tree.h

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/* 

   $Id: tree.hh,v 1.141 2007/04/07 21:43:13 peekas Exp $

   STL-like templated tree class.
   Copyright (C) 2001-2006  Kasper Peeters <kasper.peeters@aei.mpg.de>.

*/

/** \mainpage tree.hh
    \author   Kasper Peeters
    \version  2.31
    \date     21-Aug-2007
    \see      http://www.aei.mpg.de/~peekas/tree/
    \see      http://www.aei.mpg.de/~peekas/tree/ChangeLog

   The tree.hh library for C++ provides an STL-like container class
   for n-ary trees, templated over the data stored at the
   nodes. Various types of iterators are provided (post-order,
   pre-order, and others). Where possible the access methods are
   compatible with the STL or alternative algorithms are
   available. 
*/


/*
   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; version 2 or 3.
   
   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
   
   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/

/** \todo 
   - New-style move members are not completely finished yet.
   - It would be good to have an iterator which can iterate over all
     nodes below a given node.
   - Fixed depth iterators do not iterate over the entire range if there
     are 'holes' in the tree.
   - If a range uses const iter_base& as end iterator, things will
     inevitably go wrong, because upcast from iter_base to a non-sibling_iter
     is incorrect. This upcast should be removed (and then all illegal uses
     as previously in 'equal' will be flagged by the compiler). This requires
     new copy constructors though.
   - There's a bug in replace(sibling_iterator, ...) when the ranges
     sit next to each other. Turned up in append_child(iter,iter)
     but has been avoided now.
   - "std::operator<" does not work correctly on our iterators, and for some
     reason a globally defined template operator< did not get picked up. 
     Using a comparison class now, but this should be investigated.
*/

#ifndef tree_hh_
#define tree_hh_

#include <cassert>
#include <memory>
#include <stdexcept>
#include <iterator>
#include <set>
#include <queue>
#include <iostream>

// HP-style construct/destroy have gone from the standard,
// so here is a copy.

namespace kp {

template <class T1, class T2>
void constructor(T1* p, T2& val) 
   {
   new ((void *) p) T1(val);
   }

template <class T1>
void constructor(T1* p) 
   {
   new ((void *) p) T1;
   }

template <class T1>
void destructor(T1* p)
   {
   p->~T1();
   }

}

/// A node in the tree, combining links to other nodes as well as the actual data.
template<class T>
class tree_node_ { // size: 5*4=20 bytes (on 32 bit arch), can be reduced by 8.
   public:
      tree_node_<T> *parent;
      tree_node_<T> *first_child, *last_child;
      tree_node_<T> *prev_sibling, *next_sibling;
      T data;
}; // __attribute__((packed));

template <class T, class tree_node_allocator = std::allocator<tree_node_<T> > >
class tree {
   protected:
      typedef tree_node_<T> tree_node;
   public:
      /// Value of the data stored at a node.
      typedef T value_type;

      class iterator_base;
      class pre_order_iterator;
      class post_order_iterator;
      class sibling_iterator;
      class leaf_iterator;

      tree();
      tree(const T&);
      tree(const iterator_base&);
      tree(const tree<T, tree_node_allocator>&);
      ~tree();
      void operator=(const tree<T, tree_node_allocator>&);

      /// Base class for iterators, only pointers stored, no traversal logic.
#ifdef __SGI_STL_PORT
      class iterator_base : public stlport::bidirectional_iterator<T, ptrdiff_t> {
#else
      class iterator_base {
#endif
         public:
            typedef T                               value_type;
            typedef T*                              pointer;
            typedef T&                              reference;
            typedef size_t                          size_type;
            typedef ptrdiff_t                       difference_type;
            typedef std::bidirectional_iterator_tag iterator_category;

            iterator_base();
            iterator_base(tree_node *);

            T&             operator*() const;
            T*             operator->() const;

            /// When called, the next increment/decrement skips children of this node.
            void         skip_children();
            /// Number of children of the node pointed to by the iterator.
            unsigned int number_of_children() const;

            sibling_iterator begin() const;
            sibling_iterator end() const;

            tree_node *node;
         protected:
            bool skip_current_children_;
      };

