geo/convex_polygon_dp_order.hpp

• View this file on GitHub
• Last update: 2026-08-19 20:31:51+09:00
• Include: #include "geo/convex_polygon_dp_order.hpp"

Depends on

• geo/angle_sort.hpp
• geo/base.hpp

Code

#include "geo/angle_sort.hpp"

/*
点群は distinct
edge(i,j): i->j で遷移していくと偏角昇順（strict）な辺の列になる順
典型的には v を固定して v->v を作ると凸多角形になる
通常は退化ケースは別途処理し，非退化を保証するために使った辺が3個以上かのフラグを持つ
*/
template <typename P>
vc<pair<int, int>> convex_polygon_dp_order(vc<P> A) {
  int N = len(A);
  vc<pair<int, int>> E;
  FOR(i, N) FOR(j, N) {
    if (i == j) continue;
    assert(A[i] != A[j]);
    E.eb(i, j);
  }

  sort(all(E), [&](auto& X, auto& Y) -> bool {
    auto [a, b] = X;
    auto [c, d] = Y;
    int k = angle_comp_3(A[b] - A[a], A[d] - A[c]);
    if (k == -1) return true;
    if (k == 1) return false;
    P dir = A[b] - A[a];
    return dir.dot(A[b] - A[d]) > 0;
  });
  return E;
}

#line 1 "geo/angle_sort.hpp"

#line 1 "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) {}

  template <typename U>
  Point(Point<U> p) : x(p.x), y(p.y) {
    static_assert(!is_integral_v<T> || is_integral_v<U>);
  }

  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 U(a) * P.x + U(b) * P.y + U(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; }
  bool is_same(Line other) {
    if (a * other.b != b * other.a) return 0;
    if (a * other.c != c * other.a) return 0;
    if (b * other.c != c * other.b) return 0;
    return 1;
  }
};

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() {}
  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 3 "geo/angle_sort.hpp"

// lower: -1, origin: 0, upper: 1, (-pi,pi]
template <typename T> int lower_or_upper(const Point<T> &p) {
  if (p.y != 0)
    return (p.y > 0 ? 1 : -1);
  if (p.x > 0)
    return -1;
  if (p.x < 0)
    return 1;
  return 0;
}

// L<R:-1, L==R:0, L>R:1, (-pi,pi]
template <typename T> int angle_comp_3(const Point<T> &L, const Point<T> &R) {
  int a = lower_or_upper(L), b = lower_or_upper(R);
  if (a != b)
    return (a < b ? -1 : +1);
  T det = L.det(R);
  if (det > 0)
    return -1;
  if (det < 0)
    return 1;
  return 0;
}

// 偏角ソートに対する argsort, (-pi,pi]
template <typename T> vector<int> angle_sort(vector<Point<T>> &P) {
  vc<int> I(len(P));
  FOR(i, len(P)) I[i] = i;
  sort(all(I), [&](auto &L, auto &R) -> bool {
    return angle_comp_3(P[L], P[R]) == -1;
  });
  return I;
}

// 偏角ソートに対する argsort, (-pi,pi]
template <typename T> vector<int> angle_sort(vector<pair<T, T>> &P) {
  vc<Point<T>> tmp(len(P));
  FOR(i, len(P)) tmp[i] = Point<T>(P[i]);
  return angle_sort<T>(tmp);
}
#line 2 "geo/convex_polygon_dp_order.hpp"

/*
点群は distinct
edge(i,j): i->j で遷移していくと偏角昇順（strict）な辺の列になる順
典型的には v を固定して v->v を作ると凸多角形になる
通常は退化ケースは別途処理し，非退化を保証するために使った辺が3個以上かのフラグを持つ
*/
template <typename P>
vc<pair<int, int>> convex_polygon_dp_order(vc<P> A) {
  int N = len(A);
  vc<pair<int, int>> E;
  FOR(i, N) FOR(j, N) {
    if (i == j) continue;
    assert(A[i] != A[j]);
    E.eb(i, j);
  }

  sort(all(E), [&](auto& X, auto& Y) -> bool {
    auto [a, b] = X;
    auto [c, d] = Y;
    int k = angle_comp_3(A[b] - A[a], A[d] - A[c]);
    if (k == -1) return true;
    if (k == 1) return false;
    P dir = A[b] - A[a];
    return dir.dot(A[b] - A[d]) > 0;
  });
  return E;
}

Back to top page