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