tpl_2dtree.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef TPL_2DTREE_H
# define TPL_2DTREE_H
 
# include <point.H>
# include <htlist.H>
# include <ahDefs.H> // For Empty_Class
 
using namespace Aleph;
 
template <typename T = Empty_Class>
class K2Tree
{
  struct Node
  {
    Point point; 
    Rectangle rect; 
    Node *lb; 
    Node *rt; 
 
    Node(const Point & __point) noexcept
      : point(__point), lb(nullptr), rt(nullptr)
    {
      // empty
    }
 
    void set_rect(const Geom_Number & xmin, const Geom_Number & ymin,
                  const Geom_Number & xmax, const Geom_Number & ymax) noexcept
    {
      rect.set_rect(xmin, ymin, xmax, ymax);
    }
 
    void set_rect(const Point & pmin, const Point & pmax) noexcept
    {
      rect.set_rect(pmin.get_x(), pmin.get_y(), pmax.get_x(), pmax.get_y());
    }
 
    [[nodiscard]] const Geom_Number &xmin() const noexcept { return rect.get_xmin(); }
    [[nodiscard]] const Geom_Number &ymin() const noexcept { return rect.get_ymin(); }
    [[nodiscard]] const Geom_Number &xmax() const noexcept { return rect.get_xmax(); }
    [[nodiscard]] const Geom_Number &ymax() const noexcept { return rect.get_ymax(); }
    [[nodiscard]] const Geom_Number &x() const noexcept { return point.get_x(); }
    [[nodiscard]] const Geom_Number &y() const noexcept { return point.get_y(); }
  };
 
  Point pmin; 
  Point pmax; 
  size_t N; 
  Node *root; 
 
public:
  K2Tree() : pmin(0, 0), pmax(0, 0), N(0), root(nullptr)
  {
    // empty
  }
 
  K2Tree(const Point & __pmin, const Point & __pmax)
    : pmin(__pmin), pmax(__pmax), N(0), root(nullptr)
  {
    // empty
  }
 
  K2Tree(const Geom_Number & xmin, const Geom_Number & ymin,
         const Geom_Number & xmax, const Geom_Number & ymax)
    : pmin(xmin, ymin), pmax(xmax, ymax), N(0), root(nullptr)
  {
    // empty
  }
 
  K2Tree(const K2Tree &) = delete;
 
  K2Tree &operator =(const K2Tree &) = delete;
 
  [[nodiscard]] constexpr bool is_empty() const noexcept { return N == 0; }
 
  [[nodiscard]] constexpr size_t size() const noexcept { return N; }
 
private:
  Node * lr_insert(Node *root, const Point & p)
  {
    if (root == nullptr)
      return new Node(p);
 
    Node *ret_val = nullptr;
    if (p.get_x() == root->x())
      {
        if (p.get_y() == root->y())
          return nullptr; // Duplicate point
 
        ret_val = bu_insert(root->rt, p);
        if (ret_val != nullptr)
          {
            root->rt = ret_val; // Node was inserted
            root->rt->set_rect(root->x(), root->ymin(),
                               root->xmax(), root->ymax());
 
            return root;
          }
 
        return nullptr;
      }
 
    if (p.get_x() < root->x())
      {
        ret_val = bu_insert(root->lb, p);
        if (ret_val != nullptr)
          {
            root->lb = ret_val;
            root->lb->set_rect(root->xmin(), root->ymin(),
                               root->x(), root->ymax());
 
            return root;
          }
        else
          return nullptr;
      }
 
    ret_val = bu_insert(root->rt, p);
    if (ret_val != nullptr)
      {
        root->rt = ret_val;
        root->rt->set_rect(root->x(), root->ymin(),
                           root->xmax(), root->ymax());
 
        return root;
      }
 
    return nullptr;
  }
 
  Node * bu_insert(Node *root, const Point & p)
  {
    if (root == nullptr)
      return new Node(p);
 
