tpl_splay_tree.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_SPLAY_TREE_H
# define TPL_SPLAY_TREE_H
 
# include <tpl_binNode.H>
# include <tpl_binNodeUtils.H>
# include <ah-concepts.H>
 
using namespace Aleph;
 
 
template <template <class> class NodeType, typename Key, class Compare>
    requires StrictWeakOrder<Compare, Key>
class GenTdSplayTree
{
public:
  using Node = NodeType<Key>;
 
private:
  Node headnode;
  Node *head, *&root;
  Compare cmp;
  static constexpr signed char CmpLess = -1;
  static constexpr signed char CmpEqual = 0;
  static constexpr signed char CmpGreater = 1;
 
  signed char splay_impl(const Key & key) noexcept
  {
    Node headNode;
    Node *l = &headNode;
    Node *r = &headNode;
    Node *t = root;
    signed char cmp_result = CmpEqual;
 
    while (true)
      {
        if (const Key & tk = KEY(t); cmp(key, tk))  // key < tk: go left
          {
            cmp_result = CmpLess;
            if (LLINK(t) == Node::NullPtr) [[unlikely]]
              break;
 
            if (cmp(key, KEY(LLINK(t))))  // zig-zig case
              {
                t = rotate_to_right(t);
                if (LLINK(t) == Node::NullPtr) [[unlikely]]
                  break;
              }
 
            LLINK(r) = t;
            r = t;
            t = LLINK(t);
          }
        else if (cmp(tk, key))  // tk < key: go right
          {
            cmp_result = CmpGreater;
            if (RLINK(t) == Node::NullPtr) [[unlikely]]
              break;
 
            if (cmp(KEY(RLINK(t)), key))  // zig-zig case
              {
                t = rotate_to_left(t);
                if (RLINK(t) == Node::NullPtr) [[unlikely]]
                  break;
              }
 
            RLINK(l) = t;
            l = t;
            t = RLINK(t);
          }
        else [[unlikely]]  // key == tk: found
          {
            cmp_result = CmpEqual;
            break;
          }
      }
 
    /* reassembling of subtrees in one with current as root */
    RLINK(l) = LLINK(t);
    LLINK(r) = RLINK(t);
    LLINK(t) = headNode.getR();
    RLINK(t) = headNode.getL();
 
    root = t;
 
    return cmp_result;
  }
 
public:
  using key_type = Key;
 
  Compare &key_comp() noexcept { return cmp; }
 
  Compare &get_compare() noexcept { return key_comp(); }
 
  void splay(const Key & key) noexcept
  {
    (void) splay_impl(key);
  }
 
  GenTdSplayTree(Compare __cmp = Compare()) noexcept
    : head(&headnode), root(headnode.getR()), cmp(__cmp)
  {
    // Empty
  }
 
  void swap(GenTdSplayTree & tree) noexcept
  {
    std::swap(root, tree.root);
    std::swap(cmp, tree.cmp);
  }
 
  virtual ~GenTdSplayTree() = default;
 
private:
  Node * __insert(Node *p) noexcept
  {
    const Key & pk = KEY(p);
    const Key & rk = KEY(root);
    if (cmp(pk, rk))
      { /* root is predecessor of p */
        LLINK(p) = LLINK(root);
        RLINK(p) = root;
        LLINK(root) = Node::NullPtr;
      }
    else
      { /* root is successor of p */
        RLINK(p) = RLINK(root);
        LLINK(p) = root;
        RLINK(root) = Node::NullPtr;
      }
    return root = p; // inserted node become root
  }
 
public:
  Node * insert(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(LLINK(p) == Node::NullPtr and RLINK(p) == Node::NullPtr);
 
    /* test insertion in empty tree */
    if (root == Node::NullPtr)
      return root = p;
 
    const Key & key = KEY(p);
 
    const signed char cmp_result = splay_impl(key);
 
    if (cmp_result == CmpEqual)
      return nullptr; // item is already in tree
 
    return __insert(p);
  }
 
  Node * insert_dup(Node *p) noexcept
  {
    assert(p != Node::NullPtr);
    assert(LLINK(p) == Node::NullPtr and RLINK(p) == Node::NullPtr);
 
    /* test insertion in empty tree */
    if (root == Node::NullPtr)
      return root = p;
 
    splay_impl(KEY(p));
 
    return __insert(p);
  }
 
  Node * search(const Key & key) noexcept
  {
    if (root == Node::NullPtr)
      return nullptr;
      
    const signed char cmp_result = splay_impl(key);
 
    return cmp_result == CmpEqual ? root : nullptr;
  }
 
  Node * search_or_insert(Node *p) noexcept
  {
    if (root == Node::NullPtr)
      return root = p;
 
    const Key & key = KEY(p);
    const signed char cmp_result = splay_impl(key);
    if (cmp_result == CmpEqual)
      return root;
 
    return __insert(p);
  }
 
  Node * remove(const Key & key) noexcept
  {
    if (root == Node::NullPtr)
      return nullptr;
 
    const signed char cmp_result = splay_impl(key);
    if (cmp_result != CmpEqual)
      return nullptr; /* key not found */
 
    Node *ret_val = root; /* store node to delete */
 
    if (LLINK(root) == Node::NullPtr)
      root = RLINK(root);
    else
      {
        Node *p = RLINK(root);
        root = LLINK(root);
        splay_impl(key);
        RLINK(root) = p;
      }
 
    ret_val->reset();
 
    return ret_val;
  }
 
  Node *&getRoot() noexcept
  {
    return root;
  }
 
  [[nodiscard]] bool verify() const { return check_bst(root, cmp); }
 
  struct Iterator : public BinNodeInfixIterator<Node>
  {
    Iterator() noexcept = default;
    Iterator(GenTdSplayTree & t) : BinNodeInfixIterator<Node>(t.getRoot()) {}
  };
};
 
 
template <typename Key, class Compare = Aleph::less<Key>>
    requires StrictWeakOrder<Compare, Key>
struct Splay_Tree : public GenTdSplayTree<BinNode, Key, Compare>
{
  using Base = GenTdSplayTree<BinNode, Key, Compare>;
  using Base::Base;
};
 
 
template <typename Key, class Compare = Aleph::less<Key>>
    requires StrictWeakOrder<Compare, Key>
struct Splay_Tree_Vtl : public GenTdSplayTree<BinNodeVtl, Key, Compare>
{
  using Base = GenTdSplayTree<BinNodeVtl, Key, Compare>;
  using Base::Base;
};
 
 
#endif /* TPL_SPLAY_TREE_H */