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View the Project on GitHub Luzhiled/comp-geometry
// 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; }