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View the Project on GitHub Luzhiled/comp-geometry
#include "src/real-geometry/point-cloud/closest-pair.hpp"
#pragma once #include "src/real-geometry/class/point.hpp" #include "src/real-geometry/compare/compare-x.hpp" #include "src/real-geometry/compare/compare-y.hpp" #include "src/real-geometry/common/size-alias.hpp" #include "src/real-geometry/utility/sign.hpp" #include <algorithm> #include <cmath> #include <complex> #include <iterator> #include <limits> #include <utility> namespace geometry::internal { template< typename R > using closest_pair_result_t = std::pair< R, std::pair<point<R>, point<R> > >; // WARNING: pts are sorted by y after calling this function template< typename R > closest_pair_result_t<R> impl_closest_pair(points<R> &pts, usize l, usize r) { constexpr R inf = std::numeric_limits< R >::infinity(); using result_t = closest_pair_result_t<R>; auto comp = [](const result_t &lhs, const result_t &rhs) { return lhs.first < rhs.first; }; if (r - l <= 1) { return {inf, {}}; } usize m = (l + r) / 2; R x = pts[m].x(); result_t result = std::min(impl_closest_pair(pts, l, m), impl_closest_pair(pts, m, r), comp); auto f = pts.begin(); std::inplace_merge(f + l, f + m, f + r, compare_y<R>); points<R> ps; for (usize i = l; i < r; i++) { if (sign(std::abs(pts[i].x() - x) - result.first) >= 0) continue; for (usize j = 0; j < ps.size(); j++) { R dy = pts[i].y() - (*std::next(ps.rbegin(), j)).y(); if (sign(dy - result.first) >= 0) break; auto &u = pts[i]; auto &v = *std::next(ps.rbegin(), j); result = std::min(result, {std::abs(u - v), std::make_pair(u, v)}, comp); } ps.emplace_back(pts[i]); } return result; } } namespace geometry { template< typename R > internal::closest_pair_result_t<R> closest_pair(points<R> pts) { constexpr R inf = std::numeric_limits< R >::infinity(); if (pts.size() <= 1) { return {inf, {}}; } std::sort(pts.begin(), pts.end(), compare_x<R>); return internal::impl_closest_pair(pts, 0, pts.size()); } }
#line 2 "src/real-geometry/point-cloud/closest-pair.hpp" #line 2 "src/real-geometry/class/point.hpp" #line 2 "src/real-geometry/class/vector.hpp" #include <complex> #include <iostream> namespace geometry { template< typename R > class vec2d : public std::complex< R > { using complex = std::complex< R >; public: using complex::complex; vec2d(const complex &c): complex::complex(c) {} const R x() const { return this->real(); } const R y() const { return this->imag(); } friend vec2d operator*(const vec2d &v, const R &k) { return vec2d(v.x() * k, v.y() * k); } friend vec2d operator*(const R &k, const vec2d &v) { return vec2d(v.x() * k, v.y() * k); } friend std::istream &operator>>(std::istream &is, vec2d &v) { R x, y; is >> x >> y; v = vec2d(x, y); return is; } }; } #line 4 "src/real-geometry/class/point.hpp" #include <vector> namespace geometry { template< typename R > using point = vec2d<R>; template< typename R > using points = std::vector< point< R > >; } #line 2 "src/real-geometry/compare/compare-x.hpp" #line 2 "src/real-geometry/utility/equals/real-number.hpp" #line 2 "src/real-geometry/utility/sign.hpp" #line 2 "src/real-geometry/common/const/eps.hpp" #line 2 "src/real-geometry/common/float-alias.hpp" namespace geometry { using f80 = long double; using f64 = double; } #line 4 "src/real-geometry/common/const/eps.hpp" namespace geometry { inline static f80 &eps() { static f80 EPS = 1e-10; return EPS; } void set_eps(f80 EPS) { eps() = EPS; } } #line 2 "src/real-geometry/numbers/sign.hpp" #line 2 "src/real-geometry/common/int-alias.hpp" namespace geometry { using i32 = int; using i64 = long long; } #line 4 "src/real-geometry/numbers/sign.hpp" namespace geometry::number::sign { constexpr i32 PLUS = +1; constexpr i32 ZERO = 0; constexpr i32 MINUS = -1; } #line 5 "src/real-geometry/utility/sign.hpp" namespace geometry { using namespace geometry::number::sign; template< typename R > inline int sign(R r) { if (r < -eps()) return MINUS; if (r > +eps()) return PLUS; return ZERO; } } #line 4 "src/real-geometry/utility/equals/real-number.hpp" namespace geometry { template< typename R > bool equals(R a, R b) { return sign(a - b) == 0; } } #line 5 "src/real-geometry/compare/compare-x.hpp" namespace geometry { template< typename R > bool compare_x(const point<R> &a, const point<R> &b) { return not equals(a.x(), b.x()) ? a.x() < b.x() : a.y() < b.y(); } } #line 2 "src/real-geometry/compare/compare-y.hpp" #line 5 "src/real-geometry/compare/compare-y.hpp" namespace geometry { template< typename R > bool compare_y(const point<R> &a, const point<R> &b) { return not equals(a.y(), b.y()) ? a.y() < b.y() : a.x() < b.x(); } } #line 2 "src/real-geometry/common/size-alias.hpp" #include <cstddef> namespace geometry { using isize = std::ptrdiff_t; using usize = std::size_t; } #line 8 "src/real-geometry/point-cloud/closest-pair.hpp" #include <algorithm> #include <cmath> #line 12 "src/real-geometry/point-cloud/closest-pair.hpp" #include <iterator> #include <limits> #include <utility> namespace geometry::internal { template< typename R > using closest_pair_result_t = std::pair< R, std::pair<point<R>, point<R> > >; // WARNING: pts are sorted by y after calling this function template< typename R > closest_pair_result_t<R> impl_closest_pair(points<R> &pts, usize l, usize r) { constexpr R inf = std::numeric_limits< R >::infinity(); using result_t = closest_pair_result_t<R>; auto comp = [](const result_t &lhs, const result_t &rhs) { return lhs.first < rhs.first; }; if (r - l <= 1) { return {inf, {}}; } usize m = (l + r) / 2; R x = pts[m].x(); result_t result = std::min(impl_closest_pair(pts, l, m), impl_closest_pair(pts, m, r), comp); auto f = pts.begin(); std::inplace_merge(f + l, f + m, f + r, compare_y<R>); points<R> ps; for (usize i = l; i < r; i++) { if (sign(std::abs(pts[i].x() - x) - result.first) >= 0) continue; for (usize j = 0; j < ps.size(); j++) { R dy = pts[i].y() - (*std::next(ps.rbegin(), j)).y(); if (sign(dy - result.first) >= 0) break; auto &u = pts[i]; auto &v = *std::next(ps.rbegin(), j); result = std::min(result, {std::abs(u - v), std::make_pair(u, v)}, comp); } ps.emplace_back(pts[i]); } return result; } } namespace geometry { template< typename R > internal::closest_pair_result_t<R> closest_pair(points<R> pts) { constexpr R inf = std::numeric_limits< R >::infinity(); if (pts.size() <= 1) { return {inf, {}}; } std::sort(pts.begin(), pts.end(), compare_x<R>); return internal::impl_closest_pair(pts, 0, pts.size()); } }