comp-geometry

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub Luzhiled/comp-geometry

:heavy_check_mark: test/aoj/cgl/4_A.test.cpp

Depends on

Code

// 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;
  }
}
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