#include #ifndef DASSERT_H_ #define DASSERT_H_ #if DEBUG #define dassert(x) assert(x) #else #define dassert(x) ((void)0) #endif #endif // DASSERT_H_ using Float = long double; struct Point { Float x = 0, y = 0; Float Norm() const { return std::sqrt(x * x + y * y); } Point Conj() const { return {x, -y}; } Float Real() const { return x; } Float Imag() const { return y; } Float Arg() const { return std::atan2(Imag(), Real()); } Point& operator+=(const Point& p) { this->x += p.x; this->y += p.y; return *this; } Point operator+(const Point& p) const { return Point(*this) += p; } Point& operator-=(const Point& p) { this->x -= p.x; this->y -= p.y; return *this; } Point operator-(const Point& p) const { return Point(*this) -= p; } Point operator-() const { return {-x, -y}; } Point& operator*=(Float t) { this->x *= t; this->y *= t; return *this; } Point operator*(Float t) const { return Point(*this) *= t; } Point& operator*=(const Point& p) { Float r = x * p.x - y * p.y; Float i = x * p.y + y * p.x; this->x = r; this->y = i; return *this; } Point operator*(const Point& p) const { return Point(*this) *= p; } Point& operator/=(Float t) { this->x /= t; this->y /= t; return *this; } Point operator/(Float t) const { return Point(*this) /= t; } Point& operator/=(const Point& p) { Float q = p.x * p.x + p.y * p.y; dassert(q != 0); Float r = x * p.x + y * p.y; Float i = x * p.y - y * p.x; this->x = r; this->y = i; return *this; } Point operator/(const Point& p) const { return Point(*this) /= p; } bool operator<(const Point& p) const { if (x != p.x) { return x < p.x; } return y < p.y; } Point Rot90() const { return {-y, x}; } static Point Polar(Float r, Float theta) { return Point{cos(theta), sin(theta)} *= r; } }; Float Cross(const Point& p, const Point& q) { return p.x * q.y - p.y * q.x; } std::istream& operator>>(std::istream& is, Point& p) { is >> p.x >> p.y; return is; } std::ostream& operator<<(std::ostream& os, const Point& p) { os << "(" << p.x << "," << p.y << ")"; return os; } struct LineSegment { Point p, q; }; struct Line { Point p, q; }; std::ostream& operator<<(std::ostream& os, const Line& l) { os << "(" << l.p << "," << l.q << ")"; return os; } int Sign(Float x) { const Float eps = 1e-9L; if (x < -eps) return -1; if (x > eps) return 1; return 0; } bool Intersect(const LineSegment& s, const LineSegment& t) { return Sign(Cross(s.q - s.p, t.p - s.p) * Cross(s.q - s.p, t.q - s.p)) <= 0 && Sign(Cross(t.q - t.p, s.p - t.p) * Cross(t.q - t.p, s.q - t.p)) <= 0; } bool Intersect(const Line& l, const Point& p) { return Sign(Cross(l.p - p, l.q - p)) == 0; }; struct Circle { Point center; Float radius; std::vector Intersections(const Circle& c) const { // TODO: Handle cases where there is no intersection and there is only one // intersection. auto sq = [](Float x) -> Float { return x * x; }; Point p = c.center - center; Float l = p.Norm(); if (l >= radius + c.radius || (l + radius) <= c.radius || (l + c.radius) <= radius) { return {}; } Float x = (sq(radius) - sq(c.radius) + sq(l)) / (2 * l); Float a = std::sqrt(sq(radius) - sq(x)); Point perpendicular_foot = p * (x / l); Point perpendicular = p.Rot90() * (a / l); return {center + perpendicular_foot + perpendicular, center + perpendicular_foot - perpendicular}; } // TODO: Add Contains method that checks if a point is contained in the // circle. That function should use EPS on check to take into account the // computation error. Proabbly this library should also provide a commom EPS // value (or provide utility functions that uses EPS inside of it). }; const Float pi = 3.141592653589793238462643383279502884L; #ifndef CONSTANTS_H_ #define CONSTANTS_H_ // big = 2305843009213693951 = 2^61-1 ~= 2.3*10^18 const int64_t big = std::numeric_limits::max() / 4; #endif // CONSTANTS_H_ #ifndef DEBUG_H_ #define DEBUG_H_ #ifndef TYPE_TRAITS_H_ #define TYPE_TRAITS_H_ template struct is_dereferenceable : std::false_type {}; template struct is_dereferenceable())>> : std::true_type {}; template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type {}; template struct is_applicable : std::false_type {}; template struct is_applicable::value)>> : std::true_type {}; #endif // TYPE_TRAITS_H template void debug(std::ostream& os, const T& value, const Ts&... args); template void debug(std::ostream& os, const T& v) { if constexpr (std::is_same>::value) { if (v == big) { os << "big"; } else { os << v; } } else if constexpr (std::is_same>::value || std::is_same::value) { os << v; } else if constexpr (is_dereferenceable::value) { os << "{"; if (v) { debug(os, *v); } else { os << "nil"; } os << "}"; } else if constexpr (is_iterable::value) { os << "{"; for (auto it = std::begin(v); it != std::end(v); ++it) { if (it != std::begin(v)) os << ", "; debug(os, *it); } os << "}"; } else if constexpr (is_applicable::value) { os << "{"; std::apply([&os](const auto&... args) { debug(os, args...); }, v); os << "}"; } else { os << v; } } template void debug(std::ostream& os, const T& value, const Ts&... args) { debug(os, value); os << ", "; debug(os, args...); } #if DEBUG #define dbg(...) \ do { \ std::cerr << #__VA_ARGS__ << ": "; \ debug(std::cerr, __VA_ARGS__); \ std::cerr << " (L" << __LINE__ << ")\n"; \ } while (0) #else #define dbg(...) #endif #endif // DEBUG_H_ #ifndef FIX_H_ #define FIX_H_ template struct FixPoint { F f; template decltype(auto) operator()(Args&&... args) const { return f(std::ref(*this), std::forward(args)...); } }; template FixPoint> Fix(F&& f) { return {std::forward(f)}; } #endif // FIX_H_ #ifndef IO_H_ #define IO_H void read_from_cin() {} template void read_from_cin(T& value, Ts&... args) { std::cin >> value; read_from_cin(args...); } #define rd(type, ...) \ type __VA_ARGS__; \ read_from_cin(__VA_ARGS__); #define ints(...) rd(int, __VA_ARGS__); #define strings(...) rd(string, __VA_ARGS__); const char *yes_str = "Yes", *no_str = "No"; template void write_to_cout(const T& value) { if constexpr (std::is_same::value) { std::cout << (value ? yes_str : no_str); } else if constexpr (is_iterable::value && !std::is_same::value) { for (auto it = std::begin(value); it != std::end(value); ++it) { if (it != std::begin(value)) std::cout << " "; std::cout << *it; } } else { std::cout << value; } } template void write_to_cout(const T& value, const Ts&... args) { write_to_cout(value); std::cout << ' '; write_to_cout(args...); } #define wt(...) \ do { \ write_to_cout(__VA_ARGS__); \ cout << '\n'; \ } while (0) template std::istream& operator>>(std::istream& is, std::vector& v) { for (T& vi : v) is >> vi; return is; } template std::istream& operator>>(std::istream& is, std::pair& p) { is >> p.first >> p.second; return is; } #endif // IO_H_ #ifndef MACROS_H_ #define MACROS_H_ #define all(x) (x).begin(), (x).end() #define eb(...) emplace_back(__VA_ARGS__) #define pb(...) push_back(__VA_ARGS__) #define dispatch(_1, _2, _3, name, ...) name #define as_i64(x) \ ( \ [] { \ static_assert( \ std::is_integral< \ typename std::remove_reference::type>::value, \ "rep macro supports std integral types only"); \ }, \ static_cast(x)) #define rep3(i, a, b) for (int64_t i = as_i64(a); i < as_i64(b); ++i) #define rep2(i, n) rep3(i, 0, n) #define rep1(n) rep2(_loop_variable_, n) #define rep(...) dispatch(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__) #define rrep3(i, a, b) for (int64_t i = as_i64(b) - 1; i >= as_i64(a); --i) #define rrep2(i, n) rrep3(i, 0, n) #define rrep1(n) rrep2(_loop_variable_, n) #define rrep(...) dispatch(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__) #define each3(k, v, c) for (auto&& [k, v] : c) #define each2(e, c) for (auto&& e : c) #define each(...) dispatch(__VA_ARGS__, each3, each2)(__VA_ARGS__) template bool chmax(T& a, U b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, U b) { if (a > b) { a = b; return true; } return false; } template auto max(T a, U b) { return a > b ? a : b; } template auto min(T a, U b) { return a < b ? a : b; } template auto max(const T& v) { return *std::max_element(v.begin(), v.end()); } template auto min(const T& v) { return *std::min_element(v.begin(), v.end()); } template int64_t sz(const T& v) { return std::size(v); } template int64_t popcount(T i) { return std::bitset::digits>(i).count(); } template bool hasbit(T s, int i) { return std::bitset::digits>(s)[i]; } template auto div_floor(T n, U d) { if (d < 0) { n = -n; d = -d; } if (n < 0) { return -((-n + d - 1) / d); } return n / d; }; template auto div_ceil(T n, U d) { if (d < 0) { n = -n; d = -d; } if (n < 0) { return -(-n / d); } return (n + d - 1) / d; } template bool even(T x) { return x % 2 == 0; } std::array, 4> adjacent(int64_t i, int64_t j) { return {{{i + 1, j}, {i, j + 1}, {i - 1, j}, {i, j - 1}}}; } bool inside(int64_t i, int64_t j, int64_t I, int64_t J) { return 0 <= i && i < I && 0 <= j && j < J; } template void sort(T& v) { return std::sort(v.begin(), v.end()); } template void sort(T& v, Compare comp) { return std::sort(v.begin(), v.end(), comp); } template void reverse(T& v) { return std::reverse(v.begin(), v.end()); } template typename T::value_type accumulate(const T& v) { return std::accumulate(v.begin(), v.end(), typename T::value_type()); } using i64 = int64_t; using i32 = int32_t; template using low_priority_queue = std::priority_queue, std::greater>; template using V = std::vector; template using VV = V>; #endif // MACROS_H_ void Main(); int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); std::cout << std::fixed << std::setprecision(20); Main(); return 0; } using namespace std; #define int i64 void Main() { ints(n); rd(Point, p); using ld = long double; V r(n); cin >> r; ld sum = accumulate(r); wt([&] { rep(i, n) { ld d = abs(p.Norm() - r[i]); ld e = sum - r[i]; if (d - 1e-6 < e * 2) return true; } return false; }()); }