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
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  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 <optional>
# include <algorithm>
# include <htlist.H>
# include <ahSort.H>
# include <tpl_array.H>
# include <ahDefs.H> // For Empty_Class
# include <utility>
 
using Aleph::Empty_Class;
 
template <typename T = Empty_Class>
class K2Tree
{
  struct Node
  {
    Point point_; 
    Rectangle rect_; 
    Node *lb_; 
    Node *rt_; 
 
    Node(Point p) noexcept
      : point_(std::move(p)), 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(Point pmin, Point pmax)
    : pmin_(std::move(pmin)), pmax_(std::move(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;
 
  K2Tree(K2Tree && other) noexcept
    : pmin_(std::move(other.pmin_)), pmax_(std::move(other.pmax_)),
      N_(other.N_), root_(other.root_)
  {
    other.N_ = 0;
    other.root_ = nullptr;
  }
 
  K2Tree &operator =(K2Tree && other) noexcept
  {
    if (this != &other)
      {
        destroy_tree(root_);
        pmin_ = other.pmin_;
        pmax_ = other.pmax_;
        N_ = other.N_;
        root_ = other.root_;
        other.N_ = 0;
        other.root_ = nullptr;
      }
    return *this;
  }
 
  [[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;
          }
        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:
  bool insert(const Point & p)
  {
    if (root_ == nullptr)
      {
        root_ = new Node(p);
        root_->set_rect(pmin_, pmax_);
        ++N_;
        return true;
      }
 
    Node *ret = lr_insert(root_, p);
    if (ret == nullptr)
      return false;
 
    ++N_;
    return true;
  }
 
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;
 
    if (const Point & point = root->point_; 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) const
  {
    if (N_ == 0)
      return;
 
    range(root_, rect, l);
  }
 
private:
  struct NearestState
  {
    Node *node = nullptr;
    Geom_Number dist2;
  };
 
  static void lr_nearest(Node *root, const Point & p,
                         NearestState & st) noexcept
  {
    if (root == nullptr)
      return;
 
    if (root->rect_.distance_squared_to(p) > st.dist2)
      return;
 
    if (const Geom_Number d2 = root->point_.distance_squared_to(p); d2 < st.dist2)
      {
        st.dist2 = d2;
        st.node = root;
      }
 
    if (p.get_x() < root->x()) // Is p to left of this?
      {
        bu_nearest(root->lb_, p, st);
        bu_nearest(root->rt_, p, st);
      }
    else
      {
        bu_nearest(root->rt_, p, st);
        bu_nearest(root->lb_, p, st);
      }
  }
 
  static void bu_nearest(Node *root, const Point & p,
                         NearestState & st) noexcept
  {
    if (root == nullptr)
      return;
 
    if (root->rect_.distance_squared_to(p) > st.dist2)
      return;
 
    if (const Geom_Number d2 = root->point_.distance_squared_to(p); d2 < st.dist2)
      {
        st.dist2 = d2;
        st.node = root;
      }
 
    if (p.get_y() < root->y()) // Is p below this?
      {
        lr_nearest(root->lb_, p, st);
        lr_nearest(root->rt_, p, st);
      }
    else
      {
        lr_nearest(root->rt_, p, st);
        lr_nearest(root->lb_, p, st);
      }
  }
 
public:
  [[nodiscard]] std::optional<Point> nearest(const Point & p) const noexcept
  {
    if (N_ == 0)
      return std::nullopt;
 
    NearestState st;
    st.node = root_;
    st.dist2 = root_->point_.distance_squared_to(p);
 
    lr_nearest(root_, p, st);
 
    return st.node != nullptr ? std::optional<Point>(st.node->point_) : std::nullopt;
  }
 
  template <typename Op>
  void for_each(Op && op) const
  {
    for_each_node(root_, std::forward<Op>(op));
  }
 
  [[nodiscard]] static K2Tree build(Array<Point> points,
                                    const Point & pmin,
                                    const Point & pmax)
  {
    // Sort lexicographically and remove duplicates
    if (points.size() > 1)
      {
        Aleph::in_place_sort(points, [](const Point & a, const Point & b)
                             {
                               if (a.get_x() < b.get_x()) return true;
                               if (b.get_x() < a.get_x()) return false;
                               return a.get_y() < b.get_y();
                             });
 
        size_t w = 1;
        for (size_t r = 1; r < points.size(); ++r)
          if (points(r) != points(w - 1))
            points(w++) = points(r);
 
        while (points.size() > w)
          static_cast<void>(points.remove_last());
      }
 
    K2Tree tree(pmin, pmax);
    if (points.is_empty())
      return tree;
 
    tree.root_ = build_balanced(points, 0, points.size(), true,
                                pmin, pmax);
    tree.N_ = points.size();
    return tree;
  }
 
private:
  static Node * build_balanced(Array<Point> & pts,
                               const size_t lo, const size_t hi,
                               const bool split_x,
                               const Point & rmin, const Point & rmax)
  {
    if (lo >= hi)
      return nullptr;
 
    const size_t mid = lo + (hi - lo) / 2;
 
    if (split_x)
      std::nth_element(&pts(lo), &pts(mid), &pts(hi),
                       [](const Point & a, const Point & b)
                         {
                           return a.get_x() < b.get_x();
                         });
    else
      std::nth_element(&pts(lo), &pts(mid), &pts(hi),
                       [](const Point & a, const Point & b)
                         {
                           return a.get_y() < b.get_y();
                         });
 
    // Ensure the left partition [lo, root_pos) has only elements with
    // split-coord strictly less than the median, matching the search
    // invariant (equal goes right).
    const Geom_Number mv = split_x ? pts(mid).get_x() : pts(mid).get_y();
 
    size_t strict_end = lo;
    for (size_t i = lo; i < mid; ++i)
      if (const Geom_Number v = split_x ? pts(i).get_x() : pts(i).get_y(); v < mv)
        {
          if (i != strict_end)
            {
              const Point tmp = pts(i);
              pts(i) = pts(strict_end);
              pts(strict_end) = tmp;
            }
          ++strict_end;
        }
 
    // If equal-valued elements were found in [strict_end, mid), move
    // the median to strict_end so that those elements fall into the
    // right subtree.
    size_t root_pos = mid;
    if (strict_end < mid)
      {
        const Point median_pt = pts(mid);
        pts(mid) = pts(strict_end);
        pts(strict_end) = median_pt;
        root_pos = strict_end;
      }
 
    Node *node = new Node(pts(root_pos));
    node->set_rect(rmin, rmax);
 
    if (split_x)
      {
        node->lb_ = build_balanced(pts, lo, root_pos, false,
                                   rmin, Point(node->x(), rmax.get_y()));
        node->rt_ = build_balanced(pts, root_pos + 1, hi, false,
                                   Point(node->x(), rmin.get_y()), rmax);
      }
    else
      {
        node->lb_ = build_balanced(pts, lo, root_pos, true,
                                   rmin, Point(rmax.get_x(), node->y()));
        node->rt_ = build_balanced(pts, root_pos + 1, hi, true,
                                   Point(rmin.get_x(), node->y()), rmax);
      }
 
    return node;
  }
 
  template <typename Op>
  static void for_each_node(const Node *node, Op && op)
  {
    if (node == nullptr)
      return;
 
    for_each_node(node->lb_, op);
    op(node->point_);
    for_each_node(node->rt_, op);
  }
 
  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