      /// Depth-first iterator, first accessing the node, then its children.
      class pre_order_iterator : public iterator_base { 
         public:
            pre_order_iterator();
            pre_order_iterator(tree_node *);
            pre_order_iterator(const iterator_base&);
            pre_order_iterator(const sibling_iterator&);

            bool    operator==(const pre_order_iterator&) const;
            bool    operator!=(const pre_order_iterator&) const;
            pre_order_iterator&  operator++();
            pre_order_iterator&  operator--();
            pre_order_iterator   operator++(int);
            pre_order_iterator   operator--(int);
            pre_order_iterator&  operator+=(unsigned int);
            pre_order_iterator&  operator-=(unsigned int);
      };

      /// Depth-first iterator, first accessing the children, then the node itself.
      class post_order_iterator : public iterator_base {
         public:
            post_order_iterator();
            post_order_iterator(tree_node *);
            post_order_iterator(const iterator_base&);
            post_order_iterator(const sibling_iterator&);

            bool    operator==(const post_order_iterator&) const;
            bool    operator!=(const post_order_iterator&) const;
            post_order_iterator&  operator++();
            post_order_iterator&  operator--();
            post_order_iterator   operator++(int);
            post_order_iterator   operator--(int);
            post_order_iterator&  operator+=(unsigned int);
            post_order_iterator&  operator-=(unsigned int);

            /// Set iterator to the first child as deep as possible down the tree.
            void descend_all();
      };

      /// Breadth-first iterator, using a queue
      class breadth_first_queued_iterator : public iterator_base {
         public:
            breadth_first_queued_iterator();
            breadth_first_queued_iterator(tree_node *);
            breadth_first_queued_iterator(const iterator_base&);

            bool    operator==(const breadth_first_queued_iterator&) const;
            bool    operator!=(const breadth_first_queued_iterator&) const;
            breadth_first_queued_iterator&  operator++();
            breadth_first_queued_iterator   operator++(int);
            breadth_first_queued_iterator&  operator+=(unsigned int);

         private:
            std::queue<tree_node *> traversal_queue;
      };

      /// The default iterator types throughout the tree class.
      typedef pre_order_iterator            iterator;
      typedef breadth_first_queued_iterator breadth_first_iterator;

      /// Iterator which traverses only the nodes at a given depth from the root.
      class fixed_depth_iterator : public iterator_base {
         public:
            fixed_depth_iterator();
            fixed_depth_iterator(tree_node *);
            fixed_depth_iterator(const iterator_base&);
            fixed_depth_iterator(const sibling_iterator&);
            fixed_depth_iterator(const fixed_depth_iterator&);

            bool    operator==(const fixed_depth_iterator&) const;
            bool    operator!=(const fixed_depth_iterator&) const;
            fixed_depth_iterator&  operator++();
            fixed_depth_iterator&  operator--();
            fixed_depth_iterator   operator++(int);
            fixed_depth_iterator   operator--(int);
            fixed_depth_iterator&  operator+=(unsigned int);
            fixed_depth_iterator&  operator-=(unsigned int);

            tree_node *first_parent_;
         private:
            void set_first_parent_();
            void find_leftmost_parent_();
      };

      /// Iterator which traverses only the nodes which are siblings of each other.
      class sibling_iterator : public iterator_base {
         public:
            sibling_iterator();
            sibling_iterator(tree_node *);
            sibling_iterator(const sibling_iterator&);
            sibling_iterator(const iterator_base&);

            bool    operator==(const sibling_iterator&) const;
            bool    operator!=(const sibling_iterator&) const;
            sibling_iterator&  operator++();
            sibling_iterator&  operator--();
            sibling_iterator   operator++(int);
            sibling_iterator   operator--(int);
            sibling_iterator&  operator+=(unsigned int);
            sibling_iterator&  operator-=(unsigned int);

            tree_node *range_first() const;
            tree_node *range_last() const;
            tree_node *parent_;
         private:
            void set_parent_();
      };

