avl_tree

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// vi:set ft=cpp: -*- Mode: C++ -*-
/*
 * (c) 2008-2009 Alexander Warg <warg@os.inf.tu-dresden.de>,
 *               Carsten Weinhold <weinhold@os.inf.tu-dresden.de>
 *     economic rights: Technische Universität Dresden (Germany)
 *
 * License: see LICENSE.spdx (in this directory or the directories above)
 */
 
#pragma once
 
#include "std_ops"
#include "pair"
 
#include "bits/bst.h"
#include "bits/bst_iter.h"
 
struct Avl_set_tester;
 
namespace cxx {

class Avl_tree_node : public Bits::Bst_node
{
  friend struct ::Avl_set_tester;
 
private:
  template< typename Node, typename Get_key, typename Compare >
  friend class Avl_tree;

  typedef Bits::Direction Bal;
  typedef Bits::Direction Dir;
 
  // We are a final BST node, hide interior.
  using Bits::Bst_node::next;
  using Bits::Bst_node::next_p;
  using Bits::Bst_node::rotate;

  Bal _balance;
 
protected:
  Avl_tree_node() = default;
 
private:
  Avl_tree_node(Avl_tree_node const &o) = delete;
  Avl_tree_node(Avl_tree_node &&o) = delete;

  Avl_tree_node &operator = (Avl_tree_node const &o) = default;
  Avl_tree_node &operator = (Avl_tree_node &&o) = default;

  explicit Avl_tree_node(bool) : Bits::Bst_node(true), _balance(Dir::N) {}

  static Bits::Bst_node *rotate2(Bst_node **t, Bal idir, Bal pre);

  bool balanced() const { return _balance == Bal::N; }

  Bal balance() const { return _balance; }

  void balance(Bal b) { _balance = b; }
};
 

template< typename Node, typename Get_key,
          typename Compare = Lt_functor<typename Get_key::Key_type> >
class Avl_tree : public Bits::Bst<Node, Get_key, Compare>
{
private:
  typedef Bits::Bst<Node, Get_key, Compare> Bst;

  using Bst::_head;

  using Bst::k;

  typedef typename Avl_tree_node::Bal Bal;
  typedef typename Avl_tree_node::Bal Dir;
 
  Avl_tree(Avl_tree const &o) = delete;
  Avl_tree &operator = (Avl_tree const &o) = delete;
  Avl_tree(Avl_tree &&o) = delete;
  Avl_tree &operator = (Avl_tree &&o) = delete;
 
public:
  typedef typename Bst::Key_type Key_type;
  typedef typename Bst::Key_param_type Key_param_type;
 
  // Grab iterator types from Bst
  typedef typename Bst::Iterator Iterator;
  typedef typename Bst::Const_iterator Const_iterator;
  typedef typename Bst::Rev_iterator Rev_iterator;
  typedef typename Bst::Const_rev_iterator Const_rev_iterator;

  Pair<Node *, bool> insert(Node *new_node);

  Node *remove(Key_param_type key);
  Node *erase(Key_param_type key) { return remove(key); }

  Avl_tree() = default;

  ~Avl_tree() noexcept
  {
    this->remove_all([](Node *){});
  }
 
#ifdef __DEBUG_L4_AVL
  bool rec_dump(Avl_tree_node *n, int depth, int *dp, bool print, char pfx);
  bool rec_dump(bool print)
  {
    int dp=0;
    return rec_dump(static_cast<Avl_tree_node *>(_head), 0, &dp, print, '+');
  }
#endif
};
 
 
//----------------------------------------------------------------------------
/* IMPLEMENTATION: Bits::__Bst_iter_b */
 
 
inline
Bits::Bst_node *
Avl_tree_node::rotate2(Bst_node **t, Bal idir, Bal pre)
{
  typedef Bits::Bst_node N;
  typedef Avl_tree_node A;
  N *tmp[2] = { *t, N::next(*t, idir) };
  *t = N::next(tmp[1], !idir);
  A *n = static_cast<A*>(*t);
 
  N::next(tmp[0], idir, N::next(n, !idir));
  N::next(tmp[1], !idir, N::next(n, idir));
  N::next(n, !idir, tmp[0]);
  N::next(n, idir, tmp[1]);
 
  n->balance(Bal::N);
 
  if (pre == Bal::N)
    {
      static_cast<A*>(tmp[0])->balance(Bal::N);
      static_cast<A*>(tmp[1])->balance(Bal::N);
      return 0;
    }
 
  static_cast<A*>(tmp[pre != idir])->balance(!pre);
  static_cast<A*>(tmp[pre == idir])->balance(Bal::N);
 
  return N::next(tmp[pre == idir], !pre);
}
 
//----------------------------------------------------------------------------
/* Implementation of AVL Tree */
 
/* Insert new _Node. */
template< typename Node, typename Get_key, class Compare>
Pair<Node *, bool>
Avl_tree<Node, Get_key, Compare>::insert(Node *new_node)
{
  typedef Avl_tree_node A;
  typedef Bits::Bst_node N;
  N **t = &_head; /* search variable */
  N **s = &_head; /* node where rebalancing may occur */
  Key_param_type new_key = Get_key::key_of(new_node);
 
