tpl_binTreeOps.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_BINTREEOPS_H
# define TPL_BINTREEOPS_H
 
# include <tpl_binNodeUtils.H>
# include <tpl_binNodeXt.H>
# include <ah-concepts.H>
 
namespace Aleph
{
  template <class Node, class Cmp = Aleph::less<typename Node::key_type>>
    requires StrictWeakOrder<Cmp, typename Node::key_type>
  class BinTree_Operation
  {
  protected:
    Cmp cmp;
 
  public:
    Cmp &key_comp() noexcept { return cmp; }
 
    Cmp &get_compare() noexcept { return cmp; }
 
    using Key = typename Node::key_type; 
 
    using key_type = typename Node::key_type; 
 
    BinTree_Operation(Cmp cmp_ = Cmp()) noexcept : cmp(cmp_)
    { /* empty */
    }
 
    [[nodiscard]] Node * search(Node *root, const Key & key) noexcept
    {
      return searchInBinTree(root, key, cmp);
    }
 
    [[nodiscard]] Node * search_parent(Node *root, const Key & key, Node *& parent) noexcept
    {
      return Aleph::search_parent<Node, Cmp>(root, key, parent, cmp);
    }
 
    [[nodiscard]] Node * search_rank_parent(Node *root, const Key & key) noexcept
    {
      return Aleph::search_rank_parent<Node, Cmp>(root, key, cmp);
    }
 
    [[nodiscard]] Node * insert(Node *& root, Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return root = p;
 
      if (cmp(KEY(p), KEY(root))) // p < root
        {
          if (LLINK(root) != Node::NullPtr) [[likely]]
            __builtin_prefetch(LLINK(root));
          return insert(LLINK(root), p);
        }
      if (cmp(KEY(root), KEY(p))) // p > root
        {
          if (RLINK(root) != Node::NullPtr) [[likely]]
            __builtin_prefetch(RLINK(root));
          return insert(RLINK(root), p);
        }
 
      return Node::NullPtr; // Repeated key ==> no insertion
    }
 
    Node * insert_dup(Node *& root, Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return root = p;
 
      if (cmp(KEY(p), KEY(root))) // p < root
        {
          if (LLINK(root) != Node::NullPtr) [[likely]]
            __builtin_prefetch(LLINK(root));
          return insert_dup(LLINK(root), p);
        }
 
      if (RLINK(root) != Node::NullPtr) [[likely]]
        __builtin_prefetch(RLINK(root));
      return insert_dup(RLINK(root), p);
    }
 
    Node * search_or_insert(Node *& r, Node *p) noexcept
    {
      if (r == Node::NullPtr)
        return r = p;
 
      if (cmp(KEY(p), KEY(r))) // p < root
        {
          if (LLINK(r) != Node::NullPtr) [[likely]]
            __builtin_prefetch(LLINK(r));
          return search_or_insert(LLINK(r), p);
        }
      if (cmp(KEY(r), KEY(p))) // p > root
        {
          if (RLINK(r) != Node::NullPtr) [[likely]]
            __builtin_prefetch(RLINK(r));
          return search_or_insert(RLINK(r), p);
        }
 
      return r; // key found
    }
 
  private:
    bool split_key_rec_helper(Node *root, const Key & key, Node *& ts, Node *& tg)
      noexcept
    {
      if (root == Node::NullPtr)
        {
          ts = tg = Node::NullPtr;
          return true;
        }
 
      if (cmp(key, KEY(root))) // ¿key < KEY(root)?
        {
          if (split_key_rec_helper(LLINK(root), key, ts, LLINK(root)))
            {
              tg = root;
              return true;
            }
          return false;
        }
 
      if (cmp(KEY(root), key)) // ¿key > KEY(root)?
        if (split_key_rec_helper(RLINK(root), key, RLINK(root), tg))
          {
            ts = root;
            return true;
          }
 
      return false;
    }
 
  public:
    bool split_key_rec(Node *& root, const Key & key, Node *& ts, Node *& tg)
      noexcept
    {
      const bool ret = split_key_rec_helper(root, key, ts, tg);
      if (ret)
        root = Node::NullPtr;
      return ret;
    }
 
  private:
    void split_key_dup_rec_helper(Node *root, const typename Node::key_type & key,
                             Node *& ts, Node *& tg) noexcept
    {
      if (root == Node::NullPtr)
        { // Key is not in tree ==> split will succeed
          ts = tg = Node::NullPtr;
          return;
        }
 
      if (cmp(key, KEY(root))) // ¿key < KEY(root)?
        split_key_dup_rec_helper(LLINK(root), key, ts, LLINK(root));
      else if (cmp(KEY(root), key)) // ¿key > KEY(root)?
        split_key_dup_rec_helper(RLINK(root), key, RLINK(root), tg);
      else // key == KEY(root)
        split_key_dup_rec_helper(LLINK(root), key, ts, LLINK(root));
    }
 
  public:
    void split_key_dup_rec(Node *& root, const typename Node::key_type & key,
                           Node *& ts, Node *& tg) noexcept
    {
      split_key_dup_rec_helper(root, key, ts, tg);
      root = Node::NullPtr;
    }
 
    [[nodiscard]] Node * remove(Node *& root, const Key & key) noexcept
    {
      if (root == Node::NullPtr)
        return Node::NullPtr;
 
      if (cmp(key, KEY(root))) // ¿key < KEY(root)?
        return remove(LLINK(root), key);
      if (cmp(KEY(root), key)) // ¿key > KEY(root)?
        return remove(RLINK(root), key);
 
      Node *ret_val = root;
      root = join_exclusive(LLINK(root), RLINK(root));
 
      ret_val->reset();
 
      return ret_val;
    }
 
    Node * insert_root(Node *& root, Node *p) noexcept
    {
      Node *l = Node::NullPtr, *r = Node::NullPtr;
 
      if (not split_key_rec(root, KEY(p), l, r))
        return Node::NullPtr;
 
      LLINK(p) = l;
      RLINK(p) = r;
      root = p;
 
      return root;
    }
 
    Node * insert_dup_root(Node *& root, Node *p) noexcept
    {
      split_key_dup_rec(root, KEY(p), LLINK(p), RLINK(p));
 
      return root = p;
    }
 
    [[nodiscard]] Node * join_preorder(Node *t1, Node *t2, Node *& dup) noexcept
    {
      if (t2 == Node::NullPtr)
        return t1;
 
      Node *l = LLINK(t2);
      Node *r = RLINK(t2);
 
      if (insert(t1, t2) == Node::NullPtr)
        insert(dup, t2);
 
      join_preorder(t1, l, dup);
      join_preorder(t1, r, dup);
 
      return t1;
    }
 
    [[nodiscard]] Node * join(Node *t1, Node *t2, Node *& dup) noexcept
    {
      if (t1 == Node::NullPtr)
        return t2;
 
      if (t2 == Node::NullPtr)
        return t1;
 
      Node *l = LLINK(t1);
      Node *r = RLINK(t1);
 
      t1->reset();
 
      while (insert_root(t2, t1) == Node::NullPtr)
        {
          Node *p = remove(t1, KEY(t1));
 
          assert(p != Node::NullPtr);
 
          insert(dup, p);  // Insert the removed node, not t1
        }
 
      LLINK(t2) = join(l, LLINK(t2), dup);
      RLINK(t2) = join(r, RLINK(t2), dup);
 
      return t2;
    }
 
    void split_key(Node *root, const Key & key, Node *& l, Node *& r) noexcept
    {
      if (root == Node::NullPtr)
        {
          l = r = Node::NullPtr;
          return;
        }
 
      Node **current_parent = nullptr;
      Node **pending_child = nullptr;
      bool current_is_right;
      if (cmp(key, KEY(root)))
        {
          r = root;
          pending_child = &l;
          current_is_right = true;
        }
      else
        {
          l = root;
          pending_child = &r;
          current_is_right = false;
        }
 
      Node *current = root;
      while (current != Node::NullPtr)
        {
          if (cmp(key, KEY(current)))
            { /* current must be in right side */
              if (not current_is_right)
                {
                  current_is_right = not current_is_right;
                  *pending_child = *current_parent; /* change of side */
                  pending_child = current_parent;
                }
 
              current_parent = &LLINK(current);
            }
          else
            { /* current must be in left side */
              if (current_is_right)
                {
                  current_is_right = not current_is_right;
                  *pending_child = *current_parent; /* change of side */
                  pending_child = current_parent;
                }
              current_parent = &RLINK(current);
            }
 
          current = *current_parent;
        }
 
      *pending_child = Node::NullPtr;
      root = Node::NullPtr;
    }
 
    Node * insert_root_rec(Node *root, Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return p; /* insertion in an empty tree */
 
      if (cmp(KEY(p), KEY(root)))
        { /* insert in the left subtree */
          Node *left_branch = insert_root_rec(LLINK(root), p);
          if (left_branch == Node::NullPtr)
            return Node::NullPtr;
 
          LLINK(root) = left_branch;
          root = rotate_to_right(root);
        }
      else if (cmp(KEY(root), KEY(p)))
        { /* insert in the right subtree */
          Node *right_branch = insert_root_rec(RLINK(root), p);
          if (right_branch == Node::NullPtr)
            return Node::NullPtr;
 
