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/icpc/3034.test.cpp

Depends on

Code

// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/3034
// verification-helper: ERROR 1e-3

#include "src/real-geometry/class/point.hpp"
#include "src/real-geometry/point-cloud/minimum-covering-circle.hpp"
#include "src/real-geometry/utility/io-set.hpp"

#include <iostream>

using namespace geometry;

int main() {
  using R = long double;
  IoSetup(20);

  int n, m;
  std::cin >> n >> m;

  points<R> pts(n);
  for (auto &p : pts) std::cin >> p;

  std::vector< R > min_cov(1 << n, 1e10);
  for (int bit = 0; bit < (1 << n); bit++) {
    points<R> npts;
    for (int i = 0; i < n; i++) {
      if (not ((1 << i) & bit)) continue;
      npts.emplace_back(pts[i]);
    }

    min_cov[bit] = minimum_covering_circle(npts, 133333333).r;
  }


  auto dp = std::vector(m + 1, std::vector(1 << n, R(1e10)));
  dp[0][0] = 0;

  for (int s = 0; s < m; s++) {
    for (int bit = 0; bit < (1 << n); bit++) {
      int msk = ((1 << n) - 1) - bit;
      for (int sub = msk; ; sub = (sub - 1) & msk) {
        dp[s + 1][bit | sub] = std::min(dp[s + 1][bit | sub], std::max(dp[s][bit], min_cov[sub]));
        if (sub == 0) break;
      }
    }
  }

  std::cout << dp[m][(1 << n) - 1] << std::endl;
}
#line 1 "test/aoj/icpc/3034.test.cpp"
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/3034
// verification-helper: ERROR 1e-3

#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/point-cloud/minimum-covering-circle.hpp"

#line 2 "src/real-geometry/circle-lib/circumscribed-circle.hpp"

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

#line 4 "src/real-geometry/class/circle.hpp"

#line 6 "src/real-geometry/class/circle.hpp"

// circle
namespace geometry {

  template< typename R >
  class circle {
   public:
    point<R> o;
    R r;

    circle() = default;
    circle(point<R> o, R r) : o(o), r(r) {}

    const point<R> center() const {
      return o;
    }

    const R radius() const {
      return r;
    }
  };


  template< typename R >
  using circles = std::vector< circle<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/circle-lib/circumscribed-circle.hpp"

namespace geometry {

  template< typename R >
  circle<R> circumscribed_circle(const point<R> &a, const point<R> &b, const point<R> &c) {
    R A = std::norm(b - c), B = std::norm(c - a), C = std::norm(a - b);

    R S = std::norm(cross_product<R>(b - a, c - a));
    R T = A + B + C;

    point<R> o{(A*(T - 2*A) * a + B*(T - 2*B) * b + C*(T - 2*C) * c) / (4 * S)};

    return circle(o, std::abs(o - a));
  }

}
#line 2 "src/real-geometry/position/in-circle.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 6 "src/real-geometry/position/in-circle.hpp"

#line 8 "src/real-geometry/position/in-circle.hpp"

namespace geometry {

  template< typename R >
  bool in_circle(const circle<R> &c, const point<R> &p) {
    return sign(std::abs(c.o - p) - c.r) == -1;
  }

}
#line 7 "src/real-geometry/point-cloud/minimum-covering-circle.hpp"

#include <random>
#include <algorithm>

namespace geometry {

  template< typename R >
  circle<R> minimum_covering_circle(points<R> pts, unsigned int seed) {
    auto make_circle = [](const point<R> &a, const point<R> &b) {
      return circle<R>(point<R>(a + b) * 0.5, abs(a - b) * 0.5);
    };

    int n = pts.size();
    if (n == 1) return circle<R>(pts[0], 0);

    std::mt19937 engine(seed);
    std::shuffle(pts.begin(), pts.end(), engine);
    circle<R> res(point<R>(), -1);

    for (int i = 0; i < n; i++) {
      if (in_circle(res, pts[i])) continue;
      res = circle<R>(pts[i], 0);

      for (int j = 0; j < i; j++) {
        if (in_circle(res, pts[j])) continue;
        res = make_circle(pts[i], pts[j]);

        for (int k = 0; k < j; k++) {
          if (in_circle(res, pts[k])) continue;
          res = circumscribed_circle(pts[i], pts[j], pts[k]);
        }
      }
    }

    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 7 "test/aoj/icpc/3034.test.cpp"

#line 9 "test/aoj/icpc/3034.test.cpp"

using namespace geometry;

int main() {
  using R = long double;
  IoSetup(20);

  int n, m;
  std::cin >> n >> m;

  points<R> pts(n);
  for (auto &p : pts) std::cin >> p;

  std::vector< R > min_cov(1 << n, 1e10);
  for (int bit = 0; bit < (1 << n); bit++) {
    points<R> npts;
    for (int i = 0; i < n; i++) {
      if (not ((1 << i) & bit)) continue;
      npts.emplace_back(pts[i]);
    }

    min_cov[bit] = minimum_covering_circle(npts, 133333333).r;
  }


  auto dp = std::vector(m + 1, std::vector(1 << n, R(1e10)));
  dp[0][0] = 0;

  for (int s = 0; s < m; s++) {
    for (int bit = 0; bit < (1 << n); bit++) {
      int msk = ((1 << n) - 1) - bit;
      for (int sub = msk; ; sub = (sub - 1) & msk) {
        dp[s + 1][bit | sub] = std::min(dp[s + 1][bit | sub], std::max(dp[s][bit], min_cov[sub]));
        if (sub == 0) break;
      }
    }
  }

  std::cout << dp[m][(1 << n) - 1] << std::endl;
}
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