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#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_5_A" #define ERROR 0.000001 #include <bits/stdc++.h> #include "geometry/closest_pair.hpp" int main() { int N; std::cin >> N; std::vector<Point<double>> P(N); for (int i = 0; i < N; i++) std::cin >> P[i]; auto [i, j, d] = closest_pair(P); assert(equal(d, abs(P[i] - P[j]))); std::cout << std::fixed << std::setprecision(15) << d << '\n'; return 0; }
#line 1 "verify/aoj_cgl/aoj_cgl_5_a.test.cpp" #define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_5_A" #define ERROR 0.000001 #include <bits/stdc++.h> #line 2 "geometry/closest_pair.hpp" #line 2 "geometry/point.hpp" // point template <typename T> struct Point { static T EPS; static constexpr T PI = 3.1415926535'8979323846'2643383279L; static void set_eps(const T &e) { EPS = e; } T x, y; Point(const T x = T(0), const T y = T(0)) : x(x), y(y) {} Point &operator+=(const Point &p) { x += p.x; y += p.y; return *this; } Point &operator-=(const Point &p) { x -= p.x; y -= p.y; return *this; } Point &operator*=(const Point &p) { return *this = Point(x * p.x - y * p.y, x * p.y + y * p.x); } Point &operator*=(const T &k) { x *= k; y *= k; return *this; } Point &operator/=(const Point &p) { return *this = Point(x * p.x + y * p.y, -x * p.y + y * p.x) / (p.x * p.x + p.y * p.y); } Point &operator/=(const T &k) { x /= k; y /= k; return *this; } Point operator+() const { return *this; } Point operator-() const { return Point(-x, -y); } friend Point operator+(const Point &a, const Point &b) { return Point(a) += b; } friend Point operator-(const Point &a, const Point &b) { return Point(a) -= b; } friend Point operator*(const Point &a, const Point &b) { return Point(a) *= b; } friend Point operator*(const Point &p, const T &k) { return Point(p) *= k; } friend Point operator/(const Point &a, const Point &b) { return Point(a) /= b; } friend Point operator/(const Point &p, const T &k) { return Point(p) /= k; } // for std::set, std::map, compare_arg, ... friend bool operator<(const Point &a, const Point &b) { return a.x == b.x ? a.y < b.y : a.x < b.x; } friend bool operator>(const Point &a, const Point &b) { return a.x == b.x ? a.y > b.y : a.x > b.x; } // I/O friend std::istream &operator>>(std::istream &is, Point &p) { return is >> p.x >> p.y; } friend std::ostream &operator<<(std::ostream &os, const Point &p) { return os << '(' << p.x << ' ' << p.y << ')'; } }; // template template <typename T> inline int sign(const T &x) { return x < -Point<T>::EPS ? -1 : (x > Point<T>::EPS ? 1 : 0); } template <typename T> inline bool equal(const T &a, const T &b) { return sign(a - b) == 0; } template <typename T> inline T radian_to_degree(const T &r) { return r * 180.0 / Point<T>::PI; } template <typename T> inline T degree_to_radian(const T &d) { return d * Point<T>::PI / 180.0; } // contain enum constexpr int IN = 2; constexpr int ON = 1; constexpr int OUT = 0; // equal (point and point) template <typename T> inline bool equal(const Point<T> &a, const Point<T> &b) { return equal(a.x, b.x) and equal(a.y, b.y); } // inner product template <typename T> inline T dot(const Point<T> &a, const Point<T> &b) { return a.x * b.x + a.y * b.y; } // outer product template <typename T> inline T cross(const Point<T> &a, const Point<T> &b) { return a.x * b.y - a.y * b.x; } // rotate Point p counterclockwise by theta radian template <typename T> inline Point<T> rotate(const Point<T> &p, const T &theta) { return p * Point<T>(std::cos(theta), std::sin(theta)); } // compare (x, y) template <typename T> inline bool