binSearchTree_tpl.h

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#include <sstream>
#include <string>

#include <agrum/core/binSearchTree.h>
#include <agrum/core/exceptions.h>

#ifndef DOXYGEN_SHOULD_SKIP_THIS

namespace gum {

  // ===========================================================================
  // ===========================================================================
  // ===                 GENERIC BINARY SEARCH TREE ITERATORS                ===
  // ===========================================================================
  // ===========================================================================

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >::BinSearchTreeIterator() :
      _node(0), _next_node(0), _prev_node(0), _parent(0), _left_child(0),
      _right_child(0), _tree(0), _next_iter(0) {
    GUM_CONSTRUCTOR(BinSearchTreeIterator);
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >::BinSearchTreeIterator(
     const BinSearchTreeIterator< Val, Cmp, Node >& from) :
      _node(from._node),
      _next_node(from._next_node), _prev_node(from._prev_node),
      _parent(from._parent), _left_child(from._left_child),
      _right_child(from._right_child), _tree(from._tree) {
    GUM_CONS_CPY(BinSearchTreeIterator);

    if (_tree) {
      _next_iter = _tree->_iterator_list;
      _tree->_iterator_list = this;
    } else
      _next_iter = 0;
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTreeIterator< Val, Cmp, Node >::_initialize(
     const BinSearchTree< Val, Cmp, Node >* tree,
     const Node*                            current_node,
     bool                                   add_to_iterator_list) {
    // remember: we do not check here whether the iterator already belongs to
    // a tree. We assume that it is not so.

    _tree = const_cast< BinSearchTree< Val, Cmp, Node >* >(tree);
    _node = const_cast< Node* >(current_node);

    if (add_to_iterator_list && _tree) {
      _next_iter = _tree->_iterator_list;
      _tree->_iterator_list = this;
    }
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTreeIterator< Val, Cmp, Node >::_detachFromTree() {
    if (_tree) {
      BinSearchTreeIterator< Val, Cmp, Node >*iter, *prev_iter = 0;

      for (iter = _tree->_iterator_list; iter != this && iter;
           prev_iter = iter, iter = iter->_next_iter) {}

      if (iter) {
        if (prev_iter)
          prev_iter->_next_iter = _next_iter;
        else
          _tree->_iterator_list = _next_iter;
      }
    }
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >::~BinSearchTreeIterator() {
    GUM_DESTRUCTOR(BinSearchTreeIterator);

    // remove the iterator from its tree iterator's list
    _detachFromTree();
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTreeIterator< Val, Cmp, Node >::clear() {
    // remove the iterator from its tree iterator's list
    _detachFromTree();

    // reset the iterator
    _node = 0;
    _next_node = 0;
    _prev_node = 0;
    _parent = 0;
    _left_child = 0;
    _right_child = 0;
    _tree = 0;
    _next_iter = 0;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >&
         BinSearchTreeIterator< Val, Cmp, Node >::
         operator=(const BinSearchTreeIterator< Val, Cmp, Node >& from) {
    // avoid self assignment
    if (this != &from) {
      GUM_OP_CPY(BinSearchTreeIterator);

      // if from and this belong to different trees, detach this from its
      // current tree
      if (from._tree != _tree) {
        _detachFromTree();
        _tree = from._tree;

        if (_tree) {
          _next_iter = _tree->_iterator_list;
          _tree->_iterator_list = this;
        } else
          _next_iter = 0;
      }

      // make the iterators point to the same element
      _node = from._node;
      _next_node = from._next_node;
      _prev_node = from._prev_node;
      _parent = from._parent;
      _left_child = from._left_child;
      _right_child = from._right_child;
    }

    return *this;
  }

  template < typename Val, class Cmp, class Node >
  INLINE const Val& BinSearchTreeIterator< Val, Cmp, Node >::operator*() const {
    if (_node) return _node->value();

