Manhattan segments intersections
(Mylib/Geometry/Float/manhattan_segments_intersections.cpp)

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• Last update: 2021-04-23 23:44:44+09:00
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Operations

Requirements

Notes

Problems

References

Depends on

• Geometry template (Mylib/Geometry/Float/geometry_template.cpp)

Verified with

• test/aoj/CGL_6_A/main.test.cpp

Code

#pragma once
#include <algorithm>
#include <climits>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <tuple>
#include <utility>
#include <vector>
#include "Mylib/Geometry/Float/geometry_template.cpp"

namespace haar_lib {
  template <typename T>
  int manhattan_segments_intersections(std::vector<segment<T>> segs) {
    std::vector<segment<T>> hs;
    std::vector<std::tuple<point<T>, bool, int>> vs;
    int count = 0;

    for (auto s : segs) {
      if (s.from.y == s.to.y) {
        hs.push_back(s);
      } else {
        vs.emplace_back(s.from, s.from.y < s.to.y, count);
        vs.emplace_back(s.to, s.from.y > s.to.y, count);
        ++count;
      }
    }

    std::sort(hs.rbegin(), hs.rend(), [](const auto &a, const auto &b) { return a.from.y < b.from.y; });
    std::sort(vs.rbegin(), vs.rend(), [](const auto &a, const auto &b) { return std::get<0>(a).y < std::get<0>(b).y; });

    __gnu_pbds::tree<
        std::pair<T, int>,
        __gnu_pbds::null_type,
        std::less<std::pair<T, int>>,
        __gnu_pbds::rb_tree_tag,
        __gnu_pbds::tree_order_statistics_node_update>
        set;
    int64_t ans = 0;

    while (true) {
      if (hs.empty() or vs.empty()) break;

      T ymin = std::min(hs.back().from.y, std::get<0>(vs.back()).y);

      std::vector<segment<T>> rs;
      std::vector<std::tuple<point<T>, bool, int>> ps;

      while (not hs.empty() and hs.back().from.y == ymin) {
        rs.push_back(hs.back());
        hs.pop_back();
      }

      while (not vs.empty() and std::get<0>(vs.back()).y == ymin) {
        ps.push_back(vs.back());
        vs.pop_back();
      }

      for (auto [a, b, c] : ps) {
        if (b) set.insert(std::make_pair(a.x, c));
      }

      for (auto [a, b] : rs) {
        auto [x1, x2] = std::minmax(a.x, b.x);

        auto ix1 = set.order_of_key(std::make_pair(x1, 0));
        auto ix2 = set.order_of_key(std::make_pair(x2, INT_MAX));

        ans += ix2 - ix1;
      }

      for (auto [a, b, c] : ps) {
        if (not b) set.erase(std::make_pair(a.x, c));
      }
    }

    return ans;
  }
}  // namespace haar_lib

#line 2 "Mylib/Geometry/Float/manhattan_segments_intersections.cpp"
#include <algorithm>
#include <climits>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <tuple>
#include <utility>
#include <vector>
#line 2 "Mylib/Geometry/Float/geometry_template.cpp"
#include <cmath>
#include <iostream>
#line 5 "Mylib/Geometry/Float/geometry_template.cpp"

namespace haar_lib {
  template <typename T>
  struct vec {
    T x, y;
    vec() {}
    vec(T x, T y) : x(x), y(y) {}

    friend auto operator+(const vec &a, const vec &b) { return vec(a.x + b.x, a.y + b.y); }
    friend auto operator-(const vec &a, const vec &b) { return vec(a.x - b.x, a.y - b.y); }
    friend auto operator-(const vec &a) { return vec(-a.x, -a.y); }

    friend bool operator==(const vec &a, const vec &b) { return a.x == b.x and a.y == b.y; }
    friend bool operator!=(const vec &a, const vec &b) { return !(a == b); }
    friend bool operator<(const vec &a, const vec &b) { return a.x < b.x or (a.x == b.x and a.y < b.y); }

    friend std::istream &operator>>(std::istream &s, vec &a) {
      s >> a.x >> a.y;
      return s;
    }
  };

  template <typename T, typename U>
  auto operator*(const vec<T> &a, const U &k) { return vec<T>(a.x * k, a.y * k); }
  template <typename T, typename U>
  auto operator*(const U &k, const vec<T> &a) { return vec<T>(a.x * k, a.y * k); }
  template <typename T, typename U>
  auto operator/(const vec<T> &a, const U &k) { return vec<T>(a.x / k, a.y / k); }

  template <typename T>
  using point = vec<T>;

  template <typename T>
  T abs(const vec<T> &a) { return sqrt(a.x * a.x + a.y * a.y); }
  template <typename T>
  T abs_sq(const vec<T> &a) { return a.x * a.x + a.y * a.y; }

  template <typename T>
  T dot(const vec<T> &a, const vec<T> &b) { return a.x * b.x + a.y * b.y; }
  template <typename T>
  T cross(const vec<T> &a, const vec<T> &b) { return a.x * b.y - a.y * b.x; }

