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: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: void gen( vector<int>& X, vector<LL>& R, int n )
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: 	int j = 0;
4fd800b3a8 2011-02-23        kinaba: 	int m = X.size();
4fd800b3a8 2011-02-23        kinaba: 	for(int i=0; i<n; ++i)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		R[i] = X[j];
4fd800b3a8 2011-02-23        kinaba: 		int s = (j+1)%m;
4fd800b3a8 2011-02-23        kinaba: 		X[j] = ( ( X[j] ^ X[s] ) + 13 ) % 49999;
4fd800b3a8 2011-02-23        kinaba: 		j = s;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class RandomFights
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	double expectedNrOfPoints(vector <int> Aseed, vector <int> Bseed, int n)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		vector<LL> A(n), B(n);
4fd800b3a8 2011-02-23        kinaba: 		gen(Aseed, A, n);
4fd800b3a8 2011-02-23        kinaba: 		gen(Bseed, B, n);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		// expected gain by A[i] = sqSum{B[j] | B[j]<A[i]} - sqSum{B[j] | B[j]>A[i]}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		sort(B.begin(), B.end());
4fd800b3a8 2011-02-23        kinaba: 		vector<LL> B2(n);
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<n; ++i) B2[i] = B[i]*B[i];
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		vector<LL> L1(n), R1(n), L2(n), R2(n);
4fd800b3a8 2011-02-23        kinaba: 		partial_sum( B.begin(),   B.end(),   L1.begin()  );
4fd800b3a8 2011-02-23        kinaba: 		partial_sum( B.rbegin(),  B.rend(),  R1.rbegin() );
4fd800b3a8 2011-02-23        kinaba: 		partial_sum( B2.begin(),  B2.end(),  L2.begin()  );
4fd800b3a8 2011-02-23        kinaba: 		partial_sum( B2.rbegin(), B2.rend(), R2.rbegin() );
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		LL e = 0;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<n; ++i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			int j = lower_bound(B.begin(), B.end(), A[i]) - B.begin();
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 			LL ln  = j;
4fd800b3a8 2011-02-23        kinaba: 			LL ls  = (j==0 ? 0 : L1[j-1]);
4fd800b3a8 2011-02-23        kinaba: 			LL ls2 = (j==0 ? 0 : L2[j-1]);
4fd800b3a8 2011-02-23        kinaba: 			LL rn  = n-j;
4fd800b3a8 2011-02-23        kinaba: 			LL rs  = (j==n ? 0 : R1[j]);
4fd800b3a8 2011-02-23        kinaba: 			LL rs2 = (j==n ? 0 : R2[j]);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 			e += (ls2-rs2) - 2*A[i]*(ls-rs) + (ln-rn)*A[i]*A[i];
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return double(e) / n;
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 A_[] = {6};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
4fd800b3a8 2011-02-23        kinaba: 	int B_[] = {4};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
4fd800b3a8 2011-02-23        kinaba: 	int n = 1;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 4.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, RandomFights().expectedNrOfPoints(A, B, n)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<1>) {
4fd800b3a8 2011-02-23        kinaba: 	int A_[] = {1,7};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
4fd800b3a8 2011-02-23        kinaba: 	int B_[] = {3,5};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
4fd800b3a8 2011-02-23        kinaba: 	int n = 2;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 0.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, RandomFights().expectedNrOfPoints(A, B, n)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<2>) {
4fd800b3a8 2011-02-23        kinaba: 	int A_[] = {3,7};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
4fd800b3a8 2011-02-23        kinaba: 	int B_[] = {1,5};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
4fd800b3a8 2011-02-23        kinaba: 	int n = 2;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 20.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, RandomFights().expectedNrOfPoints(A, B, n)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<3>) {
4fd800b3a8 2011-02-23        kinaba: 	int A_[] = {45,35,236,2342,5543,21,32,2,6,23,24,23,41,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
4fd800b3a8 2011-02-23        kinaba: 	int B_[] = {2345,45,2345,345};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
4fd800b3a8 2011-02-23        kinaba: 	int n = 50;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 1.2721986164E8;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, RandomFights().expectedNrOfPoints(A, B, n)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<4>) {
4fd800b3a8 2011-02-23        kinaba: 	int A_[] = {34,3245,2534,53,53,46,346,246,346,2,624,624,6,245,6324,6542,624,6};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
4fd800b3a8 2011-02-23        kinaba: 	int B_[] = {345,234,523,4624,6,2456,345,634,634,7,3457,376,34,6234,62,523,52,35,32};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
4fd800b3a8 2011-02-23        kinaba: 	int n = 7;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = -9713701.714285715;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, RandomFights().expectedNrOfPoints(A, B, n)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<5>) {
4fd800b3a8 2011-02-23        kinaba: 	int A_[] = {1,2,3,4};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> A(A_, A_+sizeof(A_)/sizeof(*A_));
4fd800b3a8 2011-02-23        kinaba: 	int B_[] = {1,2,3,4};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> B(B_, B_+sizeof(B_)/sizeof(*B_));
4fd800b3a8 2011-02-23        kinaba: 	int n = 50000;
4fd800b3a8 2011-02-23        kinaba: 	double RetVal = 0.0;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, RandomFights().expectedNrOfPoints(A, B, n)); }
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: