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#include "library/integral_geom/convex_hull.hpp"
#ifndef SUISEN_CONVEX_HULL_INTEGRAL #define SUISEN_CONVEX_HULL_INTEGRAL #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 #endif // SUISEN_CONVEX_HULL_INTEGRAL
#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