e16cea6bfe 2012-02-19        kinaba: #include <iostream>
e16cea6bfe 2012-02-19        kinaba: #include <sstream>
e16cea6bfe 2012-02-19        kinaba: #include <iomanip>
e16cea6bfe 2012-02-19        kinaba: #include <vector>
e16cea6bfe 2012-02-19        kinaba: #include <string>
e16cea6bfe 2012-02-19        kinaba: #include <map>
e16cea6bfe 2012-02-19        kinaba: #include <set>
e16cea6bfe 2012-02-19        kinaba: #include <algorithm>
e16cea6bfe 2012-02-19        kinaba: #include <numeric>
e16cea6bfe 2012-02-19        kinaba: #include <iterator>
e16cea6bfe 2012-02-19        kinaba: #include <functional>
e16cea6bfe 2012-02-19        kinaba: #include <complex>
e16cea6bfe 2012-02-19        kinaba: #include <queue>
e16cea6bfe 2012-02-19        kinaba: #include <stack>
e16cea6bfe 2012-02-19        kinaba: #include <cmath>
e16cea6bfe 2012-02-19        kinaba: #include <cassert>
e16cea6bfe 2012-02-19        kinaba: #include <cstring>
e16cea6bfe 2012-02-19        kinaba: #ifdef __GNUC__
e16cea6bfe 2012-02-19        kinaba: #include <ext/hash_map>
e16cea6bfe 2012-02-19        kinaba: #define unordered_map __gnu_cxx::hash_map
e16cea6bfe 2012-02-19        kinaba: #else
e16cea6bfe 2012-02-19        kinaba: #include <unordered_map>
e16cea6bfe 2012-02-19        kinaba: #endif
e16cea6bfe 2012-02-19        kinaba: using namespace std;
e16cea6bfe 2012-02-19        kinaba: typedef long long LL;
e16cea6bfe 2012-02-19        kinaba: typedef complex<double> CMP;
e16cea6bfe 2012-02-19        kinaba: 
e16cea6bfe 2012-02-19        kinaba: template<typename T>
e16cea6bfe 2012-02-19        kinaba: struct DP2
e16cea6bfe 2012-02-19        kinaba: {
e16cea6bfe 2012-02-19        kinaba: 	const int N1, N2;
e16cea6bfe 2012-02-19        kinaba: 	vector<T> data;
e16cea6bfe 2012-02-19        kinaba: 	DP2(int N1, int N2, const T& t = T())
e16cea6bfe 2012-02-19        kinaba: 		: N1(N1), N2(N2), data(N1*N2, t) { assert(data.size()*sizeof(T)<(1<<26)); }
e16cea6bfe 2012-02-19        kinaba: 	T& operator()(int i1, int i2)
e16cea6bfe 2012-02-19        kinaba: 		{ return data[ (i1*N2)+i2 ]; }
e16cea6bfe 2012-02-19        kinaba: 	void swap(DP2& rhs)
e16cea6bfe 2012-02-19        kinaba: 		{ data.swap(rhs.data); }
e16cea6bfe 2012-02-19        kinaba: };
e16cea6bfe 2012-02-19        kinaba: 
e16cea6bfe 2012-02-19        kinaba: class MagicalGirl { public:
e16cea6bfe 2012-02-19        kinaba: 	double maxExpectation(int M, vector <int> day, vector <int> win, vector <int> gain)
e16cea6bfe 2012-02-19        kinaba: 	{
e16cea6bfe 2012-02-19        kinaba: 		vector< pair< int, pair<double, int> > > majos;
e16cea6bfe 2012-02-19        kinaba: 		for(int i=0; i<day.size(); ++i)
e16cea6bfe 2012-02-19        kinaba: 			majos.push_back( make_pair(day[i], make_pair(win[i]/100.0, gain[i])) );
e16cea6bfe 2012-02-19        kinaba: 		sort(majos.begin(), majos.end());
e16cea6bfe 2012-02-19        kinaba: 
e16cea6bfe 2012-02-19        kinaba: 		DP2<double> dp(day.size()+1, M+1);
e16cea6bfe 2012-02-19        kinaba: 		for(int i=majos.size(); i>=0; --i)
e16cea6bfe 2012-02-19        kinaba: 		for(int hp=0; hp<=M; ++hp)
e16cea6bfe 2012-02-19        kinaba: 		{
e16cea6bfe 2012-02-19        kinaba: 			// Days passed from the last Witch's attack.
e16cea6bfe 2012-02-19        kinaba: 			const int days = i==majos.size() ? INT_MAX
e16cea6bfe 2012-02-19        kinaba: 			                                 : majos[i].first - (i==0 ? 0 : majos[i-1].first);
e16cea6bfe 2012-02-19        kinaba: 			if( hp <= days )
e16cea6bfe 2012-02-19        kinaba: 				dp(i, hp) = hp; // no way to gain power any more...
