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 AlternatingLane { public:
4fd800b3a8 2011-02-23        kinaba: 	double expectedBeauty(vector <int> low, vector <int> high)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		double eSum = 0.0;
4fd800b3a8 2011-02-23        kinaba: 		for(int i=1; i<low.size(); ++i)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			// ランダムに
4fd800b3a8 2011-02-23        kinaba: 			//   h ∈ [low[i-1], high[i-1]]
4fd800b3a8 2011-02-23        kinaba: 			//   g ∈ [low[i],   high[i]  ]
4fd800b3a8 2011-02-23        kinaba: 			// を取ってきたときの、|h-g| の期待値…
4fd800b3a8 2011-02-23        kinaba: 			double e = 0;
4fd800b3a8 2011-02-23        kinaba: 			for(int h=low[i-1]; h<=high[i-1]; ++h)
4fd800b3a8 2011-02-23        kinaba: 				if( h <= low[i] )
4fd800b3a8 2011-02-23        kinaba: 					e += sequenceSum(low[i]-h, high[i]-h);
4fd800b3a8 2011-02-23        kinaba: 				else if( high[i] <= h )
4fd800b3a8 2011-02-23        kinaba: 					e += sequenceSum(h-high[i], h-low[i]);
4fd800b3a8 2011-02-23        kinaba: 				else
4fd800b3a8 2011-02-23        kinaba: 					e += sequenceSum(0, h-low[i]) + sequenceSum(0, high[i]-h);
4fd800b3a8 2011-02-23        kinaba: 			eSum += e / (high[i]-low[i]+1) / (high[i-1]-low[i-1]+1);
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return eSum; // …の和、が答え
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	LL sequenceSum(LL a, LL b) // a+(a+1)+...+b
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		return (a+b) * (b-a+1) / 2;
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(_, AlternatingLane().expectedBeauty(low, high));}
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 low_[] = {1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> low(low_, low_+sizeof(low_)/sizeof(*low_));
4fd800b3a8 2011-02-23        kinaba: 	int high_[] = {100};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> high(high_, high_+sizeof(high_)/sizeof(*high_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 0.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int low_[] = {1, 1, 1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> low(low_, low_+sizeof(low_)/sizeof(*low_));
4fd800b3a8 2011-02-23        kinaba: 	int high_[] = {2, 2, 2};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> high(high_, high_+sizeof(high_)/sizeof(*high_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 1.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int low_[] = {1, 3, 5, 7, 9};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> low(low_, low_+sizeof(low_)/sizeof(*low_));
4fd800b3a8 2011-02-23        kinaba: 	int high_[] = {2, 4, 6, 8, 10};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> high(high_, high_+sizeof(high_)/sizeof(*high_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 8.0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int low_[] = {4, 3, 3, 7};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> low(low_, low_+sizeof(low_)/sizeof(*low_));
4fd800b3a8 2011-02-23        kinaba: 	int high_[] = {10, 7, 7, 7};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> high(high_, high_+sizeof(high_)/sizeof(*high_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = 6.171428571428572;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: int low_[] = {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> low(low_, low_+sizeof(low_)/sizeof(*low_));
4fd800b3a8 2011-02-23        kinaba: 	  int high_[] = {100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000,100000};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> high(high_, high_+sizeof(high_)/sizeof(*high_));
4fd800b3a8 2011-02-23        kinaba: 	double _ = -1;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: /*
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int low_[] = ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> low(low_, low_+sizeof(low_)/sizeof(*low_));
4fd800b3a8 2011-02-23        kinaba: 	int high_[] = ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> high(high_, high_+sizeof(high_)/sizeof(*high_));
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