      /// Iterator which traverses only the leaves.
      class leaf_iterator : public iterator_base {
         public:
            leaf_iterator();
            leaf_iterator(tree_node *);
            leaf_iterator(const sibling_iterator&);
            leaf_iterator(const iterator_base&);

            bool    operator==(const leaf_iterator&) const;
            bool    operator!=(const leaf_iterator&) const;
            leaf_iterator&  operator++();
            leaf_iterator&  operator--();
            leaf_iterator   operator++(int);
            leaf_iterator   operator--(int);
            leaf_iterator&  operator+=(unsigned int);
            leaf_iterator&  operator-=(unsigned int);
      };

      /// Return iterator to the beginning of the tree.
      inline pre_order_iterator   begin() const;
      /// Return iterator to the end of the tree.
      inline pre_order_iterator   end() const;
      /// Return post-order iterator to the beginning of the tree.
      post_order_iterator  begin_post() const;
      /// Return post-order iterator to the end of the tree.
      post_order_iterator  end_post() const;
      /// Return fixed-depth iterator to the first node at a given depth.
      fixed_depth_iterator begin_fixed(const iterator_base&, unsigned int) const;
      /// Return fixed-depth iterator to end of the nodes at given depth.
      fixed_depth_iterator end_fixed(const iterator_base&, unsigned int) const;
      /// Return breadth-first iterator to the first node at a given depth.
      breadth_first_queued_iterator begin_breadth_first() const;
      /// Return breadth-first iterator to end of the nodes at given depth.
      breadth_first_queued_iterator end_breadth_first() const;
      /// Return sibling iterator to the first child of given node.
      sibling_iterator     begin(const iterator_base&) const;
      /// Return sibling iterator to the end of the children of a given node.
      sibling_iterator     end(const iterator_base&) const;
      /// Return leaf iterator to the first leaf of the tree.
      leaf_iterator   begin_leaf() const;
      /// Return leaf iterator to the last leaf of the tree.
      leaf_iterator   end_leaf() const;

      /// Return iterator to the parent of a node.
      template<typename iter> static iter parent(iter);
      /// Return iterator to the previous sibling of a node.
      template<typename iter> iter previous_sibling(iter) const;
      /// Return iterator to the next sibling of a node.
      template<typename iter> iter next_sibling(iter) const;
      /// Return iterator to the next node at a given depth.
      template<typename iter> iter next_at_same_depth(iter) const;

      /// Erase all nodes of the tree.
      void     clear();
      /// Erase element at position pointed to by iterator, return incremented iterator.
      template<typename iter> iter erase(iter);
      /// Erase all children of the node pointed to by iterator.
      void     erase_children(const iterator_base&);

      /// Insert empty node as last/first child of node pointed to by position.
      template<typename iter> iter append_child(iter position); 
      template<typename iter> iter prepend_child(iter position); 
      /// Insert node as last/first child of node pointed to by position.
      template<typename iter> iter append_child(iter position, const T& x);
      template<typename iter> iter prepend_child(iter position, const T& x);
      /// Append the node (plus its children) at other_position as last/first child of position.
      template<typename iter> iter append_child(iter position, iter other_position);
      template<typename iter> iter prepend_child(iter position, iter other_position);
      /// Append the nodes in the from-to range (plus their children) as last/first children of position.
      template<typename iter> iter append_children(iter position, sibling_iterator from, sibling_iterator to);
      template<typename iter> iter prepend_children(iter position, sibling_iterator from, sibling_iterator to);

      /// Short-hand to insert topmost node in otherwise empty tree.
      pre_order_iterator set_head(const T& x);
      /// Insert node as previous sibling of node pointed to by position.
      template<typename iter> iter insert(iter position, const T& x);
      /// Specialisation of previous member.
      sibling_iterator insert(sibling_iterator position, const T& x);
      /// Insert node (with children) pointed to by subtree as previous sibling of node pointed to by position.
      template<typename iter> iter insert_subtree(iter position, const iterator_base& subtree);
      /// Insert node as next sibling of node pointed to by position.
      template<typename iter> iter insert_after(iter position, const T& x);
      /// Insert node (with children) pointed to by subtree as next sibling of node pointed to by position.
      template<typename iter> iter insert_subtree_after(iter position, const iterator_base& subtree);

