test/aoj/icpc/2442.test.cpp

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Last update: 2023-06-05 11:13:22+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/problems/2442

Depends on

Code

// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2442
// verification-helper: ERROR 0.0001

#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/class/segment.hpp"
#include "src/real-geometry/position/is-parallel.hpp"

#include <iostream>
#include <cstdlib>

using namespace geometry;

void drop() {
  std::cout << "NA" << std::endl;
  exit(0);
}

int main() {
  using R = long double;

  int n;
  std::cin >> n;

  if (n & 1) drop();

  points<R> ps(n);
  for (auto &p : ps) {
    std::cin >> p;
  }

  segments<R> ss;
  for (int i = 0; i < n; i++) {
    ss.emplace_back(ps[i], ps[(i + 1) % n]);
  }

  for (int i = 0; i < n; i++) {
    int j = (i + n / 2) % n;
    if (is_parallel<R>({ss[i].a, ss[i].b}, {ss[j].a, ss[j].b}) == false) {
      drop();
    }

    if (equals(std::abs(ss[i].a - ss[i].b), std::abs(ss[j].a - ss[j].b)) == false) {
      drop();
    }
  }

  point<R> ans{ps[0] + ps[n / 2]};
  ans *= 0.5;
  std::cout << ans.x() << " " << ans.y() << std::endl;
}

#line 1 "test/aoj/icpc/2442.test.cpp"
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2442
// verification-helper: ERROR 0.0001

#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/class/segment.hpp"

#line 2 "src/real-geometry/utility/equals/vector.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/utility/equals/vector.hpp"

namespace geometry {

  template< typename R >
  bool equals(const vec2d<R> &a, const vec2d<R> &b) {
    return equals(a.x(), b.x()) and equals(a.y(), b.y());
  }

}
#line 5 "src/real-geometry/class/segment.hpp"

#include <cassert>
#line 8 "src/real-geometry/class/segment.hpp"

namespace geometry {

  template< typename R >
  class segment {
   public:
    point<R> a, b;

    segment() = default;
    segment(point<R> a, point<R> b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using segments = std::vector< segment<R> >;

}
#line 2 "src/real-geometry/position/is-parallel.hpp"

#line 2 "src/real-geometry/class/line.hpp"

#line 5 "src/real-geometry/class/line.hpp"

#line 8 "src/real-geometry/class/line.hpp"

namespace geometry {

  template< typename R >
  class line {
    using P = point<R>;

   public:
    P a, b;

    line() = default;
    line(P a, P b) : a(a), b(b) {
      assert(not equals(a, b));
    }

  };

  template< typename R >
  using lines = std::vector< line<R> >;

}
#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 6 "src/real-geometry/position/is-parallel.hpp"

// parallel
namespace geometry {

  template< typename R >
  bool is_parallel(const line<R> &l1, const line<R> &l2) {
    return equals<R>(cross_product<R>(l1.b - l1.a, l2.b - l2.a), 0);
  }

}
#line 7 "test/aoj/icpc/2442.test.cpp"

#line 9 "test/aoj/icpc/2442.test.cpp"
#include <cstdlib>

using namespace geometry;

void drop() {
  std::cout << "NA" << std::endl;
  exit(0);
}

int main() {
  using R = long double;

  int n;
  std::cin >> n;

  if (n & 1) drop();

  points<R> ps(n);
  for (auto &p : ps) {
    std::cin >> p;
  }

  segments<R> ss;
  for (int i = 0; i < n; i++) {
    ss.emplace_back(ps[i], ps[(i + 1) % n]);
  }

  for (int i = 0; i < n; i++) {
    int j = (i + n / 2) % n;
    if (is_parallel<R>({ss[i].a, ss[i].b}, {ss[j].a, ss[j].b}) == false) {
      drop();
    }

    if (equals(std::abs(ss[i].a - ss[i].b), std::abs(ss[j].a - ss[j].b)) == false) {
      drop();
    }
  }

  point<R> ans{ps[0] + ps[n / 2]};
  ans *= 0.5;
  std::cout << ans.x() << " " << ans.y() << std::endl;
}