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#include "geo/incremental_convexhull.hpp"
#include "geo/base.hpp" // 下側凸包 template <typename T, bool strict = true> struct IncrementalConvexHull_Lower { using P = Point<T>; set<P> S; IncrementalConvexHull_Lower() {} int size() { return len(S); } template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E> void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) { int s = side(p); if (strict && s >= 0) return; if (!strict && s > 0) return; // 点追加 add_v(p); S.insert(p); vc<P> left; { auto it = S.find(p); while (it != S.begin()) { --it; if (left.empty()) { left.eb(*it); continue; } auto a = *it; auto b = left.back(); T det = (b - a).det(p - a); if (strict && det > 0) break; if (!strict && det >= 0) break; left.eb(a); } } vc<P> right; { auto it = S.find(p); while (1) { ++it; if (it == S.end()) break; if (right.empty()) { right.eb(*it); continue; } auto a = right.back(); auto b = *it; T det = (a - p).det(b - p); if (strict && det > 0) break; if (!strict && det >= 0) break; right.eb(b); } } // 点削除 if (len(left) > 1) { S.erase(next(S.find(left.back())), S.find(p)); } if (len(right) > 1) { S.erase(next(S.find(p)), S.find(right.back())); } FOR(i, len(left) - 1) rm_v(left[i]); FOR(i, len(right) - 1) rm_v(right[i]); // 辺削除 if (len(left) && len(right)) { auto a = left[0], b = right[0]; rm_e(a, b); } FOR(i, len(left) - 1) { auto a = left[i + 1], b = left[i]; rm_e(a, b); } FOR(i, len(right) - 1) { auto a = right[i], b = right[i + 1]; rm_e(a, b); } // 辺追加 if (len(left)) { add_e(left.back(), p); } if (len(right)) { add_e(p, right.back()); } } // 中:1, 境界:0, 外:-1 int side(Point<T> p) { auto r = S.lower_bound(p); if (r == S.begin()) { // 全部 p 以上 if (len(S) && (*r) == p) return 0; return -1; } if (r == S.end()) { // p は max より大きい return -1; } auto l = prev(r); auto p1 = *l, p2 = *r; T det = (p - p1).det(p2 - p1); if (det == 0) return 0; return (det > 0 ? -1 : 1); } }; template <typename T, bool strict = true> struct Incremental_ConvexHull { using P = Point<T>; IncrementalConvexHull_Lower<T, strict> LOWER, UPPER; int cnt_E; T det_sum; bool is_empty; Incremental_ConvexHull() : cnt_E(0), det_sum(0), is_empty(1) {} int size() { return cnt_E; } bool empty() { return is_empty; } template <typename REAL> REAL area() { return det_sum * 0.5; } T area_2() { return det_sum; } template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E> void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) { is_empty = 0; LOWER.add( p, add_v, rm_v, [&](Point<T> a, Point<T> b) { add_e(a, b); ++cnt_E; det_sum += a.det(b); }, [&](Point<T> a, Point<T> b) { rm_e(a, b); --cnt_E; det_sum -= a.det(b); }); UPPER.add( -p, [&](Point<T> p) { add_v(-p); }, [&](Point<T> p) { rm_v(-p); }, [&](Point<T> a, Point<T> b) { add_e(-a, -b); ++cnt_E; det_sum += a.det(b); }, [&](Point<T> a, Point<T> b) { rm_e(-a, -b); --cnt_E; det_sum -= a.det(b); }); } void add(Point<T> p) { add( p, [](Point<T> p) {}, [](Point<T> p) {}, [](Point<T> s, Point<T> t) {}, [](Point<T> s, Point<T> t) {}); } // 中:1、境界:0、外:-1 int side(Point<T> p) { int a = LOWER.side(p); int b = UPPER.side(-p); if (a == 0 || b == 0) return 0; return min(a, b); } };
#line 2 "geo/base.hpp" template <typename T> struct Point { T x, y; Point() : x(0), y(0) {} template <typename A, typename B> Point(A x, B y) : x(x), y(y) {} template <typename A, typename B> Point(pair<A, B> p) : x(p.fi), y(p.se) {} Point operator+=(const Point p) { x += p.x, y += p.y; return *this; } Point operator-=(const Point p) { x -= p.x, y -= p.y; return *this; } Point operator+(Point p) const { return {x + p.x, y + p.y}; } Point operator-(Point p) const { return {x - p.x, y - p.y}; } bool operator==(Point p) const { return x == p.x && y == p.y; } bool operator!=(Point p) const { return x != p.x || y != p.y; } Point operator-() const { return {-x, -y}; } Point operator*(T t) const { return {x * t, y * t}; } Point operator/(T t) const { return {x / t, y / t}; } bool operator<(Point p) const { if (x != p.x) return x < p.x; return y < p.y; } T dot(const Point& other) const { return x * other.x + y * other.y; } T det(const Point& other) const { return x * other.y - y * other.x; } double norm() { return sqrtl(x * x + y * y); } double angle() { return atan2(y, x); } Point rotate(double theta) { static_assert(!is_integral<T>::value); double c = cos(theta), s = sin(theta); return Point{c * x - s * y, s * x + c * y}; } Point rot90(bool ccw) { return (ccw ? Point{-y, x} : Point{y, -x}); } }; #ifdef FASTIO template <typename T> void rd(Point<T>& p) { fastio::rd(p.x), fastio::rd(p.y); } template <typename T> void wt(Point<T>& p) { fastio::wt(p.x); fastio::wt(' '); fastio::wt(p.y); } #endif // A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1 template <typename T> int