#line 1 "test/aoj/3034/main.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3034"
#define ERROR 1e-3
#include <iomanip>
#include <iostream>
#include <vector>
#line 2 "Mylib/Bit/enumerate_subsets_asc.cpp"
namespace haar_lib {
template <typename Func>
void enumerate_subsets_asc(int a, const Func &f) {
for (int t = 0;; t = (t - a) & a) {
if (not f(t)) break;
if (t == a) break;
}
}
} // namespace haar_lib
#line 2 "Mylib/Geometry/Float/double_eps.cpp"
#include <cmath>
#line 4 "Mylib/Geometry/Float/double_eps.cpp"
#include <limits>
namespace haar_lib {
template <typename T, const T &eps>
struct double_eps {
using value_type = T;
private:
T value_;
public:
double_eps() : value_(0) {}
double_eps(T value_) : value_(value_) {}
auto &operator=(const double_eps &rhs) {
this->value_ = rhs.value_;
return *this;
}
auto &operator+=(const double_eps &rhs) {
this->value_ += rhs.value_;
return *this;
}
auto &operator-=(const double_eps &rhs) {
this->value_ -= rhs.value_;
return *this;
}
auto &operator*=(const double_eps &rhs) {
this->value_ *= rhs.value_;
return *this;
}
auto &operator/=(const double_eps &rhs) {
this->value_ /= rhs.value_;
return *this;
}
auto operator+(const double_eps &rhs) const { return double_eps(this->value_ + rhs.value_); }
auto operator-(const double_eps &rhs) const { return double_eps(this->value_ - rhs.value_); }
auto operator*(const double_eps &rhs) const { return double_eps(this->value_ * rhs.value_); }
auto operator/(const double_eps &rhs) const { return double_eps(this->value_ / rhs.value_); }
bool operator==(const double_eps &rhs) const { return std::abs(this->value_ - rhs.value_) < eps; }
bool operator!=(const double_eps &rhs) const { return !(*this == rhs); }
bool operator<(const double_eps &rhs) const { return this->value_ - rhs.value_ < -eps; }
bool operator<=(const double_eps &rhs) const { return this->value_ - rhs.value_ < eps; }
bool operator>(const double_eps &rhs) const { return !(*this <= rhs); }
bool operator>=(const double_eps &rhs) const { return !(*this < rhs); }
auto operator-() const { return double_eps(-(this->value_)); }
explicit operator double() const noexcept { return value_; }
explicit operator long double() const noexcept { return value_; }
friend std::ostream &operator<<(std::ostream &s, const double_eps &rhs) {
s << rhs.value_;
return s;
}
friend std::istream &operator>>(std::istream &s, double_eps &rhs) {
s >> rhs.value_;
return s;
}
friend double_eps sin(double_eps x) { return std::sin((T) x); }
friend double_eps cos(double_eps x) { return std::cos((T) x); }
friend double_eps tan(double_eps x) { return std::tan((T) x); }
friend double_eps acos(double_eps x) { return std::acos((T) x); }
friend double_eps atan2(double_eps y, double_eps x) { return std::atan2((T) y, (T) x); }
friend double_eps abs(double_eps x) { return std::abs((T) x); }
friend double_eps sqrt(double_eps x) { return std::sqrt(std::max<T>(0, (T) x)); }
};
} // namespace haar_lib
namespace std {
template <typename T, const T &eps>
class numeric_limits<haar_lib::double_eps<T, eps>> {
public:
static haar_lib::double_eps<T, eps> infinity() { return numeric_limits<T>::infinity(); }
static haar_lib::double_eps<T, eps> min() { return numeric_limits<T>::min(); }
static haar_lib::double_eps<T, eps> max() { return numeric_limits<T>::max(); }
static haar_lib::double_eps<T, eps> lowest() { return numeric_limits<T>::lowest(); }
};
} // namespace std
#line 5 "Mylib/Geometry/Float/geometry_template.cpp"
namespace haar_lib {
template <typename T>
struct vec {
T x, y;
vec() {}
vec(T x, T y) : x(x), y(y) {}