      /// Replace node at 'position' with other node (keeping same children); 'position' becomes invalid.
      template<typename iter> iter replace(iter position, const T& x);
      /// Replace node at 'position' with subtree starting at 'from' (do not erase subtree at 'from'); see above.
      template<typename iter> iter replace(iter position, const iterator_base& from);
      /// Replace string of siblings (plus their children) with copy of a new string (with children); see above
      sibling_iterator replace(sibling_iterator orig_begin, sibling_iterator orig_end, 
                               sibling_iterator new_begin,  sibling_iterator new_end); 

      /// Move all children of node at 'position' to be siblings, returns position.
      template<typename iter> iter flatten(iter position);
      /// Move nodes in range to be children of 'position'.
      template<typename iter> iter reparent(iter position, sibling_iterator begin, sibling_iterator end);
      /// Move all child nodes of 'from' to be children of 'position'.
      template<typename iter> iter reparent(iter position, iter from);

      /// Replace node with a new node, making the old node a child of the new node.
      template<typename iter> iter wrap(iter position, const T& x);

      /// Move 'source' node (plus its children) to become the next sibling of 'target'.
      template<typename iter> iter move_after(iter target, iter source);
      /// Move 'source' node (plus its children) to become the previous sibling of 'target'.
      template<typename iter> iter move_before(iter target, iter source);
      sibling_iterator move_before(sibling_iterator target, sibling_iterator source);
      /// Move 'source' node (plus its children) to become the node at 'target' (erasing the node at 'target').
      template<typename iter> iter move_ontop(iter target, iter source);

      /// Merge with other tree, creating new branches and leaves only if they are not already present.
      void     merge(sibling_iterator, sibling_iterator, sibling_iterator, sibling_iterator, 
                     bool duplicate_leaves=false);
      /// Sort (std::sort only moves values of nodes, this one moves children as well).
      void     sort(sibling_iterator from, sibling_iterator to, bool deep=false);
      template<class StrictWeakOrdering>
      void     sort(sibling_iterator from, sibling_iterator to, StrictWeakOrdering comp, bool deep=false);
      /// Compare two ranges of nodes (compares nodes as well as tree structure).
      template<typename iter>
      bool     equal(const iter& one, const iter& two, const iter& three) const;
      template<typename iter, class BinaryPredicate>
      bool     equal(const iter& one, const iter& two, const iter& three, BinaryPredicate) const;
      template<typename iter>
      bool     equal_subtree(const iter& one, const iter& two) const;
      template<typename iter, class BinaryPredicate>
      bool     equal_subtree(const iter& one, const iter& two, BinaryPredicate) const;
      /// Extract a new tree formed by the range of siblings plus all their children.
      tree     subtree(sibling_iterator from, sibling_iterator to) const;
      void     subtree(tree&, sibling_iterator from, sibling_iterator to) const;
      /// Exchange the node (plus subtree) with its sibling node (do nothing if no sibling present).
      void     swap(sibling_iterator it);
      /// Exchange two nodes (plus subtrees)
      void     swap(iterator, iterator);
      
      /// Count the total number of nodes.
      int      size() const;
      /// Count the total number of nodes below the indicated node (plus one).
      int      size(const iterator_base&) const;
      /// Check if tree is empty.
      bool     empty() const;
      /// Compute the depth to the root.
      int      depth(const iterator_base&) const;
      /// Count the number of children of node at position.
      static unsigned int number_of_children(const iterator_base&);
      /// Count the number of 'next' siblings of node at iterator.
      unsigned int number_of_siblings(const iterator_base&) const;
      /// Determine whether node at position is in the subtrees with root in the range.
      bool     is_in_subtree(const iterator_base& position, const iterator_base& begin, 
                             const iterator_base& end) const;
      /// Determine whether the iterator is an 'end' iterator and thus not actually pointing to a node.
      bool     is_valid(const iterator_base&) const;