ccw(Point<T> A, Point<T> B, Point<T> C) { T x = (B - A).det(C - A); if (x > 0) return 1; if (x < 0) return -1; return 0; } template <typename REAL, typename T, typename U> REAL dist(Point<T> A, Point<U> B) { REAL dx = REAL(A.x) - REAL(B.x); REAL dy = REAL(A.y) - REAL(B.y); return sqrt(dx * dx + dy * dy); } // ax+by+c template <typename T> struct Line { T a, b, c; Line(T a, T b, T c) : a(a), b(b), c(c) {} Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; } Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {} template <typename U> U eval(Point<U> P) { return a * P.x + b * P.y + c; } template <typename U> T eval(U x, U y) { return a * x + b * y + c; } // 同じ直線が同じ a,b,c で表現されるようにする void normalize() { static_assert(is_same_v<T, int> || is_same_v<T, long long>); T g = gcd(gcd(abs(a), abs(b)), abs(c)); a /= g, b /= g, c /= g; if (b < 0) { a = -a, b = -b, c = -c; } if (b == 0 && a < 0) { a = -a, b = -b, c = -c; } } bool is_parallel(Line other) { return a * other.b - b * other.a == 0; } bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; } }; template <typename T> struct Segment { Point<T> A, B; Segment(Point<T> A, Point<T> B) : A(A), B(B) {} Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {} bool contain(Point<T> C) { T det = (C - A).det(B - A); if (det != 0) return 0; return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0; } Line<T> to_Line() { return Line(A, B); } }; template <typename REAL> struct Circle { Point<REAL> O; REAL r; Circle(Point<REAL> O, REAL r) : O(O), r(r) {} Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {} template <typename T> bool contain(Point<T> p) { REAL dx = p.x - O.x, dy = p.y - O.y; return dx * dx + dy * dy <= r * r; } }; #line 2 "geo/incremental_convexhull.hpp" // 下側凸包 template <typename T, bool strict = true> struct IncrementalConvexHull_Lower { using P = Point<T>; set<P> S; IncrementalConvexHull_Lower() {} int size() { return len(S); } template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E> void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) { int s = side(p); if (strict && s >= 0) return; if (!strict && s > 0) return; // 点追加 add_v(p); S.insert(p); vc<P> left; { auto it = S.find(p); while (it != S.begin()) { --it; if (left.empty()) { left.eb(*it); continue; } auto a = *it; auto b = left.back(); T det = (b - a).det(p - a); if (strict && det > 0) break; if (!strict && det >= 0) break; left.eb(a); } } vc<P> right; { auto it = S.find(p); while (1) { ++it; if (it == S.end()) break; if (right.empty()) { right.eb(*it); continue; } auto a = right.back(); auto b = *it; T det = (a - p).det(b - p); if (strict && det > 0) break; if (!strict && det >= 0) break; right.eb(b); } } // 点削除 if (len(left) > 1) { S.erase(next(S.find(left.back())), S.find(p)); } if (len(right) > 1) { S.erase(next(S.find(p)), S.find(right.back())); } FOR(i, len(left) - 1) rm_v(left[i]); FOR(i, len(right) - 1) rm_v(right[i]); // 辺削除 if (len(left) && len(right)) { auto a = left[0], b = right[0]; rm_e(a, b); } FOR(i, len(left) - 1) { auto a = left[i + 1], b = left[i]; rm_e(a, b); } FOR(i, len(right) - 1) { auto a = right[i], b = right[i + 1]; rm_e(a, b); } // 辺追加 if (len(left)) { add_e(left.back(), p); } if (len(right)) { add_e(p, right.back()); } } // 中:1, 境界:0, 外:-1 int side(Point<T> p) { auto r = S.lower_bound(p); if (r == S.begin()) { // 全部 p 以上 if (len(S) && (*r) == p) return 0; return -1; } if (r == S.end()) { // p は max より大きい return -1; } auto l = prev(r); auto p1 = *l, p2 = *r; T det = (p - p1).det(p2 - p1); if (det == 0) return 0; return (det > 0 ? -1 : 1); } }; template <typename T, bool strict = true> struct Incremental_ConvexHull { using P = Point<T>; IncrementalConvexHull_Lower<T, strict> LOWER, UPPER; int cnt_E; T det_sum; bool is_empty; Incremental_ConvexHull() : cnt_E(0), det_sum(0), is_empty(1) {} int size() { return cnt_E; } bool empty() { return is_empty; } template <typename REAL> REAL area() { return det_sum * 0.5; } T area_2() { return det_sum; } template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E> void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) { is_empty = 0; LOWER.add( p, add_v, rm_v, [&](Point<T> a, Point<T> b) { add_e(a, b); ++cnt_E; det_sum += a.det(b); }, [&](Point<T> a, Point<T> b) { rm_e(a, b); --cnt_E; det_sum -= a.det(b); }); UPPER.add( -p, [&](Point<T> p) { add_v(-p); }, [&](Point<T> p) { rm_v(-p); }, [&](Point<T> a, Point<T> b) { add_e(-a, -b); ++cnt_E; det_sum += a.det(b); }, [&](Point<T> a, Point<T> b) { rm_e(-a, -b); --cnt_E; det_sum -= a.det(b); }); } void add(Point<T> p) { add( p, [](Point<T> p) {}, [](Point<T> p) {}, [](Point<T> s, Point<T> t) {}, [](Point<T> s, Point<T> t) {}); } // 中:1、境界:0、外:-1 int side(Point<T> p) { int a = LOWER.side(p); int b = UPPER.side(-p); if (a == 0 || b == 0) return 0; return min(a, b); } };