geo/incremental_convexhull.hpp

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• Last update: 2023-12-21 22:18:31+09:00
• Include: #include "geo/incremental_convexhull.hpp"

Depends on

• geo/base.hpp

Verified with

• test/mytest/incremental_ch.test.cpp
• test_atcoder/abc266c.test.cpp

Code

#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+(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/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);
  }
};

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