tpl_avl.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
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  copies of the Software, and to permit persons to whom the Software is
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*/
 
 
# ifndef TPL_AVL_H
# define TPL_AVL_H
 
# include <algorithm>
# include <ahFunction.H>
# include <tpl_arrayStack.H>
# include <avlNode.H>
# include <tpl_binNodeUtils.H>
 
using namespace Aleph;
 
namespace Aleph
{
  template <template <typename> class NodeType, typename Key, class Compare>
  class Gen_Avl_Tree
  {
  public:
    using Node = NodeType<Key>; 
 
  private:
    FixedStack<Node *> avl_stack;
    Node head_node;
    Node *head_ptr;
    Node *& root;
    Compare cmp;
 
    bool avl_stack_empty() noexcept { return avl_stack.top() == head_ptr; }
 
    void clean_avl_stack() noexcept { avl_stack.popn(avl_stack.size() - 1); }
 
    Node * search_and_stack_avl(const Key & key,
                                signed char & cmp_result) noexcept
    {
      assert(avl_stack_empty());
 
      Node *p = root;
      Node *candidate = nullptr;  // Tracks potential duplicate when going right
      size_t candidate_pos = 0;   // Stack size when candidate was set
 
      do // descend searching for key and push the search path
        {
          avl_stack.push(p);
          if (cmp(key, KEY(p)))  // key < KEY(p)
            {
              cmp_result = CmpLess;
              p = LLINK(p);
              // Prefetch only the child we'll visit next iteration
              if (p != Node::NullPtr) [[likely]]
                __builtin_prefetch(p);
            }
          else  // key >= KEY(p), could be equal
            {
              candidate = p;
              candidate_pos = avl_stack.size();
              cmp_result = CmpGreater;
              p = RLINK(p);
              // Prefetch only the child we'll visit next iteration
              if (p != Node::NullPtr) [[likely]]
                __builtin_prefetch(p);
            }
        }
      while (p != Node::NullPtr);
 
      // Optimistic duplicate check: when going right, key >= KEY(candidate)
      // If also KEY(candidate) >= key (i.e., not less), then key == KEY(candidate)
      if (candidate != nullptr and not cmp(KEY(candidate), key)) [[unlikely]]
        {
          cmp_result = CmpEqual;
          // Truncate stack: remove nodes pushed after candidate
          avl_stack.popn(avl_stack.size() - candidate_pos);
          return candidate;
        }
 
      return avl_stack.top();
    }
 
    Node * search_dup_and_stack_avl(const Key & key,
                                    signed char & cmp_result) noexcept
    {
      assert(avl_stack_empty());
      cmp_result = CmpEqual;
 
      Node *p = root;
      do // descend searching for key and push the search path
        {
          avl_stack.push(p);
          if (cmp(key, KEY(p))) // key < KEY(p)?
            {
              cmp_result = CmpLess;
              p = LLINK(p);
              // Prefetch only the child we'll visit next iteration
              if (p != Node::NullPtr) [[likely]]
                __builtin_prefetch(p);
            }
          else // key >= KEY(p)
            {
              cmp_result = CmpGreater;
              p = RLINK(p);
              // Prefetch only the child we'll visit next iteration
              if (p != Node::NullPtr) [[likely]]
                __builtin_prefetch(p);
            }
        }
      while (p != Node::NullPtr);
 
      return avl_stack.top();
    }
 
    [[gnu::always_inline]] static Node * rotateLeft(Node *p) noexcept
    {
      assert(DIFF(p) == 2);
      assert(RLINK(p) != Node::NullPtr);
 
      Node *q = RLINK(p);
      RLINK(p) = LLINK(q);
      LLINK(q) = p;
 
      if (DIFF(q) == 0) // balance factors adjustment
        { // this case happens during deletion
          DIFF(q) = -1;
          DIFF(p) = 1;
        }
      else
        DIFF(q) = DIFF(p) = 0;
 
      return q;
    }
 
    [[gnu::always_inline]] static Node * rotateRight(Node *p) noexcept
    {
      assert(DIFF(p) == -2);
      assert(LLINK(p) != Node::NullPtr);
 