      /// Determine the index of a node in the range of siblings to which it belongs.
      unsigned int index(sibling_iterator it) const;
      /// Inverse of 'index': return the n-th child of the node at position.
      sibling_iterator  child(const iterator_base& position, unsigned int) const;
      
      /// Comparator class for iterators (compares pointer values; why doesn't this work automatically?)
      class iterator_base_less {
         public:
            bool operator()(const typename tree<T, tree_node_allocator>::iterator_base& one,
                            const typename tree<T, tree_node_allocator>::iterator_base& two) const
               {
               return one.node < two.node;
               }
      };
      tree_node *head, *feet;    // head/feet are always dummy; if an iterator points to them it is invalid
   private:
      tree_node_allocator alloc_;
      void head_initialise_();
      void copy_(const tree<T, tree_node_allocator>& other);

      /// Comparator class for two nodes of a tree (used for sorting and searching).
      template<class StrictWeakOrdering>
      class compare_nodes {
         public:
            compare_nodes(StrictWeakOrdering comp) : comp_(comp) {};
            
            bool operator()(const tree_node *a, const tree_node *b) 
               {
               static StrictWeakOrdering comp;
               return comp(a->data, b->data);
               }
         private:
            StrictWeakOrdering comp_;
      };
};

//template <class T, class tree_node_allocator>
//class iterator_base_less {
// public:
//    bool operator()(const typename tree<T, tree_node_allocator>::iterator_base& one,
//                  const typename tree<T, tree_node_allocator>::iterator_base& two) const
//       {
//       txtout << "operatorclass<" << one.node < two.node << std::endl;
//       return one.node < two.node;
//       }
//};

// template <class T, class tree_node_allocator>
// bool operator<(const typename tree<T, tree_node_allocator>::iterator& one,
//                const typename tree<T, tree_node_allocator>::iterator& two)
//    {
//    txtout << "operator< " << one.node < two.node << std::endl;
//    if(one.node < two.node) return true;
//    return false;
//    }
// 
// template <class T, class tree_node_allocator>
// bool operator==(const typename tree<T, tree_node_allocator>::iterator& one,
//                const typename tree<T, tree_node_allocator>::iterator& two)
//    {
//    txtout << "operator== " << one.node == two.node << std::endl;
//    if(one.node == two.node) return true;
//    return false;
//    }
// 
// template <class T, class tree_node_allocator>
// bool operator>(const typename tree<T, tree_node_allocator>::iterator_base& one,
//                const typename tree<T, tree_node_allocator>::iterator_base& two)
//    {
//    txtout << "operator> " << one.node < two.node << std::endl;
//    if(one.node > two.node) return true;
//    return false;
//    }



// Tree

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::tree() 
   {
   head_initialise_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::tree(const T& x) 
   {
   head_initialise_();
   set_head(x);
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::tree(const iterator_base& other)
   {
   head_initialise_();
   set_head((*other));
   replace(begin(), other);
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::~tree()
   {
   clear();
   alloc_.deallocate(head,1);
   alloc_.deallocate(feet,1);
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::head_initialise_() 
   { 
   head = alloc_.allocate(1,0); // MSVC does not have default second argument 
   feet = alloc_.allocate(1,0);

   head->parent=0;
   head->first_child=0;
   head->last_child=0;
   head->prev_sibling=0; //head;
   head->next_sibling=feet; //head;

   feet->parent=0;
   feet->first_child=0;
   feet->last_child=0;
   feet->prev_sibling=head;
   feet->next_sibling=0;
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::operator=(const tree<T, tree_node_allocator>& other)
   {
   copy_(other);
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::tree(const tree<T, tree_node_allocator>& other)
   {
   head_initialise_();
   copy_(other);
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::copy_(const tree<T, tree_node_allocator>& other) 
   {
   clear();
   pre_order_iterator it=other.begin(), to=begin();
   while(it!=other.end()) {
      to=insert(to, (*it));
      it.skip_children();
      ++it;
      }
   to=begin();
   it=other.begin();
   while(it!=other.end()) {
      to=replace(to, it);
      to.skip_children();
      it.skip_children();
      ++to;
      ++it;
      }
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::clear()
   {
   if(head)
      while(head->next_sibling!=feet)
         erase(pre_order_iterator(head->next_sibling));
   }

template<class T, class tree_node_allocator> 
void tree<T, tree_node_allocator>::erase_children(const iterator_base& it)
   {
// std::cout << "erase_children " << it.node << std::endl;
   if(it.node==0) return;

   tree_node *cur=it.node->first_child;
   tree_node *prev=0;

   while(cur!=0) {
      prev=cur;
      cur=cur->next_sibling;
      erase_children(pre_order_iterator(prev));
      kp::destructor(&prev->data);
      alloc_.deallocate(prev,1);
      }
   it.node->first_child=0;
   it.node->last_child=0;
// std::cout << "exit" << std::endl;
   }

template<class T, class tree_node_allocator> 
template<class iter>
iter tree<T, tree_node_allocator>::erase(iter it)
   {
   tree_node *cur=it.node;
   assert(cur!=head);
   iter ret=it;
   ret.skip_children();
   ++ret;
   erase_children(it);
   if(cur->prev_sibling==0) {
      cur->parent->first_child=cur->next_sibling;
      }
   else {
      cur->prev_sibling->next_sibling=cur->next_sibling;
      }
   if(cur->next_sibling==0) {
      cur->parent->last_child=cur->prev_sibling;
      }
   else {
      cur->next_sibling->prev_sibling=cur->prev_sibling;
      }

   kp::destructor(&cur->data);
   alloc_.deallocate(cur,1);
   return ret;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::begin() const
   {
   return pre_order_iterator(head->next_sibling);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::end() const
   {
   return pre_order_iterator(feet);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::begin_breadth_first() const
   {
   return breadth_first_queued_iterator(head->next_sibling);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::end_breadth_first() const
   {
   return breadth_first_queued_iterator();
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::begin_post() const
   {
   tree_node *tmp=head->next_sibling;
   if(tmp!=feet) {
      while(tmp->first_child)
         tmp=tmp->first_child;
      }
   return post_order_iterator(tmp);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::end_post() const
   {
   return post_order_iterator(feet);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::begin_fixed(const iterator_base& pos, unsigned int dp) const
   {
   tree_node *tmp=pos.node;
   unsigned int curdepth=0;
   while(curdepth<dp) { // go down one level
      while(tmp->first_child==0) {
         tmp=tmp->next_sibling;
         if(tmp==0)
            throw std::range_error("tree: begin_fixed out of range");
         }
      tmp=tmp->first_child;
      ++curdepth;
      }
   return tmp;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::end_fixed(const iterator_base& pos, unsigned int dp) const
   {
   assert(1==0); // FIXME: not correct yet
   tree_node *tmp=pos.node;
   unsigned int curdepth=1;
   while(curdepth<dp) { // go down one level
      while(tmp->first_child==0) {
         tmp=tmp->next_sibling;
         if(tmp==0)
            throw std::range_error("tree: end_fixed out of range");
         }
      tmp=tmp->first_child;
      ++curdepth;
      }
   return tmp;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::begin(const iterator_base& pos) const
   {
   assert(pos.node!=0);
   if(pos.node->first_child==0) {
      return end(pos);
      }
   return pos.node->first_child;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::end(const iterator_base& pos) const
   {
   sibling_iterator ret(0);
   ret.parent_=pos.node;
   return ret;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::begin_leaf() const
   {
   tree_node *tmp=head->next_sibling;
   if(tmp!=feet) {
      while(tmp->first_child)
         tmp=tmp->first_child;
      }
   return leaf_iterator(tmp);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::end_leaf() const
   {
   return leaf_iterator(feet);
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::parent(iter position) 
   {
   assert(position.node!=0);
   return iter(position.node->parent);
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::previous_sibling(iter position) const
   {
   assert(position.node!=0);
   iter ret(position);
   ret.node=position.node->prev_sibling;
   return ret;
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::next_sibling(iter position) const
   {
   assert(position.node!=0);
   iter ret(position);
   ret.node=position.node->next_sibling;
   return ret;
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::next_at_same_depth(iter position) const
   {
   assert(position.node!=0);
   iter ret(position);