friend auto operator+(const vec &a, const vec &b) { return vec(a.x + b.x, a.y + b.y); }
friend auto operator-(const vec &a, const vec &b) { return vec(a.x - b.x, a.y - b.y); }
friend auto operator-(const vec &a) { return vec(-a.x, -a.y); }
friend bool operator==(const vec &a, const vec &b) { return a.x == b.x and a.y == b.y; }
friend bool operator!=(const vec &a, const vec &b) { return !(a == b); }
friend bool operator<(const vec &a, const vec &b) { return a.x < b.x or (a.x == b.x and a.y < b.y); }
friend std::istream &operator>>(std::istream &s, vec &a) {
s >> a.x >> a.y;
return s;
}
};
template <typename T, typename U>
auto operator*(const vec<T> &a, const U &k) { return vec<T>(a.x * k, a.y * k); }
template <typename T, typename U>
auto operator*(const U &k, const vec<T> &a) { return vec<T>(a.x * k, a.y * k); }
template <typename T, typename U>
auto operator/(const vec<T> &a, const U &k) { return vec<T>(a.x / k, a.y / k); }
template <typename T>
using point = vec<T>;
template <typename T>
T abs(const vec<T> &a) { return sqrt(a.x * a.x + a.y * a.y); }
template <typename T>
T abs_sq(const vec<T> &a) { return a.x * a.x + a.y * a.y; }
template <typename T>
T dot(const vec<T> &a, const vec<T> &b) { return a.x * b.x + a.y * b.y; }
template <typename T>
T cross(const vec<T> &a, const vec<T> &b) { return a.x * b.y - a.y * b.x; }
template <typename T>
auto unit(const vec<T> &a) { return a / abs(a); }
template <typename T>
auto normal(const vec<T> &p) { return vec<T>(-p.y, p.x); }
template <typename T>
auto polar(const T &r, const T &ang) { return vec<T>(r * cos(ang), r * sin(ang)); }
template <typename T>
T angle(const vec<T> &a, const vec<T> &b) { return atan2(b.y - a.y, b.x - a.x); }
template <typename T>
T phase(const vec<T> &a) { return atan2(a.y, a.x); }
template <typename T>
T angle_diff(const vec<T> &a, const vec<T> &b) {
T r = phase(b) - phase(a);
if (r < -M_PI)
return r + 2 * M_PI;
else if (r > M_PI)
return r - 2 * M_PI;
return r;
}
template <typename T>
struct line {
point<T> from, to;
line() : from(), to() {}
line(const point<T> &from, const point<T> &to) : from(from), to(to) {}
};
template <typename T>
using segment = line<T>;
template <typename T>
auto unit(const line<T> &a) { return unit(a.to - a.from); }
template <typename T>
auto normal(const line<T> &a) { return normal(a.to - a.from); }
template <typename T>
auto diff(const segment<T> &a) { return a.to - a.from; }
template <typename T>
T abs(const segment<T> &a) { return abs(diff(a)); }
template <typename T>
T dot(const line<T> &a, const line<T> &b) { return dot(diff(a), diff(b)); }
template <typename T>
T cross(const line<T> &a, const line<T> &b) { return cross(diff(a), diff(b)); }
template <typename T>
using polygon = std::vector<point<T>>;
template <typename T>
struct circle {
point<T> center;
T radius;
circle() : center(), radius(0) {}
circle(const point<T> ¢er, T radius) : center(center), radius(radius) {}
};
template <typename T>
std::ostream &operator<<(std::ostream &s, const vec<T> &a) {
s << "(" << a.x << ", " << a.y << ")";
return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const line<T> &a) {
s << "(" << a.from << " -> " << a.to << ")";
return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const circle<T> &a) {
s << "("
<< "center: " << a.center << ", "
<< "radius: " << a.radius << ")";
return s;
}
} // namespace haar_lib
#line 2 "Mylib/Geometry/Float/minimum_covering_circle.cpp"
#include <algorithm>
#include <random>
#line 3 "Mylib/Geometry/Float/circumscribed_circle_of_triangle.cpp"
namespace haar_lib {