      Node *q = LLINK(p);
      LLINK(p) = RLINK(q);
      RLINK(q) = p;
 
      if (DIFF(q) == 0) // balance factors adjustment
        { // this case happens during deletion
          DIFF(q) = 1;
          DIFF(p) = -1;
        }
      else
        DIFF(q) = DIFF(p) = 0;
 
      return q;
    }
 
    [[gnu::always_inline]] static Node * doubleRotateLeft(Node *p) noexcept
    {
      assert(DIFF(p) == 2 or DIFF(p) == -2);
      assert(RLINK(p) != Node::NullPtr and LLINK(RLINK(p)) != Node::NullPtr);
 
      Node *q = RLINK(p);
      Node *r = LLINK(q);
      RLINK(p) = LLINK(r);
      LLINK(q) = RLINK(r);
      LLINK(r) = p;
      RLINK(r) = q;
 
      unsigned char b; // logical height of r's left child
      unsigned char c; // logical height of r's right child
 
      // Determine logical heights of p, q and r
      if (DIFF(r) == 1) // ==> c > b ==> c-b == 1
        {
          c = 1;
          b = 0;
        }
      else if (DIFF(r) == -1) // ==> c < b ==> c-b = -1
        {
          c = 0;
          b = 1;
        }
      else
        c = b = 1;
 
      // balance factors adjustment
      DIFF(r) = 0;
      DIFF(p) = b - 1; // logical height of p's left child is 1
      DIFF(q) = 1 - c; // logical height of q's right child is 1
 
      return r;
    }
 
    [[gnu::always_inline]] static Node * doubleRotateRight(Node *p) noexcept
    {
      assert(DIFF(p) == 2 or DIFF(p) == -2);
      assert(LLINK(p) != Node::NullPtr and RLINK(LLINK(p)) != Node::NullPtr);
 
      Node *q = LLINK(p);
      Node *r = RLINK(q);
      LLINK(p) = RLINK(r);
      RLINK(q) = LLINK(r);
      RLINK(r) = p;
      LLINK(r) = q;
 
      unsigned char b; // logical height of r's left child
      unsigned char c; // logical height of r's right child
 
      // determine logical heights of children of p, q and r
      if (DIFF(r) == 1) // ==> c > b ==> c-b == 1
        {
          c = 1;
          b = 0;
        }
      else if (DIFF(r) == -1) // ==> c < b ==> c-b == -1
        {
          c = 0;
          b = 1;
        }
      else
        c = b = 1;
 
      // balance factors adjustment
      DIFF(r) = 0;
      DIFF(p) = 1 - c; // logical height of p's right child is 1
      DIFF(q) = b - 1; // logical height of p's left child is 1
 
      return r;
    }
 
    enum Rotation_Type
    {
      ROTATE_LEFT, ROTATE_RIGHT, DOUBLE_ROTATE_LEFT, DOUBLE_ROTATE_RIGHT
    };
 
    static Rotation_Type rotation_type(Node *p) noexcept
    {
      assert(DIFF(p) == 2 or DIFF(p) == -2);
 
      Node *pc; // saves p's child
      if (DIFF(p) == 2) // to the left
        {
          pc = RLINK(p);
          if (DIFF(pc) == 1 or DIFF(pc) == 0)
            return ROTATE_LEFT;
 
          return DOUBLE_ROTATE_LEFT;
        }
 
      pc = LLINK(p);
      if (DIFF(pc) == -1 or DIFF(pc) == 0)
        return ROTATE_RIGHT;
 
      return DOUBLE_ROTATE_RIGHT;
    }
 
    static Node * restore_avl(Node *p, Node *pp) noexcept
    {
      assert(LLINK(pp) == p or RLINK(pp) == p);
      assert(DIFF(p) == -2 or DIFF(p) == 2);
 
      Node **link = LLINK(pp) == p ? &LLINK(pp) : &RLINK(pp);
      switch (rotation_type(p))
        {
        case ROTATE_LEFT: return *link = rotateLeft(p);
        case ROTATE_RIGHT: return *link = rotateRight(p);
        case DOUBLE_ROTATE_LEFT: return *link = doubleRotateLeft(p);
        case DOUBLE_ROTATE_RIGHT: return *link = doubleRotateRight(p);
 
        default:
          AH_ERROR("Invalid rotation type");
          break;
        }
 
      return nullptr;
    }
 
    void restore_avl_after_insertion(Node *p) noexcept
    {
      Node *pp = avl_stack.pop(); // parent of the inserted node
      if (LLINK(pp) == p) // adjust parent's balance factor
        --DIFF(pp);
      else
        ++DIFF(pp);
 