   if(position.node->next_sibling) {
      ret.node=position.node->next_sibling;
      }
   else { 
      int relative_depth=0;
      upper:
      do {
         ret.node=ret.node->parent;
         if(ret.node==0) return ret;
         --relative_depth;
         } while(ret.node->next_sibling==0);
      lower:
      ret.node=ret.node->next_sibling;
      while(ret.node->first_child==0) {
         if(ret.node->next_sibling==0)
            goto upper;
         ret.node=ret.node->next_sibling;
         if(ret.node==0) return ret;
         }
      while(relative_depth<0 && ret.node->first_child!=0) {
         ret.node=ret.node->first_child;
         ++relative_depth;
         }
      if(relative_depth<0) {
         if(ret.node->next_sibling==0) goto upper;
         else                          goto lower;
         }
      }
   return ret;
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::append_child(iter position)
   {
   assert(position.node!=head);
   assert(position.node);

   tree_node *tmp=alloc_.allocate(1,0);
   kp::constructor(&tmp->data);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->parent=position.node;
   if(position.node->last_child!=0) {
      position.node->last_child->next_sibling=tmp;
      }
   else {
      position.node->first_child=tmp;
      }
   tmp->prev_sibling=position.node->last_child;
   position.node->last_child=tmp;
   tmp->next_sibling=0;
   return tmp;
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::prepend_child(iter position)
   {
   assert(position.node!=head);
   assert(position.node);

   tree_node *tmp=alloc_.allocate(1,0);
   kp::constructor(&tmp->data);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->parent=position.node;
   if(position.node->first_child!=0) {
      position.node->first_child->prev_sibling=tmp;
      }
   else {
      position.node->last_child=tmp;
      }
   tmp->next_sibling=position.node->first_child;
   position.node->prev_child=tmp;
   tmp->prev_sibling=0;
   return tmp;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::append_child(iter position, const T& x)
   {
   // If your program fails here you probably used 'append_child' to add the top
   // node to an empty tree. From version 1.45 the top element should be added
   // using 'insert'. See the documentation for further information, and sorry about
   // the API change.
   assert(position.node!=head);
   assert(position.node);

   tree_node* tmp = alloc_.allocate(1,0);
   kp::constructor(&tmp->data, x);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->parent=position.node;
   if(position.node->last_child!=0) {
      position.node->last_child->next_sibling=tmp;
      }
   else {
      position.node->first_child=tmp;
      }
   tmp->prev_sibling=position.node->last_child;
   position.node->last_child=tmp;
   tmp->next_sibling=0;
   return tmp;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::prepend_child(iter position, const T& x)
   {
   assert(position.node!=head);
   assert(position.node);

   tree_node* tmp = alloc_.allocate(1,0);
   kp::constructor(&tmp->data, x);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->parent=position.node;
   if(position.node->first_child!=0) {
      position.node->first_child->prev_sibling=tmp;
      }
   else {
      position.node->last_child=tmp;
      }
   tmp->next_sibling=position.node->first_child;
   position.node->first_child=tmp;
   tmp->prev_sibling=0;
   return tmp;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::append_child(iter position, iter other)
   {
   assert(position.node!=head);
   assert(position.node);

   sibling_iterator aargh=append_child(position, value_type());
   return replace(aargh, other);
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::prepend_child(iter position, iter other)
   {
   assert(position.node!=head);
   assert(position.node);

   sibling_iterator aargh=prepend_child(position, value_type());
   return replace(aargh, other);
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::append_children(iter position, sibling_iterator from, sibling_iterator to)
   {
   assert(position.node!=head);
   assert(position.node);

   iter ret=from;

   while(from!=to) {
      insert_subtree(position.end(), from);
      ++from;
      }
   return ret;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::prepend_children(iter position, sibling_iterator from, sibling_iterator to)
   {
   assert(position.node!=head);
   assert(position.node);

   iter ret=from;