    GUM_ERROR(UndefinedIteratorValue,
              "the iterator does not point to a node of the binary tree");
  }

  template < typename Val, class Cmp, class Node >
  INLINE Node* BinSearchTree< Val, Cmp, Node >::_minNode(Node* node) const {
    Node* prevNode = 0;

    for (; node; prevNode = node, node = node->leftChild()) {}

    return prevNode;
  }

  template < typename Val, class Cmp, class Node >
  INLINE Node* BinSearchTree< Val, Cmp, Node >::_maxNode(Node* node) const {
    Node* prevNode = 0;

    for (; node; prevNode = node, node = node->rightChild()) {}

    return prevNode;
  }

  template < typename Val, class Cmp, class Node >
  INLINE Node* BinSearchTree< Val, Cmp, Node >::_succNode(Node* node) const {
    if (!node) return 0;

    if (node->rightChild()) return _minNode(node->rightChild());

    Node* par = node->parent();

    while (par && (node->parentDir() == BinTreeDir::RIGHT_CHILD)) {
      node = par;
      par = par->parent();
    }

    return par;
  }

  template < typename Val, class Cmp, class Node >
  INLINE Node* BinSearchTree< Val, Cmp, Node >::_prevNode(Node* node) const {
    if (!node) return 0;

    if (node->leftChild()) return _maxNode(node->leftChild());

    Node* par = node->parent();

    while (par && (node->parentDir() == BinTreeDir::LEFT_CHILD)) {
      node = par;
      par = par->parent();
    }

    return par;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >&
     BinSearchTreeIterator< Val, Cmp, Node >::operator++() {
    // if there is a current node, use it to compute the next node, else use
    // directly _next_node (this case obtains when the iterator was pointing
    // toward a node that has been deleted before we use operator++)
    _node = _node ? _tree->_succNode(_node) : _next_node;

    if (!_node) {
      _next_node = 0;
      _prev_node = 0;
      _parent = 0;
      _left_child = 0;
      _right_child = 0;
    }

    return *this;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >&
     BinSearchTreeIterator< Val, Cmp, Node >::operator--() {
    // if there is a current node, use it to compute the preceding node, else
    // use
    // directly _prev_node (this case obtains when the iterator was pointing
    // toward a node that has been deleted before we use operator--)
    _node = _node ? _tree->_prevNode(_node) : _prev_node;

    if (!_node) {
      _next_node = 0;
      _prev_node = 0;
      _parent = 0;
      _left_child = 0;
      _right_child = 0;
    }

    return *this;
  }

  template < typename Val, class Cmp, class Node >
  INLINE bool BinSearchTreeIterator< Val, Cmp, Node >::
              operator==(const BinSearchTreeIterator< Val, Cmp, Node >& from) const {
    if (_node)
      return (_node == from._node);
    else
      return ((_node == from._node) && (_tree == from._tree)
              && (_next_node == from._next_node) && (_prev_node == from._prev_node)
              && (_parent == from._parent) && (_left_child == from._left_child)
              && (_right_child == from._right_child));
  }

  template < typename Val, class Cmp, class Node >
  INLINE bool BinSearchTreeIterator< Val, Cmp, Node >::
              operator!=(const BinSearchTreeIterator< Val, Cmp, Node >& from) const {
    if (_node)
      return (_node != from._node);
    else
      return ((_node != from._node) || (_tree != from._tree)
              || (_next_node != from._next_node) || (_prev_node != from._prev_node)
              || (_parent != from._parent) || (_left_child != from._left_child)
              || (_right_child != from._right_child));
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >&
         BinSearchTreeIterator< Val, Cmp, Node >::up() {
    // if there is a current node, use it to compute its parent node, else use
    // directly _parent (this case obtains when the iterator was pointing
    // toward a node that has been deleted before we use operation up)
    _node = _node ? _node->parent() : _parent;

    if (!_node) {
      _next_node = 0;
      _prev_node = 0;
      _parent = 0;
      _left_child = 0;
      _right_child = 0;
    }

    return *this;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >&
         BinSearchTreeIterator< Val, Cmp, Node >::downLeft() {
    // if there is a current node, use it to compute its left child, else use
    // directly _left_child (this case obtains when the iterator was pointing
    // toward a node that has been deleted before we use operation downLeft)
    _node = _node ? _node->leftChild() : _left_child;