compare_x(const Point<T> &a, const Point<T> &b) { return equal(a.x, b.x) ? sign(a.y - b.y) < 0 : sign(a.x - b.x) < 0; } // compare (y, x) template <typename T> inline bool compare_y(const Point<T> &a, const Point<T> &b) { return equal(a.y, b.y) ? sign(a.x - b.x) < 0 : sign(a.y - b.y) < 0; } // compare by (arg(p), norm(p)) [0, 360) template <typename T> inline bool compare_arg(const Point<T> &a, const Point<T> &b) { // https://ngtkana.hatenablog.com/entry/2021/11/13/202103 assert(!equal(a, Point<T>(0, 0))); assert(!equal(b, Point<T>(0, 0))); if ((Point<T>(0, 0) < Point<T>(a.y, a.x)) == (Point<T>(0, 0) < Point<T>(b.y, b.x))) { return (a.x * b.y == a.y * b.x) ? norm(a) < norm(b) : a.x * b.y > a.y * b.x; } else { return Point<T>(a.y, a.x) > Point<T>(b.y, b.x); } } // |p| ^ 2 template <typename T> inline T norm(const Point<T> &p) { return p.x * p.x + p.y * p.y; } // |p| template <typename T> inline T abs(const Point<T> &p) { return std::sqrt(norm(p)); } // arg template <typename T> inline T arg(const Point<T> &p) { return std::atan2(p.y, p.x); } // polar template <typename T> inline Point<T> polar(const T &rho, const T &theta = T(0)) { return rotate(Point<T>(rho, 0), theta); } // EPS template <> double Point<double>::EPS = 1e-9; template <> long double Point<long double>::EPS = 1e-12; template <> long long Point<long long>::EPS = 0; template <> __int128_t Point<__int128_t>::EPS = 0; // change EPS // using Double = double; // using Pt = Point<Double>; // Point<Double>::set_eps(new_eps); #line 4 "geometry/closest_pair.hpp" // closest pair // http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_5_A // return {index1, index2, distance} // using divide-and-conquer algorithm // complexity: O(n \log n) (n: the number of points) template <typename T> std::tuple<int, int, T> closest_pair(const std::vector<Point<T>> &p) { int n = int(p.size()); assert(n >= 2); if (n == 2) { return {0, 1, abs(p[0] - p[1])}; } // may not be efficient due to indirect references ... std::vector<int> ind(n); std::iota(ind.begin(), ind.end(), 0); std::sort(ind.begin(), ind.end(), [&](int i, int j) { return compare_x(p[i], p[j]); }); auto divide_and_conquer = [&](auto f, int l, int r) -> std::tuple<int, int, T> { if (r - l <= 1) return {-1, -1, std::numeric_limits<T>::max()}; int md = (l + r) / 2; T x = p[ind[md]].x; // divide and conquer auto [i1l, i2l, dl] = f(f, l, md); auto [i1r, i2r, dr] = f(f, md, r); int i1, i2; T d; if (dl < dr) { d = dl, i1 = i1l, i2 = i2l; } else { d = dr, i1 = i1r, i2 = i2r; } std::inplace_merge(ind.begin() + l, ind.begin() + md, ind.begin() + r, [&](int i, int j) { return compare_y(p[i], p[j]); }); // ind are sorted by y std::vector<int> near_x; // index of vertices whose distance from the line x is less than d for (int i = l; i < r; i++) { if (sign(std::abs(p[ind[i]].x - x) - d) >= 0) continue; // std::abs(p[ind[i]].x - x) >= d int sz = int(near_x.size()); // iterate from the end until the distance in y-coordinates is greater than or equal to d for (int j = sz - 1; j >= 0; j--) { Point cp = p[ind[i]] - p[near_x[j]]; if (sign(cp.y - d) >= 0) break; // cp.y >= d T cd = abs(cp); if (cd < d) { d = cd, i1 = ind[i], i2 = near_x[j]; } } near_x.push_back(ind[i]); } return {i1, i2, d}; }; return divide_and_conquer(divide_and_conquer, 0, n); } #line 7 "verify/aoj_cgl/aoj_cgl_5_a.test.cpp" int main() { int N; std::cin >> N; std::vector<Point<double>> P(N); for (int i = 0; i < N; i++) std::cin >> P[i]; auto [i, j, d] = closest_pair(P); assert(equal(d, abs(P[i] - P[j]))); std::cout << std::fixed << std::setprecision(15) << d << '\n'; return 0; }