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 <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: 
4fd800b3a8 2011-02-23        kinaba: class KthProbableElement {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba:   double probability(int M, int lowerBound, int upperBound, int N, int K)
4fd800b3a8 2011-02-23        kinaba:   {
4fd800b3a8 2011-02-23        kinaba:     double dp1[101][101]={0}, dp2[101][101], (*P)[101]=dp1, (*Q)[101]=dp2;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba:     P[0][0] = 1.0;
4fd800b3a8 2011-02-23        kinaba:     for(int i=0; i<M; ++i)
4fd800b3a8 2011-02-23        kinaba:     {
4fd800b3a8 2011-02-23        kinaba:       memset( Q, 0, sizeof(double)*101*101 );
4fd800b3a8 2011-02-23        kinaba:       for(int a=0; a<=i; ++a)
4fd800b3a8 2011-02-23        kinaba:         for(int b=0; a+b<=i; ++b)
4fd800b3a8 2011-02-23        kinaba:         {
4fd800b3a8 2011-02-23        kinaba:           Q[a+1][b] += P[a][b] * (N-lowerBound) / (upperBound-lowerBound+1);
4fd800b3a8 2011-02-23        kinaba:           Q[a][b+1] += P[a][b] * 1 / (upperBound-lowerBound+1);
4fd800b3a8 2011-02-23        kinaba:           Q[a][b]   += P[a][b] * (upperBound-N) / (upperBound-lowerBound+1);
4fd800b3a8 2011-02-23        kinaba:         }
4fd800b3a8 2011-02-23        kinaba:       swap(P, Q);
4fd800b3a8 2011-02-23        kinaba:     }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba:     double p = 0.0;
4fd800b3a8 2011-02-23        kinaba:     for(int a=0; a<=M; ++a)
4fd800b3a8 2011-02-23        kinaba:       for(int b=0; a+b<=M; ++b)
4fd800b3a8 2011-02-23        kinaba:         if( a<K && K<=a+b )
4fd800b3a8 2011-02-23        kinaba:           p += P[a][b];
4fd800b3a8 2011-02-23        kinaba:     return p;
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() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: int verify_case(const double &Expected, const double &Received) { double diff = Expected - Received; if (diff < 0) diff = -diff; if (diff < 1e-9) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> struct Case_ { Case_(){start_time=clock();} };
4fd800b3a8 2011-02-23        kinaba: char Test_(...);
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<0>) {
4fd800b3a8 2011-02-23        kinaba:   int M = 1;
4fd800b3a8 2011-02-23        kinaba:   int lowerBound = 1;
4fd800b3a8 2011-02-23        kinaba:   int upperBound = 10;
4fd800b3a8 2011-02-23        kinaba:   int N = 3;
4fd800b3a8 2011-02-23        kinaba:   int K = 1;
4fd800b3a8 2011-02-23        kinaba:   double RetVal = 0.1;
4fd800b3a8 2011-02-23        kinaba:   return verify_case(RetVal, KthProbableElement().probability(M, lowerBound, upperBound, N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<1>) {
4fd800b3a8 2011-02-23        kinaba:   int M = 3;
4fd800b3a8 2011-02-23        kinaba:   int lowerBound = 1;
4fd800b3a8 2011-02-23        kinaba:   int upperBound = 2;
4fd800b3a8 2011-02-23        kinaba:   int N = 2;
4fd800b3a8 2011-02-23        kinaba:   int K = 2;
4fd800b3a8 2011-02-23        kinaba:   double RetVal = 0.5;
4fd800b3a8 2011-02-23        kinaba:   return verify_case(RetVal, KthProbableElement().probability(M, lowerBound, upperBound, N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<2>) {
4fd800b3a8 2011-02-23        kinaba:   int M = 3;
4fd800b3a8 2011-02-23        kinaba:   int lowerBound = 1;
4fd800b3a8 2011-02-23        kinaba:   int upperBound = 3;
4fd800b3a8 2011-02-23        kinaba:   int N = 2;
4fd800b3a8 2011-02-23        kinaba:   int K = 2;
4fd800b3a8 2011-02-23        kinaba:   double RetVal = 0.48148148148148145;
4fd800b3a8 2011-02-23        kinaba:   return verify_case(RetVal, KthProbableElement().probability(M, lowerBound, upperBound, N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<3>) {
4fd800b3a8 2011-02-23        kinaba:   int M = 10;
4fd800b3a8 2011-02-23        kinaba:   int lowerBound = 1;
4fd800b3a8 2011-02-23        kinaba:   int upperBound = 10;
4fd800b3a8 2011-02-23        kinaba:   int N = 1;
4fd800b3a8 2011-02-23        kinaba:   int K = 10;
4fd800b3a8 2011-02-23        kinaba:   double RetVal = 1.0000000000000003E-10;
4fd800b3a8 2011-02-23        kinaba:   return verify_case(RetVal, KthProbableElement().probability(M, lowerBound, upperBound, N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<4>) {
4fd800b3a8 2011-02-23        kinaba:   int M = 4;
4fd800b3a8 2011-02-23        kinaba:   int lowerBound = 61;
4fd800b3a8 2011-02-23        kinaba:   int upperBound = 65;
4fd800b3a8 2011-02-23        kinaba:   int N = 62;
4fd800b3a8 2011-02-23        kinaba:   int K = 3;
4fd800b3a8 2011-02-23        kinaba:   double RetVal = 0.15200000000000002;
4fd800b3a8 2011-02-23        kinaba:   return verify_case(RetVal, KthProbableElement().probability(M, lowerBound, upperBound, N, K)); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
4fd800b3a8 2011-02-23        kinaba: template<>      void Run_<-1>() {}
4fd800b3a8 2011-02-23        kinaba: int main() { Run_<0>(); }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE
4fd800b3a8 2011-02-23        kinaba: