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View the Project on GitHub suisen-cp/cp-library-cpp
#define PROBLEM "https://yukicoder.me/problems/no/1999" #include <iostream> #include "library/integral_geom/convex_hull.hpp" #include "library/integral_geom/count_lattice_point.hpp" #include "library/integral_geom/sort_points_by_argument.hpp" using namespace suisen::integral_geometry; int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int n; std::cin >> n; std::vector<Point> ps; for (int i = 0; i < n; ++i) { Point p; std::cin >> p; if (p.y < 0) p.x = -p.x, p.y = -p.y; if (p.x or p.y) ps.push_back(p); } sort_points_by_argument(ps); std::vector<Point> outer{ { 0, 0 } }; for (int lp = 0; lp < 2; ++lp) { Point sum{ 0, 0 }; for (const Point &p : ps) outer.push_back(sum += p); std::reverse(ps.begin(), ps.end()); } std::vector<Point> convex; for (int i : convex_hull<Point, __int128_t>(outer)) convex.push_back(outer[i]); std::cout << int(count_lattice_points<Point, __int128_t>(convex) % 1000000007) << std::endl; return 0; }
#line 1 "test/src/integral_geom/count_lattice_point/yuki1999.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/1999" #include <iostream> #line 1 "library/integral_geom/convex_hull.hpp" #include <algorithm> #include <numeric> #include <vector> namespace suisen::integral_geometry { template <typename PointType, typename MultipliedType = long long> std::vector<int> convex_hull(const std::vector<PointType> &points) { const int n = points.size(); std::vector<int> sorted(n); std::iota(sorted.begin(), sorted.end(), 0); std::sort(sorted.begin(), sorted.end(), [&points](int i, int j) { const auto &[xi, yi] = points[i]; const auto &[xj, yj] = points[j]; return xi == xj ? yi < yj : xi < xj; }); std::vector<int8_t> used(n, false); sorted.resize(2 * n - 1); std::copy(sorted.rbegin() + n, sorted.rend(), sorted.begin() + n); std::vector<int> res; res.reserve(n); int first = sorted[0], last = sorted[n - 1]; auto isp_pos = [](MultipliedType x1, MultipliedType y1, MultipliedType x2, MultipliedType y2) -> bool { auto det = x1 * y2 - y1 * x2; return det > 0 or (det == 0 and x1 * x2 + y1 * y2 > 0); }; for (int k : sorted) { if (k != first and used[k]) continue; for (int sz = res.size(); sz >= 2; --sz) { int i = res[sz - 2], j = res[sz - 1]; if (j == last) break; const auto &[xi, yi] = points[i]; const auto &[xj, yj] = points[j]; const auto &[xk, yk] = points[k]; auto ab_x = xj - xi, ab_y = yj - yi; auto bc_x = xk - xj, bc_y = yk - yj; if (isp_pos(ab_x, ab_y, bc_x, bc_y)) break; res.pop_back(), used[j] = false; } if (not used[k]) res.push_back(k); used[k] = true; } return res; } } // namespace suisen::integral_geometry #line 1 "library/integral_geom/count_lattice_point.hpp" #include <cmath> #line 7 "library/integral_geom/count_lattice_point.hpp" namespace suisen::integral_geometry { // return: calculate the number of lattice points in the polygon or on at least one of the edges of it, using Pick's theorem (https://en.wikipedia.org/wiki/Pick%27s_theorem). template <typename PointType, typename MultipliedType = long long> MultipliedType count_lattice_points(const std::vector<PointType> &polygon) { const int n = polygon.size(); MultipliedType s = 0, b = 0; for (int i = 0; i < n; ++i) { auto [x1, y1] = polygon[i]; auto [x2, y2] = polygon[(i + 1) % n]; s += MultipliedType(x1) * y2 - MultipliedType(y1) * x2; b += std::abs(std::gcd(x2 - x1, y2 - y1)); } return (s + 2 + b) / 2; } } // namespace suisen::integral_geometry #line 1 "library/integral_geom/sort_points_by_argument.hpp" #line 6 "library/integral_geom/sort_points_by_argument.hpp" #line 1 "library/integral_geom/point.hpp" #include <cassert> #line 6 "library/integral_geom/point.hpp" #include <utility> #ifndef COORDINATE_TYPE #define COORDINATE_TYPE long long #endif // COORDINATE_TYPE #ifndef MULTIPLIED_TYPE #define MULTIPLIED_TYPE long long #endif // MULTIPLIED_TYPE namespace suisen::integral_geometry { using coordinate_t = COORDINATE_TYPE; using multiplied_t = MULTIPLIED_TYPE; struct Point { coordinate_t x, y; constexpr Point(coordinate_t x = 0, coordinate_t y = 0) : x(x), y(y) {} template <typename T = coordinate_t, typename U = coordinate_t> operator std::pair<T, U>() const { return std::pair<T, U> { T{ x }, U{ y } }; } template <typename T, typename U> Point& operator=(const std::pair<T, U> &p) { x = p.first, y = p.second; return *this; } friend Point operator+(const Point& p) { return p; } friend Point operator-(const Point& p) { return { -p.x, -p.y }; } friend Point operator+(const Point& lhs, const Point& rhs) { return { lhs.x + rhs.x, lhs.y + rhs.y }; } friend Point operator-(const Point& lhs, const Point& rhs) { return { lhs.x - rhs.x, lhs.y - rhs.y }; } friend Point operator*(const Point& lhs, const Point& rhs) { return { lhs.x * rhs.x - lhs.y * rhs.y, lhs.x * rhs.y + lhs.y * rhs.x }; } friend Point& operator+=(Point& lhs, const Point& rhs) { lhs.x += rhs.x, lhs.y += rhs.y; return lhs; } friend Point& operator-=(Point& lhs, const Point& rhs) { lhs.x -= rhs.x, lhs.y -= rhs.y; return lhs; } friend Point& operator*=(Point& lhs, const Point& rhs) { return lhs = lhs * rhs; } friend Point operator+(const Point& p, coordinate_t real) { return { p.x + real, p.y }; } friend Point operator-(const Point& p, coordinate_t real) { return { p.x - real, p.y }; } friend Point operator*(const Point& p, coordinate_t real) { return { p.x * real, p.y * real }; } friend Point operator/(const Point& p, coordinate_t real) { return { p.x / real, p.y / real }; } friend Point operator+=(Point& p, coordinate_t real) { p.x += real; return p; } friend Point operator-=(Point& p, coordinate_t real) { p.x -= real; return p; } friend Point operator*=(Point& p, coordinate_t real) { p.x *= real, p.y *= real; return p; } friend Point operator/=(Point& p, coordinate_t real) { p.x /= real, p.y /= real; return p; } friend Point operator+(coordinate_t real, const Point& p) { return { real + p.x, p.y }; } friend Point operator-(coordinate_t real, const Point& p) { return { real - p.x, -p.y }; } friend Point operator*(coordinate_t real, const Point& p) { return { real * p.x, real * p.y }; } friend bool operator==(const Point& lhs, const Point& rhs) { return lhs.x == rhs.x and lhs.y == rhs.y; } friend bool operator!=(const Point& lhs, const Point& rhs) { return not (lhs == rhs); } friend std::istream& operator>>(std::istream& in, Point& p) { return in >> p.x >> p.y; } friend std::ostream& operator<<(std::ostream& out, const Point& p) { return out << p.x << ' ' << p.y; } template <std::size_t I> coordinate_t get() const { if constexpr (I == 0) return x; else if constexpr (I == 1) return y; else assert(false); } template <std::size_t I> coordinate_t& get() { if constexpr (I == 0) return x; else if constexpr (I == 1) return y; else assert(false); } }; constexpr Point ZERO = { 0, 0 }; constexpr Point ONE = { 1, 0 }; constexpr Point I = { 0, 1 }; constexpr auto XY_COMPARATOR = [](const Point& p, const Point& q) { return p.x == q.x ? p.y < q.y : p.x < q.x; }; constexpr auto XY_COMPARATOR_GREATER = [](const Point& p, const Point& q) { return p.x == q.x ? p.y > q.y : p.x > q.x; }; constexpr auto YX_COMPARATOR = [](const Point& p, const Point& q) { return p.y == q.y ? p.x < q.x : p.y < q.y; }; constexpr auto YX_COMPARATOR_GREATER = [](const Point& p, const Point& q) { return p.y == q.y ? p.x > q.x : p.y > q.y; }; } // namespace suisen::integral_geometry namespace std { template <> struct tuple_size<suisen::integral_geometry::Point> : integral_constant<size_t, 2> {}; template <size_t I> struct tuple_element<I, suisen::integral_geometry::Point> { using type = suisen::integral_geometry::coordinate_t; }; } #line 8 "library/integral_geom/sort_points_by_argument.hpp" namespace suisen::integral_geometry { /** * 1. (x < 0, y = 0) -> pi * 2. (x = 0, y = 0) -> 0 * 3. points with same argument -> arbitrary order */ template <typename PointType, typename MultipliedType = long long> bool compare_by_atan2(const PointType &p, const PointType &q) { const auto &[x1, y1] = p; const auto &[x2, y2] = q; if ((y1 < 0) xor (y2 < 0)) return y1 < y2; if ((x1 < 0) xor (x2 < 0)) return (y1 >= 0) xor (x1 < x2); if (x1 == 0 and y1 == 0) return true; if (x2 == 0 and y2 == 0) return false; return (MultipliedType(y1) * x2 < MultipliedType(y2) * x1); } template <typename PointType, typename MultipliedType = long long> void sort_points_by_argument(std::vector<PointType> &points) { std::sort(points.begin(), points.end(), compare_by_atan2<PointType, MultipliedType>); } } // namespace suisen::integral_geometry #line 8 "test/src/integral_geom/count_lattice_point/yuki1999.test.cpp" using namespace suisen::integral_geometry; int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); int n; std::cin >> n; std::vector<Point> ps; for (int i = 0; i < n; ++i) { Point p; std::cin >> p; if (p.y < 0) p.x = -p.x, p.y = -p.y; if (p.x or p.y) ps.push_back(p); } sort_points_by_argument(ps); std::vector<Point> outer{ { 0, 0 } }; for (int lp = 0; lp < 2; ++lp) { Point sum{ 0, 0 }; for (const Point &p : ps) outer.push_back(sum += p); std::reverse(ps.begin(), ps.end()); } std::vector<Point> convex; for (int i : convex_hull<Point, __int128_t>(outer)) convex.push_back(outer[i]); std::cout << int(count_lattice_points<Point, __int128_t>(convex) % 1000000007) << std::endl; return 0; }