This documentation is automatically generated by online-judge-tools/verification-helper
#include "geo/furthest_pair.hpp"
#include "geo/base.hpp"
#include "geo/convex_hull.hpp"
template <typename T>
pair<int, int> furthest_pair(vc<Point<T>> point) {
T best = -1;
pair<int, int> ANS = {-1, -1};
auto upd = [&](int i, int j) -> void {
Point<T> p = point[i] - point[j];
ll d = p.dot(p);
if (chmax(best, d)) ANS = {i, j};
};
upd(0, 1);
auto I = ConvexHull(point);
int n = len(I);
if (n == 1) return ANS;
if (n == 2) { return {I[0], I[1]}; }
/*
直径と垂直な平行線 2 本で凸包をはさめる
平行線 2 本ではさんで引っかかる 2 点が候補
p[i]p[i+1] の反対側を候補とすればよい
*/
FOR(i, n) I.eb(I[i]);
vc<Point<T>> C = rearrange(point, I);
int j = 1;
FOR(i, n) {
chmax(j, i);
while (j < 2 * n && (C[i + 1] - C[i]).det(C[j + 1] - C[j]) > 0) ++j;
upd(I[i], I[j]);
}
return ANS;
}
#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(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, 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) {
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/convex_hull.hpp"
#line 4 "geo/convex_hull.hpp"
// allow_180=true で同一座標点があるとこわれる
// full なら I[0] が sorted で min になる
template <typename T, bool allow_180 = false>
vector<int> ConvexHull(vector<Point<T>>& XY, string mode = "full", bool sorted = false) {
assert(mode == "full" || mode == "lower" || mode == "upper");
ll N = XY.size();
if (N == 1) return {0};
if (N == 2) {
if (XY[0] < XY[1]) return {0, 1};
if (XY[1] < XY[0]) return {1, 0};
return {0};
}
vc<int> I(N);
if (sorted) {
FOR(i, N) I[i] = i;
} else {
I = argsort(XY);
}
if constexpr (allow_180) { FOR(i, N - 1) assert(XY[i] != XY[i + 1]); }
auto check = [&](ll i, ll j, ll k) -> bool {
ll det = (XY[j] - XY[i]).det(XY[k] - XY[i]);
if constexpr (allow_180) return det >= 0;
return det > 0;
};
auto calc = [&]() {
vector<int> P;
for (auto&& k: I) {
while (P.size() > 1) {
auto i = P[P.size() - 2];
auto j = P[P.size() - 1];
if (check(i, j, k)) break;
P.pop_back();
}
P.eb(k);
}
return P;
};
vc<int> P;
if (mode == "full" || mode == "lower") {
vc<int> Q = calc();
P.insert(P.end(), all(Q));
}
if (mode == "full" || mode == "upper") {
if (!P.empty()) P.pop_back();
reverse(all(I));
vc<int> Q = calc();
P.insert(P.end(), all(Q));
}
if (mode == "upper") reverse(all(P));
while (len(P) >= 2 && XY[P[0]] == XY[P.back()]) P.pop_back();
return P;
}
#line 3 "geo/furthest_pair.hpp"
template <typename T>
pair<int, int> furthest_pair(vc<Point<T>> point) {
T best = -1;
pair<int, int> ANS = {-1, -1};
auto upd = [&](int i, int j) -> void {
Point<T> p = point[i] - point[j];
ll d = p.dot(p);
if (chmax(best, d)) ANS = {i, j};
};
upd(0, 1);
auto I = ConvexHull(point);
int n = len(I);
if (n == 1) return ANS;
if (n == 2) { return {I[0], I[1]}; }
/*
直径と垂直な平行線 2 本で凸包をはさめる
平行線 2 本ではさんで引っかかる 2 点が候補
p[i]p[i+1] の反対側を候補とすればよい
*/
FOR(i, n) I.eb(I[i]);
vc<Point<T>> C = rearrange(point, I);
int j = 1;
FOR(i, n) {
chmax(j, i);
while (j < 2 * n && (C[i + 1] - C[i]).det(C[j + 1] - C[j]) > 0) ++j;
upd(I[i], I[j]);
}
return ANS;
}