      if (DIFF(pp) == 0)
        { // in this case, the height of pp's ancestor does not increase
          clean_avl_stack();
          return;
        }
 
      if (avl_stack_empty())
        return; // pp is the root
      do // search a node whose balance factor becomes 0
        {
          Node *gpp = avl_stack.pop(); // parent of pp
          // update balance factors
          if (LLINK(gpp) == pp) // AH_ERROR if (Compare () (key, KEY(gpp)))
            --DIFF(gpp);
          else
            ++DIFF(gpp);
 
          if (DIFF(gpp) == 0)
            break; // no rebalancing is needed
          if (DIFF(gpp) == -2 or DIFF(gpp) == 2) // AVL violation?
            { // yes ==> rebalancing is required
              Node *ggpp = avl_stack.pop();
              restore_avl(gpp, ggpp);
              break;
            }
 
          pp = gpp; // AH_ERROR; add
        }
      while (not avl_stack_empty());
 
      clean_avl_stack();
    }
 
    Node * swapWithSuccessor(Node *p, Node *& pp) noexcept
    { // Reference to the stack top, since p will be swapped with its
      // successor and the successor will take p's position in the stack
      Node *& ref_to_stack_top = avl_stack.top();
 
      Node *fSucc = p; // successor's parent
      Node *succ = RLINK(p); // search starts from RLINK(p)
 
      avl_stack.push(succ);
 
      // find the successor while updating the stack
      while (LLINK(succ) != Node::NullPtr) // descend as far left as possible
        {
          fSucc = succ;
          succ = LLINK(succ);
          avl_stack.push(succ);
        }
 
      // update old stack entry occupied by p: it is equivalent to swapping
      // the old top (before searching succ) with the current one
      ref_to_stack_top = succ;
      avl_stack.top() = p;
      if (LLINK(pp) == p) // update pp's new child (successor)
        LLINK(pp) = succ;
      else
        RLINK(pp) = succ;
 
      LLINK(succ) = LLINK(p); // swap left subtrees
      LLINK(p) = Node::NullPtr;
      if (RLINK(p) == succ) // update right subtrees
        { // successor is exactly p's right child
          RLINK(p) = RLINK(succ);
          RLINK(succ) = p;
          pp = succ;
        }
      else
        { // successor is the leftmost descendant of RLINK(p)
          Node *succr = RLINK(succ);
          RLINK(succ) = RLINK(p);
          LLINK(fSucc) = p;
          RLINK(p) = succr;
          pp = fSucc;
        }
 
      DIFF(succ) = DIFF(p); // swap balance factors
 
      return succ;
    }
 
    void restore_avl_after_deletion(bool left_deficit) noexcept
    {
      Node *pp = avl_stack.top(1); // parent of p
      Node *ppp = avl_stack.popn(3); // remove from stack p, parent and grandparent
      while (true)
        { // update balance factors
          if (left_deficit) // AH_ERROR Compare () (key, KEY(pp)))
            ++DIFF(pp);
          else
            --DIFF(pp);
 
          if (DIFF(pp) == -2 or DIFF(pp) == 2) // still valid?
            pp = restore_avl(pp, ppp); // no
 
          if (DIFF(pp) != 0 or pp == root)
            break; // global tree height has not changed ==> stop
 
          left_deficit = LLINK(ppp) == pp;
          pp = ppp; // advance to next ancestor
          ppp = avl_stack.pop();
        }
 
      clean_avl_stack();
    }
 
  public:
    using key_type = Key; 
 
    [[nodiscard]] constexpr Compare &key_comp() noexcept { return cmp; }
 
    [[nodiscard]] constexpr Compare &get_compare() noexcept { return key_comp(); }
 
    Gen_Avl_Tree(Compare __cmp = Compare()) noexcept
      : avl_stack(Node::MaxHeight), head_ptr(&head_node),
        root(RLINK(head_ptr)), cmp(__cmp)
    {
      avl_stack.push(head_ptr);
    }
 
    void swap(Gen_Avl_Tree & tree) noexcept
    {
      std::swap(root, tree.root);
      std::swap(cmp, tree.cmp);
    }
 
    virtual ~Gen_Avl_Tree() noexcept { assert(avl_stack_empty()); }
 
    [[nodiscard]] constexpr Node *&getRoot() noexcept { return root; }
 
    [[nodiscard]] constexpr Node * getRoot() const noexcept { return root; }
 
    [[nodiscard]] Node * search(const Key & key) const noexcept
    {
      return searchInBinTree<Node, Compare>(root, key, cmp);
    }
 