          RLINK(root) = right_branch;
          root = rotate_to_left(root);
        }
      else
        return Node::NullPtr; /* duplicated key */
 
      return root;
    }
 
    Node * search_or_insert_root_rec(Node *root, Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return p; // insertion in an empty tree
 
      if (cmp(KEY(p), KEY(root)))
        { // insert in the left subtree
          Node *left_branch = search_or_insert_root_rec(LLINK(root), p);
          if (left_branch == p) // Was there insertion?
            {
              LLINK(root) = left_branch;
              root = rotate_to_right(root);
 
              return p;
            }
 
          return left_branch; // no la hubo
        }
      if (cmp(KEY(root), KEY(p)))
        { // insert in the right subtree
          Node *right_branch = search_or_insert_root_rec(RLINK(root), p);
          if (right_branch == p) //Was there insertion?
            {
              RLINK(root) = right_branch;
              root = rotate_to_left(root);
 
              return p;
            }
 
          return right_branch; // no la hubo
        }
 
      return root;
    }
  };
 
 
  template <class Node,
            class Cmp = Aleph::less<typename Node::key_type>>
  class BinTreeXt_Operation : public BinTree_Operation<Node, Cmp>
  {
  public:
    using Key = typename Node::key_type;
 
    BinTreeXt_Operation(Cmp cmp = Cmp()) noexcept
      : BinTree_Operation<Node, Cmp>(cmp)
    {
      // empty
    }
 
    long inorder_position(Node *r, const Key & key, Node *& p) noexcept
    {
      assert(COUNT(Node::NullPtr) == 0);
 
      if (r == Node::NullPtr)
        return -1;
 
      if (this->cmp(key, KEY(r)))
        {
          if (LLINK(r) != Node::NullPtr) [[likely]]
            __builtin_prefetch(LLINK(r));
          return inorder_position(LLINK(r), key, p);
        }
      if (this->cmp(KEY(r), key))
        {
          if (RLINK(r) != Node::NullPtr) [[likely]]
            __builtin_prefetch(RLINK(r));
          long ret = inorder_position(RLINK(r), key, p);
          if (ret != -1)
            return ret + COUNT(LLINK(r)) + 1;
          return ret;
        }
      p = r;
      return COUNT(LLINK(r));
    }
 
    long find_position(Node *r, const Key & key, Node *& p) noexcept
    {
      assert(COUNT(Node::NullPtr) == 0);
 
      Node *parent = nullptr;
      long pos = COUNT(LLINK(r));
 
      while (r != Node::NullPtr)
        if (const auto & kr = KEY(r); this->cmp(key, kr)) // key < KEY(r): go left
          {
            Node *next = LLINK(r);
            __builtin_prefetch(next, 0, 3);
 
            parent = r;
            r = next;
 
            // After moving left: new position is COUNT(LLINK(new_r))
            // which equals old_pos - COUNT(RLINK(new_r)) - 1
            pos -= (COUNT(RLINK(r)) + 1);
          }
        else if (this->cmp(kr, key)) // KEY(r) < key: go right
          {
            Node *next = RLINK(r);
            __builtin_prefetch(next, 0, 3);
 
            parent = r;
            r = next;
 
            // After moving right: add parent + parent's left subtree
            pos += (COUNT(LLINK(r)) + 1);
          }
        else
          {
            p = r;
            return pos;
          }
 
      p = parent;
      return pos;
    }
 
 
    bool split_key_rec(Node *root, const Key & key, Node *& l, Node *& r)
      noexcept
    {
      if (root == Node::NullPtr)
        {
          l = r = Node::NullPtr;
          return true;
        }
 
      if (this->cmp(key, KEY(root)))
        {
          if (not split_key_rec(LLINK(root), key, l, LLINK(root)))
            return false;
 
          r = root;
          COUNT(r) -= COUNT(l);
        }
      else if (this->cmp(KEY(root), key))
        {
          if (not split_key_rec(RLINK(root), key, RLINK(root), r))
            return false;
 
          l = root;
          COUNT(l) -= COUNT(r);
        }
      else
        return false; // Duplicate Key
 
      return true;
    }
 
    void split_key_dup_rec(Node *root, const Key & key, Node *& l, Node *& r)
      noexcept
    {
      if (root == Node::NullPtr)
        {
          l = r = Node::NullPtr;
          return;
        }
 
      if (this->cmp(key, KEY(root)))
        {
          split_key_dup_rec(LLINK(root), key, l, LLINK(root));
          r = root;
          COUNT(r) -= COUNT(l);
        }
      else
        {
          split_key_dup_rec(RLINK(root), key, RLINK(root), r);
          l = root;
          COUNT(l) -= COUNT(r);
        }
    }
 
    Node * insert_root(Node *& root, Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return p;
 
      if (not split_key_rec(root, KEY(p), LLINK(p), RLINK(p)))
        return Node::NullPtr;
 
      COUNT(p) = COUNT(LLINK(p)) + COUNT(RLINK(p)) + 1;
      root = p;
 
      return p;
    }
 
    Node * insert_dup_root(Node *& root, Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return p;
 
      split_key_dup_rec(root, KEY(p), LLINK(p), RLINK(p));
 
      COUNT(p) = COUNT(LLINK(p)) + COUNT(RLINK(p)) + 1;
 
      return root = p;
    }
  };
} // end namespace Aleph
 
# endif // TPL_BINTREEOPS_H