    Node *ret_val = nullptr;
    if (p.get_y() == root->y())
      {
        if (p.get_x() == root->x())
          return nullptr; // Duplicate point
 
        ret_val = lr_insert(root->rt, p);
        if (ret_val != nullptr)
          {
            root->rt = ret_val; // Node was inserted
            root->rt->set_rect(root->xmin(), root->y(),
                               root->xmax(), root->ymax());
 
            return root;
          }
 
        return nullptr;
      }
 
    if (p.get_y() < root->y())
      {
        ret_val = lr_insert(root->lb, p);
        if (ret_val != nullptr)
          {
            root->lb = ret_val;
            root->lb->set_rect(root->xmin(), root->ymin(),
                               root->xmax(), root->y());
            return root;
          }
        return nullptr;
      }
 
    ret_val = lr_insert(root->rt, p);
    if (ret_val != nullptr)
      {
        root->rt = ret_val;
        root->rt->set_rect(root->xmin(), root->y(),
                           root->xmax(), root->ymax());
 
        return root;
      }
 
    return nullptr;
  }
 
public:
  Point * insert(const Point & p)
  {
    if (root == nullptr)
      {
        root = new Node(p);
        root->set_rect(pmin, pmax);
        ++N;
 
        return &root->point;
      }
 
    Node *ret = lr_insert(root, p);
    if (ret == nullptr)
      return nullptr;
 
    ++N;
 
    return &root->point; // FIX: Was returning nullptr
  }
 
private:
  static Node * bu_search(Node *root, const Point & p) noexcept
  {
    if (root == nullptr)
      return nullptr;
 
    if (root->y() == p.get_y())
      {
        if (root->x() == p.get_x())
          return root;
 
        return lr_search(root->rt, p);
      }
 
    if (p.get_y() < root->y())
      return lr_search(root->lb, p);
    return lr_search(root->rt, p);
  }
 
  static Node * lr_search(Node *root, const Point & p) noexcept
  {
    if (root == nullptr)
      return nullptr;
 
    if (root->x() == p.get_x())
      {
        if (root->y() == p.get_y())
          return root;
 
        return bu_search(root->rt, p);
      }
 
    if (p.get_x() < root->x())
      return bu_search(root->lb, p);
    return bu_search(root->rt, p);
  }
 
public:
  [[nodiscard]] bool contains(const Point & p) const noexcept
  {
    return lr_search(root, p) != nullptr;
  }
 
private:
  static void range(Node *root, const Rectangle & rect, DynList<Point> *q)
  {
    if (root == nullptr)
      return;
 
    if (not root->rect.intersects(rect))
      return;
 
    const Point & point = root->point;
    if (rect.contains(point))
      q->append(point);
 
    range(root->lb, rect, q);
    range(root->rt, rect, q);
  }
 
public:
  void range(const Rectangle & rect, DynList<Point> *l)
  {
    if (N == 0)
      return;
 
    range(root, rect, l);
  }
 
private:
  Node *min_node; 
  Geom_Number min_dist2; 
 
  void lr_nearest(Node *root, const Point & p) noexcept
  {
    if (root == nullptr)
      return;
 
    if (root->rect.distance_squared_to(p) > min_dist2)
      return;
 
    if (const Geom_Number d2 = root->point.distance_squared_to(p); d2 < min_dist2)
      {
        min_dist2 = d2;
        min_node = root;
      }
 
    if (p.get_x() < root->x()) // Is p to left of this?
      {
        bu_nearest(root->lb, p);
        bu_nearest(root->rt, p);
      }
    else
      {
        bu_nearest(root->rt, p);
        bu_nearest(root->lb, p);
      }
  }
 
  void bu_nearest(Node *root, const Point & p) noexcept
  {
    if (root == nullptr)
      return;
 
    if (root->rect.distance_squared_to(p) > min_dist2)
      return;
 
    if (const Geom_Number d2 = root->point.distance_squared_to(p); d2 < min_dist2)
      {
        min_dist2 = d2;
        min_node = root;
      }
 
    if (p.get_y() < root->y()) // Is p below this?
      {
        lr_nearest(root->lb, p);
        lr_nearest(root->rt, p);
      }
    else
      {
        lr_nearest(root->rt, p);
        lr_nearest(root->lb, p);
      }
  }
 
public:
  [[nodiscard]] Point nearest(const Point & p) noexcept
  {
    if (N == 0)
      return NullPoint;
 
    // Initialize with distance to root (mpq_class doesn't have max())
    min_node = root;
    min_dist2 = root->point.distance_squared_to(p);
 
    lr_nearest(root, p);
 
    return min_node != nullptr ? min_node->point : NullPoint;
  }
 
private:
  void destroy_tree(Node *node) noexcept
  {
    if (node == nullptr)
      return;
 
    destroy_tree(node->lb);
    destroy_tree(node->rt);
    delete node;
  }
 
public:
  ~K2Tree()
  {
    destroy_tree(root);
  }
};
 
# endif // TPL_2DTREE_H