template <typename T>
circle<T> circumscribed_circle_of_triangle(const point<T> &a, const point<T> &b, const point<T> &c) {
const T A = abs_sq(b - c), B = abs_sq(a - c), C = abs_sq(a - b), S = A + B + C;
const T AA = A * (S - A * 2.0);
const T BB = B * (S - B * 2.0);
const T CC = C * (S - C * 2.0);
const auto center = (AA * a + BB * b + CC * c) / (AA + BB + CC);
return circle<T>(
center,
abs(center - a));
}
} // namespace haar_lib
#line 6 "Mylib/Geometry/Float/minimum_covering_circle.cpp"
namespace haar_lib {
template <typename T>
circle<T> minimum_covering_circle(std::vector<point<T>> ps, int seed = 0) {
if (ps.empty()) return circle<T>();
if (ps.size() == 1) return circle<T>(ps[0], 0);
const int N = ps.size();
std::mt19937 rand(seed);
std::shuffle(ps.begin(), ps.end(), rand);
auto make_circle_2 =
[&](const auto &p, const auto &q) {
const auto c = (p + q) / 2.0;
return circle<T>(c, abs(p - c));
};
auto check =
[](const auto &p, const auto &c) {
return abs(c.center - p) <= c.radius;
};
circle<T> ret = make_circle_2(ps[0], ps[1]);
for (int i = 2; i < N; ++i) {
if (check(ps[i], ret)) continue;
ret = make_circle_2(ps[0], ps[i]);
for (int j = 1; j < i; ++j) {
if (check(ps[j], ret)) continue;
ret = make_circle_2(ps[i], ps[j]);
for (int k = 0; k < j; ++k) {
if (check(ps[k], ret)) continue;
if (i == j or j == k or k == i) continue;
ret = circumscribed_circle_of_triangle(ps[i], ps[j], ps[k]);
}
}
}
return ret;
}
} // namespace haar_lib
#line 4 "Mylib/IO/input_vector.cpp"
namespace haar_lib {
template <typename T>
std::vector<T> input_vector(int N) {
std::vector<T> ret(N);
for (int i = 0; i < N; ++i) std::cin >> ret[i];
return ret;
}
template <typename T>
std::vector<std::vector<T>> input_vector(int N, int M) {
std::vector<std::vector<T>> ret(N);
for (int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
return ret;
}
} // namespace haar_lib
#line 2 "Mylib/Utils/fix_point.cpp"
#include <utility>
namespace haar_lib {
template <typename F>
struct fix_point : F {
explicit constexpr fix_point(F &&f) noexcept : F(std::forward<F>(f)) {}
template <typename... Args>
constexpr auto operator()(Args &&... args) const {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <typename F>
inline constexpr auto make_fix_point(F &&f) {
return fix_point<F>(std::forward<F>(f));
}
template <typename F>
inline constexpr auto make_fix_point(F &f) {
return fix_point<F>(std::forward<F>(f));
}
} // namespace haar_lib
#line 13 "test/aoj/3034/main.test.cpp"
namespace hl = haar_lib;
static constexpr double eps = ERROR;
using D = hl::double_eps<double, eps>;
D dp[15][1 << 14];
bool check[15][1 << 14];
const D INF = 1e9;
int main() {
int N, M;
std::cin >> N >> M;
auto ps = hl::input_vector<hl::point<D>>(N);
std::vector<double> memo(1 << N);
for (int t = 0; t < (1 << N); ++t) {
std::vector<hl::point<D>> q;
for (int i = 0; i < N; ++i) {
if (t & (1 << i)) q.push_back(ps[i]);
}
memo[t] = (double) hl::minimum_covering_circle(q).radius;
}
const int mask = (1 << N) - 1;
auto ans =
hl::make_fix_point(
[&](auto &&rec, int d, int s) -> D {
if (d == M) {
if (s != 0) return dp[d][s] = INF;
return dp[d][s] = 0;
}
if (check[d][s]) return dp[d][s];
check[d][s] = true;
D ret = INF;
hl::enumerate_subsets_asc(
s,
[&](int t) {
D val = std::max((double) rec(d + 1, s ^ t), memo[t]);
ret = std::min((double) ret, (double) val);
return true;
});
return dp[d][s] = ret;
})(0, mask);
std::cout << std::fixed << std::setprecision(12) << ans << std::endl;
return 0;
}
test/aoj/3034/main.test.cpp
Enumerate subsets (Ascending order)
(Mylib/Bit/enumerate_subsets_asc.cpp)