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View the Project on GitHub Luzhiled/comp-geometry
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/all/CGL_4_A #include "src/real-geometry/common/size-alias.hpp" #include "src/real-geometry/compare/compare-y.hpp" #include "src/real-geometry/class/point.hpp" #include "src/real-geometry/class/polygon.hpp" #include "src/real-geometry/point-cloud/convex-hull.hpp" #include "src/real-geometry/utility/io-set.hpp" #include <iostream> int main() { using R = long double; using usize = geometry::usize; usize n; std::cin >> n; geometry::points<R> pts(n); for (auto &p: pts) { std::cin >> p; } geometry::polygon<R> poly = geometry::convex_hull(pts); std::cout << poly.size() << std::endl; usize offset = 0; for (usize i = 0; i < poly.size(); i++) { if (geometry::compare_y(poly[i], poly[offset])) { offset = i; } } geometry::IoSetup(0); for (usize i = 0; i < poly.size(); i++) { auto p = poly[(offset + i) % poly.size()]; std::cout << p.x() << " " << p.y() << std::endl; } }
#line 1 "test/aoj/cgl/4_A.test.cpp" // verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/courses/library/4/CGL/all/CGL_4_A #line 2 "src/real-geometry/common/size-alias.hpp" #include <cstddef> namespace geometry { using isize = std::ptrdiff_t; using usize = std::size_t; } #line 2 "src/real-geometry/compare/compare-y.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/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-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/class/polygon.hpp" #line 4 "src/real-geometry/class/polygon.hpp" #line 6 "src/real-geometry/class/polygon.hpp" namespace geometry { template< typename R > using polygon = std::vector< point<R> >; template< typename R > using polygons = std::vector< polygon<R> >; } #line 2 "src/real-geometry/point-cloud/convex-hull.hpp" #line 2 "src/real-geometry/compare/compare-x.hpp" #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/operation/cross-product.hpp" #line 4 "src/real-geometry/operation/cross-product.hpp" namespace geometry { template< typename R > R cross_product(const vec2d<R> &a, const vec2d<R> &b) { return a.x() * b.y() - a.y() * b.x(); } } #line 8 "src/real-geometry/point-cloud/convex-hull.hpp" #include <algorithm> namespace geometry { template< typename R > polygon<R> convex_hull(points<R> pts) { usize n = pts.size(), k = 0; if (n <= 2) return pts; std::sort(pts.begin(), pts.end(), compare_x<R>); polygon<R> res(2 * n); auto check = [&](usize i) { return sign(cross_product<R>(res[k - 1] - res[k - 2], pts[i] - res[k - 1])) == -1; }; for (usize i = 0; i < n; res[k++] = pts[i++]) { while (k >= 2 and check(i)) --k; } usize t = k + 1; for (isize i = n - 2; i >= 0; res[k++] = pts[i--]) { while (k >= t and check(i)) --k; } res.resize(k - 1); return res; } } #line 2 "src/real-geometry/utility/io-set.hpp" #include <iomanip> namespace geometry { class IoSetup { using u32 = unsigned int; void set(std::ostream &os, u32 precision) { os << std::fixed << std::setprecision(precision); } public: IoSetup(u32 precision = 15) { std::cin.tie(0); std::ios::sync_with_stdio(0); set(std::cout, precision); set(std::cerr, precision); } } iosetup; } #line 9 "test/aoj/cgl/4_A.test.cpp" #line 11 "test/aoj/cgl/4_A.test.cpp" int main() { using R = long double; using usize = geometry::usize; usize n; std::cin >> n; geometry::points<R> pts(n); for (auto &p: pts) { std::cin >> p; } geometry::polygon<R> poly = geometry::convex_hull(pts); std::cout << poly.size() << std::endl; usize offset = 0; for (usize i = 0; i < poly.size(); i++) { if (geometry::compare_y(poly[i], poly[offset])) { offset = i; } } geometry::IoSetup(0); for (usize i = 0; i < poly.size(); i++) { auto p = poly[(offset + i) % poly.size()]; std::cout << p.x() << " " << p.y() << std::endl; } }