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#include "geo/perpendicular_bisector.hpp"
#include "geo/base.hpp" template <typename T> Line<T> perpendicular_bisector(Point<T> A, Point<T> B) { assert(A != B); T a = 2 * (B.x - A.x); T b = 2 * (B.y - A.y); T c = (A.x * A.x + A.y * A.y) - (B.x * B.x + B.y * B.y); return Line<T>(a, b, c); }
#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+(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(Point other) { return x * other.x + y * other.y; } T det(Point other) { 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}; } }; #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> REAL dist(Point<T> A, Point<T> B) { A = A - B; T p = A.dot(A); return sqrt(REAL(p)); } // 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) { static_assert(is_integral<T>::value); 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; } }; template <typename T> struct Polygon { vc<Point<T>> points; T a; template <typename A, typename B> Polygon(vc<pair<A, B>> pairs) { for (auto&& [a, b]: pairs) points.eb(Point<T>(a, b)); build(); } Polygon(vc<Point<T>> points) : points(points) { build(); } int size() { return len(points); } template <typename REAL> REAL area() { return a * 0.5; } template <enable_if_t<is_integral<T>::value, int> = 0> T area_2() { return a; } bool is_convex() { FOR(j, len(points)) { int i = (j == 0 ? len(points) - 1 : j - 1); int k = (j == len(points) - 1 ? 0 : j + 1); if ((points[j] - points[i]).det(points[k] - points[j]) < 0) return false; } return true; } private: void build() { a = 0; FOR(i, len(points)) { int j = (i + 1 == len(points) ? 0 : i + 1); a += points[i].det(points[j]); } if (a < 0) { a = -a; reverse(all(points)); } } }; #line 2 "geo/perpendicular_bisector.hpp" template <typename T> Line<T> perpendicular_bisector(Point<T> A, Point<T> B) { assert(A != B); T a = 2 * (B.x - A.x); T b = 2 * (B.y - A.y); T c = (A.x * A.x + A.y * A.y) - (B.x * B.x + B.y * B.y); return Line<T>(a, b, c); }