    if (!_node) {
      _next_node = 0;
      _prev_node = 0;
      _parent = 0;
      _left_child = 0;
      _right_child = 0;
    }

    return *this;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >&
         BinSearchTreeIterator< Val, Cmp, Node >::downRight() {
    // if there is a current node, use it to compute its right child, else use
    // directly _right_child (this case obtains when the iterator was pointing
    // toward a node that has been deleted before we use operation downRight)
    _node = _node ? _node->rightChild() : _right_child;

    if (!_node) {
      _next_node = 0;
      _prev_node = 0;
      _parent = 0;
      _left_child = 0;
      _right_child = 0;
    }

    return *this;
  }

  // ===========================================================================
  // ===========================================================================
  // ===                      GENERIC BINARY SEARCH TREE                     ===
  // ===========================================================================
  // ===========================================================================

  template < typename Val, class Cmp, class Node >
  BinSearchTree< Val, Cmp, Node >::BinSearchTree(bool uniqueness_policy) :
      _root(0), _iterator_list(0), _uniqueness_policy(uniqueness_policy),
      _nb_elements(0) {
    GUM_CONSTRUCTOR(BinSearchTree);
    _iter_end._initialize(this, 0, false);
  }

  template < typename Val, class Cmp, class Node >
  BinSearchTree< Val, Cmp, Node >::BinSearchTree(
     const BinSearchTree< Val, Cmp, Node >& from) :
      _root(0),
      _iterator_list(0), _uniqueness_policy(from._uniqueness_policy) {
    // for debugging purposes
    GUM_CONS_CPY(BinSearchTree);

    // copy the content of BinSearchTree "from"
    _root = _copy(from._root);
    _nb_elements = from._nb_elements;

    // initialize the end/rend iterator
    _iter_end._initialize(this, 0, false);
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTree< Val, Cmp, Node >::clear() {
    // first we clear all the iterators, i.e., we detach them from the tree
    for (iterator *iter = _iterator_list, *next_iter = 0; iter; iter = next_iter) {
      next_iter = iter->_next_iter;
      iter->clear();
    }

    // now, delete the whole tree
    _deleteSubTree(_root);
    _root = 0;
    _nb_elements = 0;

    // note that there is no need to redefined end/rend as they do not rely
    // on the content of the tree
  }

  template < typename Val, class Cmp, class Node >
  BinSearchTree< Val, Cmp, Node >& BinSearchTree< Val, Cmp, Node >::
                                   operator=(const BinSearchTree< Val, Cmp, Node >& from) {
    // avoid self assignment
    if (this != &from) {
      // for debugging purposes
      GUM_OP_CPY(BinSearchTree);

      // if the tree is not currently empty, remove it
      clear();

      // copy binary tree "from"
      _uniqueness_policy = from._uniqueness_policy;
      _root = _copy(from._root);   // note that we can copy from's tree structure
      // as from and this have the same ordering _cmp
      _nb_elements = from._nb_elements;

      // note that we do not need to update the end/rend iterator as, besides
      // field _tree, no other field is related to the current tree (i.e., all
      // _*_node are set to 0
    }

    return *this;
  }

  template < typename Val, class Cmp, class Node >
  BinSearchTree< Val, Cmp, Node >::~BinSearchTree() {
    // for debugging purposes
    GUM_DESTRUCTOR(BinSearchTree);

    // clear all the iterators and remove all nodes
    clear();
  }

  template < typename Val, class Cmp, class Node >
  Node* BinSearchTree< Val, Cmp, Node >::_copy(Node*      node,
                                               Node*      parent,
                                               BinTreeDir dir) {
    // if there is no node to copy, abort
    if (!node) return 0;

    // create the copy of node
    Node* new_node = new Node(*node);

    if (parent) parent->insertChild(*new_node, dir);

    // if necessary, create the left and right subgraphs
    _copy(node->leftChild(), new_node, BinTreeDir::LEFT_CHILD);
    _copy(node->rightChild(), new_node, BinTreeDir::RIGHT_CHILD);

    return new_node;
  }

  template < typename Val, class Cmp, class Node >
  void BinSearchTree< Val, Cmp, Node >::_deleteSubTree(Node* node) {
    // if there is no node to remove, return
    if (!node) return;

