結果
| 問題 | No.1999 Lattice Teleportation |
| ユーザー |
 suisen
|
| 提出日時 | 2022-07-10 18:41:18 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 126 ms / 2,000 ms |
| コード長 | 8,566 bytes |
| コンパイル時間 | 1,364 ms |
| コンパイル使用メモリ | 109,524 KB |
| 最終ジャッジ日時 | 2025-01-30 06:15:10 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 29 |
ソースコード
#define PROBLEM "https://yukicoder.me/problems/no/1999"#include <iostream>#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#include <cmath>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#include <cassert>#include <iostream>#include <utility>namespace suisen::integral_geometry {using coordinate_t = long long;struct Point {coordinate_t x, y;constexpr Point(coordinate_t x = 0, coordinate_t y = 0) : x(x), y(y) {}operator std::pair<coordinate_t, coordinate_t>() const { return std::pair<coordinate_t, coordinate_t> { x, y }; }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_geometrynamespace 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;};}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_geometryusing 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;}