e16cea6bfe 2012-02-19        kinaba: 			else {
e16cea6bfe 2012-02-19        kinaba: 				const double pWin = majos[i].second.first;
e16cea6bfe 2012-02-19        kinaba: 				const int gain = majos[i].second.second;
e16cea6bfe 2012-02-19        kinaba: 				dp(i, hp) = days + max(pWin*dp(i+1, min(M, hp-days+gain)), // fight or
e16cea6bfe 2012-02-19        kinaba: 				                       dp(i+1, min(M, hp-days))); // skip
e16cea6bfe 2012-02-19        kinaba: 			}
e16cea6bfe 2012-02-19        kinaba: 		}
e16cea6bfe 2012-02-19        kinaba: 		return dp(0, M);
e16cea6bfe 2012-02-19        kinaba: 	}
e16cea6bfe 2012-02-19        kinaba: };
e16cea6bfe 2012-02-19        kinaba: 
e16cea6bfe 2012-02-19        kinaba: // BEGIN CUT HERE
e16cea6bfe 2012-02-19        kinaba: #include <ctime>
e16cea6bfe 2012-02-19        kinaba: double start_time; string timer()
e16cea6bfe 2012-02-19        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
e16cea6bfe 2012-02-19        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
e16cea6bfe 2012-02-19        kinaba:  { os << "{ ";
e16cea6bfe 2012-02-19        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
e16cea6bfe 2012-02-19        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
e16cea6bfe 2012-02-19        kinaba: void verify_case(const double& Expected, const double& Received) {
e16cea6bfe 2012-02-19        kinaba:  bool ok = (abs(Expected - Received) < 1e-9);
e16cea6bfe 2012-02-19        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
e16cea6bfe 2012-02-19        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
e16cea6bfe 2012-02-19        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
e16cea6bfe 2012-02-19        kinaba: #define END	 verify_case(_, MagicalGirl().maxExpectation(M, day, win, gain));}
e16cea6bfe 2012-02-19        kinaba: int main(){
e16cea6bfe 2012-02-19        kinaba: 
e16cea6bfe 2012-02-19        kinaba: CASE(0)
e16cea6bfe 2012-02-19        kinaba: 	int M = 2;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {1};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {75};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {1};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 2.5;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(1)
e16cea6bfe 2012-02-19        kinaba: 	int M = 10;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {5,5,5,5};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {100,100,100,100};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {1,1,1,1};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 14.0;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(2)
e16cea6bfe 2012-02-19        kinaba: 	int M = 10;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {5,5,5,5,5};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {40,80,60,20,0};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {10,10,10,10,10};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 13.0;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(3)
e16cea6bfe 2012-02-19        kinaba: 	int M = 2;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {2};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {100};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {2};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 2.0;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(4)
e16cea6bfe 2012-02-19        kinaba: 	int M = 20;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {2,13,8,7,9,4,6,21};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {18,83,75,23,45,23,10,98};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {10,9,8,10,7,16,13,20};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 35.908;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(5)
e16cea6bfe 2012-02-19        kinaba: 	int M = 11;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {10,20,30,40,50,60,70,80,90};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {100,100,100,100,100,100,100,100,100};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {10,10,10,10,10,10,10,10,10};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 101.0;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(6)
e16cea6bfe 2012-02-19        kinaba: 	int M = 100000;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = {1000000};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = {100};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = {100000};
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = 100000.0;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: /*
e16cea6bfe 2012-02-19        kinaba: CASE(7)
e16cea6bfe 2012-02-19        kinaba: 	int M = ;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = ;
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = ;
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = ;
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = ;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: CASE(8)
e16cea6bfe 2012-02-19        kinaba: 	int M = ;
e16cea6bfe 2012-02-19        kinaba: 	int day_[] = ;
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> day(day_, day_+sizeof(day_)/sizeof(*day_));
e16cea6bfe 2012-02-19        kinaba: 	int win_[] = ;
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> win(win_, win_+sizeof(win_)/sizeof(*win_));
e16cea6bfe 2012-02-19        kinaba: 	int gain_[] = ;
e16cea6bfe 2012-02-19        kinaba: 	  vector <int> gain(gain_, gain_+sizeof(gain_)/sizeof(*gain_));
e16cea6bfe 2012-02-19        kinaba: 	double _ = ;
e16cea6bfe 2012-02-19        kinaba: END
e16cea6bfe 2012-02-19        kinaba: */
e16cea6bfe 2012-02-19        kinaba: }
e16cea6bfe 2012-02-19        kinaba: // END CUT HERE