    [[nodiscard]] Node * insert(Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return root = p;
 
      signed char cmp_result = CmpEqual;
      Node *pp = search_and_stack_avl(KEY(p), cmp_result);
      if (cmp_result == CmpLess)
        LLINK(pp) = p;
      else if (cmp_result == CmpGreater)
        RLINK(pp) = p;
      else
        { // duplicated key
          clean_avl_stack();
          return nullptr;
        }
 
      restore_avl_after_insertion(p);
 
      return p;
    }
 
    [[nodiscard]] Node * search_or_insert(Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return root = p;
 
      signed char cmp_result = CmpEqual;
      Node *pp = search_and_stack_avl(KEY(p), cmp_result);
      if (cmp_result == CmpLess)
        LLINK(pp) = p;
      else if (cmp_result == CmpGreater)
        RLINK(pp) = p;
      else
        { // duplicated key
          clean_avl_stack();
          return pp;
        }
 
      restore_avl_after_insertion(p);
 
      return p;
    }
 
    [[nodiscard]] Node * insert_dup(Node *p) noexcept
    {
      if (root == Node::NullPtr)
        return root = p;
 
      signed char cmp_result = CmpEqual;
      Node *pp = search_dup_and_stack_avl(KEY(p), cmp_result);
      if (cmp_result == CmpLess)
        LLINK(pp) = p;
      else
        RLINK(pp) = p;
 
      restore_avl_after_insertion(p);
 
      return p;
    }
 
    [[nodiscard]] Node * remove(const Key & key) noexcept
    {
      if (root == Node::NullPtr)
        return nullptr;
 
      signed char cmp_result = CmpEqual;
      Node *p = search_and_stack_avl(key, cmp_result);
      if (cmp_result != CmpEqual)
        { // key was not found
          clean_avl_stack();
          return nullptr;
        }
 
      Node *pp = avl_stack.top(1); // get parent of p
      bool left_deficit; // AH_ERROR Key removed_key = KEY(p);
      while (true)
        {
          left_deficit = LLINK(pp) == p;
          if (LLINK(p) == Node::NullPtr) // missing left child?
            { // yes: link pp to p's child
              if (LLINK(pp) == p)
                LLINK(pp) = RLINK(p);
              else
                RLINK(pp) = RLINK(p);
              break;
            }
 
          if (RLINK(p) == Node::NullPtr) // missing right child?
            { // yes: link pp to p's child
              if (LLINK(pp) == p)
                LLINK(pp) = LLINK(p);
              else
                RLINK(pp) = LLINK(p);
              break;
            }
 
          // here p is a full node ==> swap with successor
          swapWithSuccessor(p, pp);
          //    removed_key = KEY(succ); // AH_ERROR remove
        }
 
      p->reset();
 
      if (pp == head_ptr) // check if the root was removed
        { // balance factors unchanged ==> AVL condition is not violated
          clean_avl_stack();
          return p;
        }
 
      restore_avl_after_deletion(left_deficit);
 
      return p;
    }
 
    [[nodiscard]] bool verify() const noexcept
    {
      return is_avl(root);
    }
 
    struct Iterator : public BinNodeInfixIterator<Node>
    {
      Iterator() noexcept = default;
 
      Iterator(Gen_Avl_Tree & t) : BinNodeInfixIterator<Node>(t.getRoot()) {}
 
      Iterator(const Gen_Avl_Tree & tree)
        : BinNodeInfixIterator<Node>(tree.getRoot()) {}
    };
  };
 
 
  template <typename Key, class Compare = Aleph::less<Key>>
  struct Avl_Tree : public Gen_Avl_Tree<AvlNode, Key, Compare>
  {
    using Base = Gen_Avl_Tree<AvlNode, Key, Compare>;
    using Base::Base;
  };
 
 
  template <typename Key, class Compare = Aleph::less<Key>>
  struct Avl_Tree_Vtl : public Gen_Avl_Tree<AvlNodeVtl, Key, Compare>
  {
    using Base = Gen_Avl_Tree<AvlNodeVtl, Key, Compare>;
    using Base::Base;
  };
} // end namespace Aleph
# endif // TPL_AVL_H