  template <typename T>
  auto unit(const vec<T> &a) { return a / abs(a); }
  template <typename T>
  auto normal(const vec<T> &p) { return vec<T>(-p.y, p.x); }

  template <typename T>
  auto polar(const T &r, const T &ang) { return vec<T>(r * cos(ang), r * sin(ang)); }

  template <typename T>
  T angle(const vec<T> &a, const vec<T> &b) { return atan2(b.y - a.y, b.x - a.x); }
  template <typename T>
  T phase(const vec<T> &a) { return atan2(a.y, a.x); }

  template <typename T>
  T angle_diff(const vec<T> &a, const vec<T> &b) {
    T r = phase(b) - phase(a);

    if (r < -M_PI)
      return r + 2 * M_PI;
    else if (r > M_PI)
      return r - 2 * M_PI;
    return r;
  }

  template <typename T>
  struct line {
    point<T> from, to;
    line() : from(), to() {}
    line(const point<T> &from, const point<T> &to) : from(from), to(to) {}
  };

  template <typename T>
  using segment = line<T>;

  template <typename T>
  auto unit(const line<T> &a) { return unit(a.to - a.from); }
  template <typename T>
  auto normal(const line<T> &a) { return normal(a.to - a.from); }

  template <typename T>
  auto diff(const segment<T> &a) { return a.to - a.from; }

  template <typename T>
  T abs(const segment<T> &a) { return abs(diff(a)); }

  template <typename T>
  T dot(const line<T> &a, const line<T> &b) { return dot(diff(a), diff(b)); }
  template <typename T>
  T cross(const line<T> &a, const line<T> &b) { return cross(diff(a), diff(b)); }

  template <typename T>
  using polygon = std::vector<point<T>>;

  template <typename T>
  struct circle {
    point<T> center;
    T radius;
    circle() : center(), radius(0) {}
    circle(const point<T> &center, T radius) : center(center), radius(radius) {}
  };

  template <typename T>
  std::ostream &operator<<(std::ostream &s, const vec<T> &a) {
    s << "(" << a.x << ", " << a.y << ")";
    return s;
  }

  template <typename T>
  std::ostream &operator<<(std::ostream &s, const line<T> &a) {
    s << "(" << a.from << " -> " << a.to << ")";
    return s;
  }

  template <typename T>
  std::ostream &operator<<(std::ostream &s, const circle<T> &a) {
    s << "("
      << "center: " << a.center << ", "
      << "radius: " << a.radius << ")";
    return s;
  }
}  // namespace haar_lib
#line 10 "Mylib/Geometry/Float/manhattan_segments_intersections.cpp"

namespace haar_lib {
  template <typename T>
  int manhattan_segments_intersections(std::vector<segment<T>> segs) {
    std::vector<segment<T>> hs;
    std::vector<std::tuple<point<T>, bool, int>> vs;
    int count = 0;

    for (auto s : segs) {
      if (s.from.y == s.to.y) {
        hs.push_back(s);
      } else {
        vs.emplace_back(s.from, s.from.y < s.to.y, count);
        vs.emplace_back(s.to, s.from.y > s.to.y, count);
        ++count;
      }
    }

    std::sort(hs.rbegin(), hs.rend(), [](const auto &a, const auto &b) { return a.from.y < b.from.y; });
    std::sort(vs.rbegin(), vs.rend(), [](const auto &a, const auto &b) { return std::get<0>(a).y < std::get<0>(b).y; });

    __gnu_pbds::tree<
        std::pair<T, int>,
        __gnu_pbds::null_type,
        std::less<std::pair<T, int>>,
        __gnu_pbds::rb_tree_tag,
        __gnu_pbds::tree_order_statistics_node_update>
        set;
    int64_t ans = 0;

    while (true) {
      if (hs.empty() or vs.empty()) break;

      T ymin = std::min(hs.back().from.y, std::get<0>(vs.back()).y);

      std::vector<segment<T>> rs;
      std::vector<std::tuple<point<T>, bool, int>> ps;

      while (not hs.empty() and hs.back().from.y == ymin) {
        rs.push_back(hs.back());
        hs.pop_back();
      }

      while (not vs.empty() and std::get<0>(vs.back()).y == ymin) {
        ps.push_back(vs.back());
        vs.pop_back();
      }

      for (auto [a, b, c] : ps) {
        if (b) set.insert(std::make_pair(a.x, c));
      }

      for (auto [a, b] : rs) {
        auto [x1, x2] = std::minmax(a.x, b.x);

        auto ix1 = set.order_of_key(std::make_pair(x1, 0));
        auto ix2 = set.order_of_key(std::make_pair(x2, INT_MAX));

        ans += ix2 - ix1;
      }

      for (auto [a, b, c] : ps) {
        if (not b) set.erase(std::make_pair(a.x, c));
      }
    }

    return ans;
  }
}  // namespace haar_lib

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