#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 <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class RadioRange { public:
double RadiusProbability(vector <int> X, vector <int> Y, vector <int> R, int Z)
{
vector<pair<double, bool>> ev;
const int N = X.size();
for(int i=0; i<N; ++i)
{
double x = X[i];
double y = Y[i];
double r = R[i];
double d = sqrt(x*x+y*y);
// (s,e) is bad
double s = max(0.0, d-r);
double e = min(double(Z), d+r);
ev.emplace_back(s, true);
ev.emplace_back(e, false);
}
double total_bad = 0.0;
sort(ev.begin(), ev.end());
int nest = 0;
double prev_beg;
for(auto ei: ev) {
double x = ei.first;
bool beg = ei.second;
if(beg) {
if(++nest == 1)
prev_beg = x;
}
else {
if(--nest == 0)
total_bad += (x-prev_beg);
}
}
return (Z - total_bad) / Z;
}
};
// 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(_, RadioRange().RadiusProbability(X, Y, R, Z));}
int main(){
CASE(0)
int X_[] = {0};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {0};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {5};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 10;
double _ = 0.5;
END
CASE(1)
int X_[] = {0};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {0};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {10};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 10;
double _ = 0.0;
END
CASE(2)
int X_[] = {10};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {10};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {10};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 10;
double _ = 0.4142135623730951;
END
CASE(3)
int X_[] = {11, -11, 0, 0};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {0, 0, 11, -11};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {10, 10, 10, 10};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 31;
double _ = 0.3548387096774194;
END
CASE(4)
int X_[] = {100};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {100};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {1};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 10;
double _ = 1.0;
END
CASE(5)
int X_[] = {1000000000};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {1000000000};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {1000000000};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 1000000000;
double _ = 0.41421356237309503;
END
CASE(6)
int X_[] = {20, -20, 0, 0};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {0, 0, 20, -20};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {50, 50, 50, 50};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 100;
double _ = 0.3;
END
CASE(7)
int X_[] = {0, -60, -62, -60, 63, -97};
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = {-72, 67, 61, -8, -32, 89};
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = {6, 7, 8, 7, 5, 6};
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = 918;
double _ = 0.9407071068962471;
END
/*
CASE(8)
int X_[] = ;
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = ;
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = ;
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = ;
double _ = ;
END
CASE(9)
int X_[] = ;
vector <int> X(X_, X_+sizeof(X_)/sizeof(*X_));
int Y_[] = ;
vector <int> Y(Y_, Y_+sizeof(Y_)/sizeof(*Y_));
int R_[] = ;
vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
int Z = ;
double _ = ;
END
*/
}
// END CUT HERE