    // delete the left and right subgraphs
    _deleteSubTree(node->leftChild());
    _deleteSubTree(node->rightChild());

    // delete the node itself
    delete node;
  }

  template < typename Val, class Cmp, class Node >
  INLINE Node* BinSearchTree< Val, Cmp, Node >::_insert(const Val& val) {
    // if the tree is not empty, search the binary search tree to know
    // where the node should be inserted
    if (_root) {
      Node* node = _root;

      while (true) {
        if (_cmp(val, node->value()))
          if (!node->leftChild()) {
            // here we are on a leaf => insert the new node
            ++_nb_elements;
            return node->insertLeftChild(val);
          } else {
            node = node->leftChild();
          }
        else if (_cmp(node->value(), val) || !_uniqueness_policy)
          if (!node->rightChild()) {
            // here we are on a leaf => insert the new node
            ++_nb_elements;
            return node->insertRightChild(val);
          } else {
            node = node->rightChild();
          }
        else {
          // here we found a node with the same key and the uniqueness policy
          // is set. So we should raise an exception
          GUM_ERROR(DuplicateElement,
                    "Val " << val << " already in the binary search tree");
        }
      }
    }

    // here the tree is empty, just create a new node
    _root = new Node(val);
    ++_nb_elements;
    return _root;
  }

  template < typename Val, class Cmp, class Node >
  INLINE const Val& BinSearchTree< Val, Cmp, Node >::insert(const Val& val) {
    return _insert(val)->value();
  }

  template < typename Val, class Cmp, class Node >
  INLINE const Val& BinSearchTree< Val, Cmp, Node >::rootValue() const {
    if (_root == 0) {
      GUM_ERROR(NotFound, "no value in an empty Binary Search tree");
    }

    return _root->value();
  }

  template < typename Val, class Cmp, class Node >
  INLINE const Val& BinSearchTree< Val, Cmp, Node >::minValue() const {
    if (_root == 0) {
      GUM_ERROR(NotFound, "no minimal value in an empty Binary Search tree");
    }

    return _minNode(_root)->value();
  }

  template < typename Val, class Cmp, class Node >
  INLINE const Val& BinSearchTree< Val, Cmp, Node >::maxValue() const {
    if (_root == 0) {
      GUM_ERROR(NotFound, "no maximal value in an empty Binary Search tree");
    }

    return _maxNode(_root)->value();
  }

  template < typename Val, class Cmp, class Node >
  INLINE Node* BinSearchTree< Val, Cmp, Node >::_getNode(const Val& val) const {
    // if the tree is not empty, search the binary search tree to know
    // where the node could be
    if (_root) {
      Node* node = _root;

      while (true) {
        if (_cmp(val, node->value())) {
          if (!node->leftChild())
            return 0;
          else
            node = node->leftChild();
        } else if (_cmp(node->value(), val)) {
          if (!node->rightChild())
            return 0;
          else
            node = node->rightChild();
        } else
          return node;
      }
    } else {
      return 0;
    }
  }

  template < typename Val, class Cmp, class Node >
  INLINE bool BinSearchTree< Val, Cmp, Node >::contains(const Val& val) const {
    return (_getNode(val) != 0);
  }

  template < typename Val, class Cmp, class Node >
  INLINE Size BinSearchTree< Val, Cmp, Node >::size() const {
    return _nb_elements;
  }

  template < typename Val, class Cmp, class Node >
  INLINE bool BinSearchTree< Val, Cmp, Node >::empty() const {
    return (_nb_elements == 0);
  }

  template < typename Val, class Cmp, class Node >
  const std::string BinSearchTree< Val, Cmp, Node >::toString() const {
    bool              deja = false;
    std::stringstream stream;
    stream << "[";

    for (const_iterator iter = begin(); iter != end(); ++iter, deja = true) {
      if (deja) stream << " , ";

      stream << *iter;
    }

    stream << "]";

