3a8 2011-02-23        kinaba: 	double _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: */
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE