Convex Hull
(src/geometry/convex_hull.hpp)

• View this file on GitHub
• Last update: 2024-05-22 03:00:55+09:00
• Include: #include "src/geometry/convex_hull.hpp"

Depends on

• Point (src/geometry/Point.hpp)

Required by

• Furthest Pair (src/geometry/furthest_pair.hpp)

Verified with

• test/aoj/CGL_4_A.test.cpp
• test/yosupo/furthest_pair.test.cpp
• test/yosupo/static_convex_hull.test.cpp

Code

#pragma once
#include <algorithm>
#include <numeric>
#include <vector>
#include "Point.hpp"

namespace geometry {

template <typename T> std::vector<int> convex_hull(const std::vector<Point<T>>& P, bool inclusive = false) {
    int n = P.size();
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) return (P[0] != P[1] or inclusive ? std::vector<int>{0, 1} : std::vector<int>{0});
    std::vector<int> ord(n);
    std::iota(ord.begin(), ord.end(), 0);
    std::sort(ord.begin(), ord.end(), [&](int l, int r) { return P[l] < P[r]; });
    std::vector<int> ch(n + 1, -1);
    int s = 0, t = 0;
    for (int _ = 0; _ < 2; _++, s = --t, std::reverse(ord.begin(), ord.end())) {
        for (int& i : ord) {
            for (; t >= s + 2; t--) {
                auto det = (P[ch[t - 1]] - P[ch[t - 2]]).det(P[i] - P[ch[t - 2]]);
                if (inclusive ? det >= 0 : det > 0) break;
            }
            ch[t++] = i;
        }
    }
    while (not inclusive and t >= 2 and P[ch[0]] == P[ch[t - 1]]) t--;
    return {begin(ch), begin(ch) + t};
}

}  // namespace geometry

#line 2 "src/geometry/convex_hull.hpp"
#include <algorithm>
#include <numeric>
#include <vector>
#line 2 "src/geometry/Point.hpp"
#include <cassert>
#include <cmath>
#include <iostream>
#include <type_traits>

namespace geometry {

template <typename T> struct Point {
    static T EPS;

    static void set_eps(T eps) { EPS = eps; }

    T x, y;

    Point() {}

    Point(T x, T y) : x(x), y(y) {}

    Point operator+(const Point& p) const { return Point(x + p.x, y + p.y); }

    Point operator-(const Point& p) const { return Point(x - p.x, y - p.y); }

    Point operator*(T t) const { return Point(x * t, y * t); }

    Point operator/(T t) const { return Point(x / t, y / t); }

    bool operator==(const Point& p) const { return x == p.x and y == p.y; }

    bool operator!=(const Point& p) const { return not((*this) == p); }

    bool operator<(const Point& p) const { return x != p.x ? x < p.x : y < p.y; }

    friend std::istream& operator>>(std::istream& is, Point& p) { return is >> p.x >> p.y; }

    friend std::ostream& operator<<(std::ostream& os, const Point& p) { return os << p.x << ' ' << p.y; }

    T norm() { return std::sqrt(x * x + y * y); }

    T norm2() { return x * x + y * y; }

    T arg() { return std::atan2(y, x); }

    T dot(const Point& p) { return x * p.x + y * p.y; }

    T det(const Point& p) { return x * p.y - y * p.x; }

    Point perp() { return Point(-y, x); }

    Point unit() { return *this / norm(); }

    Point normal() { return perp().unit(); }

    Point rotate(T rad) { return Point(std::cos(rad) * x - std::sin(rad) * y, std::sin(rad) * x + std::cos(rad) * y); }
};

template <> double Point<double>::EPS = 1e-9;
template <> long double Point<long double>::EPS = 1e-12;
template <> int Point<int>::EPS = 0;
template <> long long Point<long long>::EPS = 0;

template <typename T> int sgn(T x) { return x < -Point<T>::EPS ? -1 : x > Point<T>::EPS ? 1 : 0; }

}  // namespace geometry
#line 6 "src/geometry/convex_hull.hpp"

namespace geometry {

template <typename T> std::vector<int> convex_hull(const std::vector<Point<T>>& P, bool inclusive = false) {
    int n = P.size();
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) return (P[0] != P[1] or inclusive ? std::vector<int>{0, 1} : std::vector<int>{0});
    std::vector<int> ord(n);
    std::iota(ord.begin(), ord.end(), 0);
    std::sort(ord.begin(), ord.end(), [&](int l, int r) { return P[l] < P[r]; });
    std::vector<int> ch(n + 1, -1);
    int s = 0, t = 0;
    for (int _ = 0; _ < 2; _++, s = --t, std::reverse(ord.begin(), ord.end())) {
        for (int& i : ord) {
            for (; t >= s + 2; t--) {
                auto det = (P[ch[t - 1]] - P[ch[t - 2]]).det(P[i] - P[ch[t - 2]]);
                if (inclusive ? det >= 0 : det > 0) break;
            }
            ch[t++] = i;
        }
    }
    while (not inclusive and t >= 2 and P[ch[0]] == P[ch[t - 1]]) t--;
    return {begin(ch), begin(ch) + t};
}

}  // namespace geometry

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