    return stream.str();
  }

  template < typename Val, class Cmp, class Node >
  INLINE bool BinSearchTree< Val, Cmp, Node >::uniquenessPolicy() const {
    return _uniqueness_policy;
  }

  template < typename Val, class Cmp, class Node >
  INLINE void
     BinSearchTree< Val, Cmp, Node >::setUniquenessPolicy(const bool new_policy) {
    _uniqueness_policy = new_policy;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >
         BinSearchTree< Val, Cmp, Node >::begin() {
    BinSearchTreeIterator< Val, Cmp, Node > iter;
    iter._initialize(this, _minNode(_root), true);
    return iter;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >
         BinSearchTree< Val, Cmp, Node >::begin() const {
    BinSearchTreeIterator< Val, Cmp, Node > iter;
    iter._initialize(this, _minNode(_root), true);
    return iter;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >
         BinSearchTree< Val, Cmp, Node >::rbegin() {
    BinSearchTreeIterator< Val, Cmp, Node > iter;
    iter._initialize(this, _maxNode(_root), true);
    return iter;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >
         BinSearchTree< Val, Cmp, Node >::rbegin() const {
    BinSearchTreeIterator< Val, Cmp, Node > iter;
    iter._initialize(this, _maxNode(_root), true);
    return iter;
  }

  template < typename Val, class Cmp, class Node >
  INLINE const BinSearchTreeIterator< Val, Cmp, Node >&
               BinSearchTree< Val, Cmp, Node >::end() {
    return _iter_end;
  }

  template < typename Val, class Cmp, class Node >
  INLINE const BinSearchTreeIterator< Val, Cmp, Node >&
               BinSearchTree< Val, Cmp, Node >::end() const {
    return _iter_end;
  }

  template < typename Val, class Cmp, class Node >
  INLINE const BinSearchTreeIterator< Val, Cmp, Node >&
               BinSearchTree< Val, Cmp, Node >::rend() {
    return _iter_end;
  }

  template < typename Val, class Cmp, class Node >
  INLINE const BinSearchTreeIterator< Val, Cmp, Node >&
               BinSearchTree< Val, Cmp, Node >::rend() const {
    return _iter_end;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >
         BinSearchTree< Val, Cmp, Node >::root() {
    BinSearchTreeIterator< Val, Cmp, Node > iter;
    iter._initialize(this, _root, true);
    return iter;
  }

  template < typename Val, class Cmp, class Node >
  INLINE BinSearchTreeIterator< Val, Cmp, Node >
         BinSearchTree< Val, Cmp, Node >::root() const {
    BinSearchTreeIterator< Val, Cmp, Node > iter;
    iter._initialize(this, _root, true);
    return iter;
  }

  template < typename Val, class Cmp, class Node >
  void BinSearchTree< Val, Cmp, Node >::_erase(Node* node) {
    if (!node) return;

    // update all the iterators pointing to node that they should point
    // elsewhere
    __updateEraseIterators(node);

    // update the number of elements contained in the tree
    --_nb_elements;

    // now remove the node from the tree:

    // if the node has no children, then just remove it
    if (!node->leftChild() && !node->rightChild()) {
      // if the node was the only one in the tree, then the tree becomes empty
      if (!node->parent()) _root = 0;

      // note that, when node has a parent, there is no need to remove the
      // link between node and this parent: this will be taken care of by
      // node's destructor.
    }
    // if there is just a right child
    else if (!node->leftChild()) {
      // just relink the right child with the parent (if any)
      if (!node->parent()) {
        // in this case, no need to remove the link between "node" and its
        // child:
        // this will be taken care of by the destructor of "node"
        _root = node->rightChild();
      } else {
        Node *     parent = node->parent(), *child = node->rightChild();
        BinTreeDir dir = node->parentDir();
        parent->eraseLink(dir);
        node->eraseRightLink();
        parent->insertChild(*child, dir);
      }
    }
    // if there is just a left child
    else if (!node->rightChild()) {
      // just relink the left child with the parent (if any)
      if (!node->parent()) {
        // in this case, no need to remove the link between "node" and its
        // child:
        // this will be taken care of by the destructor of "node"
        _root = node->leftChild();
      } else {
        Node *     parent = node->parent(), *child = node->leftChild();
        BinTreeDir dir = node->parentDir();
        parent->eraseLink(dir);
        node->eraseLeftLink();
        parent->insertChild(*child, dir);
      }
    }
    // ok, here there are two children
    else {
      __eraseWithTwoChildren(node);
    }

    // now we shall physically remove node from memory
    delete node;
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTree< Val, Cmp, Node >::__eraseWithTwoChildren(Node* node) {
    // the idea is to get the successor of "node" and substitute "node" by
    // it.  As "node" has two children, we are sure that the successor is one
    // of node's descendants. Moreover, by its very definition, this
    // successor has no left child. Hence, two cases can obtain:
    // 1/ the successor is precisely node's right child. In this case, we just
    //    have to make node's left child be the left child of the successor,
    //    and node's parent be the successor's parent, and the tree is again
    //    a binary search tree.
    // 2/ the successor is not node's right child. In this case, we know that
    //    the successor has a parent different from node and that the
    //    successor
    //    is a left child of this parent. We just need to put the right child
    //    of the successor (if any) as the left child of its parent, and to
    //    replace "node" by the successor.
    Node* successor = _succNode(node);

    if (successor == node->rightChild()) {   // proceed to case 1:
      Node* left_child = node->leftChild();
      node->eraseLeftLink();
      node->eraseRightLink();
      successor->insertLeftChild(*left_child);

      if (!node->parent()) {
        // in this case, no need to remove the link between "node" and the
        // successor: this will be taken care of by the destructor of "node"
        _root = successor;
      } else {
        // rechain node's parent with its successor
        BinTreeDir par_dir = node->parentDir();
        Node*      parent = node->parent();
        parent->eraseLink(par_dir);
        parent->insertChild(*successor, par_dir);
      }
    } else {   // proceed to case 2:
      Node* parent = successor->parent();
      parent->eraseLeftLink();

      if (successor->rightChild()) {
        Node* succ_child = successor->rightChild();
        successor->eraseRightLink();
        parent->insertLeftChild(*succ_child);
      }

      Node *left = node->leftChild(), *right = node->rightChild();
      node->eraseLeftLink();
      node->eraseRightLink();
      successor->insertLeftChild(*left);
      successor->insertRightChild(*right);

      if (!node->parent()) {
        _root = successor;
      } else {
        // rechain node's parent with its successor
        BinTreeDir par_dir = node->parentDir();
        Node*      parent = node->parent();
        parent->eraseLink(par_dir);
        parent->insertChild(*successor, par_dir);
      }
    }
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTree< Val, Cmp, Node >::erase(const Val& val) {
    Node* n = _getNode(val);

    if (n == nullptr)
      GUM_ERROR(gum::NotFound, "Value \"" << val << "\" not found");

    _erase(n);
  }

  template < typename Val, class Cmp, class Node >
  INLINE void BinSearchTree< Val, Cmp, Node >::erase(const iterator& iter) {
    _erase(iter._node);
  }

  template < typename Val, class Cmp, class Node >
  void BinSearchTree< Val, Cmp, Node >::__updateEraseIterators(Node* node) {
    for (iterator* iter = _iterator_list; iter; iter = iter->_next_iter) {
      // if the iterator points toward the node to be deleted, make its _node
      // field point to 0 and update accordingly its other fields
      if (iter->_node == node) {
        iter->_node = 0;
        iter->_next_node = _succNode(node);
        iter->_prev_node = _prevNode(node);
        iter->_parent = node->parent();
        iter->_left_child = node->leftChild();
        iter->_right_child = node->rightChild();
      } else if (!iter->_node) {
        if (iter->_next_node == node) iter->_next_node = _succNode(node);

        if (iter->_prev_node == node) iter->_prev_node = _prevNode(node);

        if (iter->_parent == node) iter->_parent = node->parent();

        if (iter->_left_child == node) iter->_left_child = node->leftChild();

        if (iter->_right_child == node) iter->_right_child = node->rightChild();
      }
    }
  }

}   // namespace gum

#endif   // DOXYGEN_SHOULD_SKIP_THIS