  // search insertion point
  for (N *p; (p = *t);)
    {
      Dir b = this->dir(new_key, p);
      if (b == Dir::N)
  return pair(static_cast<Node*>(p), false);
 
      if (!static_cast<A const *>(p)->balanced())
  s = t;
 
      t = A::next_p(p, b);
    }
 
  *static_cast<A*>(new_node) = A(true);
  *t = new_node;
 
  N *n = *s;
  A *a = static_cast<A*>(n);
  if (!a->balanced())
    {
      A::Bal b(this->greater(new_key, n));
      if (a->balance() != b)
  {
    // ok we got in balance the shorter subtree go higher
    a->balance(Bal::N);
    // propagate the new balance down to the new node
    n = A::next(n, b);
  }
      else if (b == Bal(this->greater(new_key, A::next(n, b))))
  {
    // left-left or right-right case -> single rotation
    A::rotate(s, b);
    a->balance(Bal::N);
    static_cast<A*>(*s)->balance(Bal::N);
    n = A::next(*s, b);
  }
      else
  {
    // need a double rotation
    n = A::next(A::next(n, b), !b);
    n = A::rotate2(s, b, n == new_node ? Bal::N : Bal(this->greater(new_key, n)));
  }
    }
 
  for (A::Bal b; n && n != new_node; static_cast<A*>(n)->balance(b), n = A::next(n, b))
    b = Bal(this->greater(new_key, n));
 
  return pair(new_node, true);
}
 
 
/* remove an element */
template< typename Node, typename Get_key, class Compare>
inline
Node *Avl_tree<Node, Get_key, Compare>::remove(Key_param_type key)
{
  typedef Avl_tree_node A;
  typedef Bits::Bst_node N;
  N **q = &_head; /* search variable */
  N **s = &_head; /* last ('deepest') node on the search path to q
                   * with balance 0, at this place the rebalancing
                   * stops in any case */
  N **t = 0;
  Dir dir;
 
  // find target node and rebalancing entry
  for (N *n; (n = *q); q = A::next_p(n, dir))
    {
      dir = Dir(this->greater(key, n));
      if (dir == Dir::L && !this->greater(k(n), key))
  /* found node */
  t = q;
 
      if (!A::next(n, dir))
  break;
 
      A const *a = static_cast<A const *>(n);
      if (a->balanced() || (a->balance() == !dir && A::next<A>(n, !dir)->balanced()))
  s = q;
    }
 
  // nothing found
  if (!t)
    return 0;
 
  A *i = static_cast<A*>(*t);
 
  for (N *n; (n = *s); s = A::next_p(n, dir))
    {
      dir = Dir(this->greater(key, n));
 
      if (!A::next(n, dir))
  break;
 
      A *a = static_cast<A*>(n);
      // got one out of balance
      if (a->balanced())
  a->balance(!dir);
      else if (a->balance() == dir)
  a->balance(Bal::N);
      else
  {
    // we need rotations to get in balance
    Bal b = A::next<A>(n, !dir)->balance();
    if (b == dir)
      A::rotate2(s, !dir, A::next<A>(A::next(n, !dir), dir)->balance());
    else
      {
        A::rotate(s, !dir);
        if (b != Bal::N)
    {
      a->balance(Bal::N);
      static_cast<A*>(*s)->balance(Bal::N);
    }
        else
    {
      a->balance(!dir);
      static_cast<A*>(*s)->balance(dir);
    }
      }
    if (n == i)
      t = A::next_p(*s, dir);
  }
    }
 
  A *n = static_cast<A*>(*q);
  *t = n;
  *q = A::next(n, !dir);
  *n = *i;
 
  return static_cast<Node*>(i);
}
 
#ifdef __DEBUG_L4_AVL
template< typename Node, typename Get_key, class Compare>
bool Avl_tree<Node, Get_key, Compare>::rec_dump(Avl_tree_node *n, int depth, int *dp, bool print, char pfx)
{
  typedef Avl_tree_node A;
 
  if (!n)
    return true;
 
  int dpx[2] = {depth,depth};
  bool res = true;
 
  res = rec_dump(A::next<A>(n, Dir::R), depth + 1, dpx + 1, print, '/');
 
  if (print)
    {
      fprintf(stderr, "%2d: [%8p] b=%1d: ", depth, n, (int)n->balance().d);
 
      for (int i = 0; i < depth; ++i)
  std::cerr << "    ";
 
      std::cerr << pfx << (static_cast<Node*>(n)->item) << std::endl;
    }
 
  res = res & rec_dump(A::next<A>(n, Dir::L), depth + 1, dpx, print, '\\');
 
  int b = dpx[1] - dpx[0];
 
  if (b < 0)
    *dp = dpx[0];
  else
    *dp = dpx[1];
 
  Bal x = n->balance();
  if ((b < -1 || b > 1) ||
      (b == 0 && x != Bal::N) ||
      (b == -1 && x != Bal::L) ||
      (b == 1 && x != Bal::R))
    {
      if (print)
  fprintf(stderr, "%2d: [%8p] b=%1d: balance error %d\n", depth, n, (int)n->balance().d, b);
      return false;
    }
  return res;
}
#endif
 
}