   while(from!=to) {
      insert_subtree(position.begin(), from);
      ++from;
      }
   return ret;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::set_head(const T& x)
   {
   assert(head->next_sibling==feet);
   return insert(iterator(feet), x);
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::insert(iter position, const T& x)
   {
   if(position.node==0) {
      position.node=feet; // Backward compatibility: when calling insert on a null node,
                          // insert before the feet.
      }
   tree_node* tmp = alloc_.allocate(1,0);
   kp::constructor(&tmp->data, x);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->parent=position.node->parent;
   tmp->next_sibling=position.node;
   tmp->prev_sibling=position.node->prev_sibling;
   position.node->prev_sibling=tmp;

   if(tmp->prev_sibling==0) {
      if(tmp->parent) // when inserting nodes at the head, there is no parent
         tmp->parent->first_child=tmp;
      }
   else
      tmp->prev_sibling->next_sibling=tmp;
   return tmp;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::insert(sibling_iterator position, const T& x)
   {
   tree_node* tmp = alloc_.allocate(1,0);
   kp::constructor(&tmp->data, x);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->next_sibling=position.node;
   if(position.node==0) { // iterator points to end of a subtree
      tmp->parent=position.parent_;
      tmp->prev_sibling=position.range_last();
      tmp->parent->last_child=tmp;
      }
   else {
      tmp->parent=position.node->parent;
      tmp->prev_sibling=position.node->prev_sibling;
      position.node->prev_sibling=tmp;
      }

   if(tmp->prev_sibling==0) {
      if(tmp->parent) // when inserting nodes at the head, there is no parent
         tmp->parent->first_child=tmp;
      }
   else
      tmp->prev_sibling->next_sibling=tmp;
   return tmp;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::insert_after(iter position, const T& x)
   {
   tree_node* tmp = alloc_.allocate(1,0);
   kp::constructor(&tmp->data, x);
   tmp->first_child=0;
   tmp->last_child=0;

   tmp->parent=position.node->parent;
   tmp->prev_sibling=position.node;
   tmp->next_sibling=position.node->next_sibling;
   position.node->next_sibling=tmp;

   if(tmp->next_sibling==0) {
      if(tmp->parent) // when inserting nodes at the head, there is no parent
         tmp->parent->last_child=tmp;
      }
   else {
      tmp->next_sibling->prev_sibling=tmp;
      }
   return tmp;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::insert_subtree(iter position, const iterator_base& subtree)
   {
   // insert dummy
   iter it=insert(position, value_type());
   // replace dummy with subtree
   return replace(it, subtree);
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::insert_subtree_after(iter position, const iterator_base& subtree)
   {
   // insert dummy
   iter it=insert_after(position, value_type());
   // replace dummy with subtree
   return replace(it, subtree);
   }

// template <class T, class tree_node_allocator>
// template <class iter>
// iter tree<T, tree_node_allocator>::insert_subtree(sibling_iterator position, iter subtree)
//    {
//    // insert dummy
//    iter it(insert(position, value_type()));
//    // replace dummy with subtree
//    return replace(it, subtree);
//    }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::replace(iter position, const T& x)
   {
   kp::destructor(&position.node->data);
   kp::constructor(&position.node->data, x);
   return position;
   }

template <class T, class tree_node_allocator>
template <class iter>
iter tree<T, tree_node_allocator>::replace(iter position, const iterator_base& from)
   {
   assert(position.node!=head);
   tree_node *current_from=from.node;
   tree_node *start_from=from.node;
   tree_node *current_to  =position.node;

   // replace the node at position with head of the replacement tree at from
// std::cout << "warning!" << position.node << std::endl;
   erase_children(position);  
// std::cout << "no warning!" << std::endl;
   tree_node* tmp = alloc_.allocate(1,0);
   kp::constructor(&tmp->data, (*from));
   tmp->first_child=0;
   tmp->last_child=0;
   if(current_to->prev_sibling==0) {
      if(current_to->parent!=0)
         current_to->parent->first_child=tmp;
      }
   else {
      current_to->prev_sibling->next_sibling=tmp;
      }
   tmp->prev_sibling=current_to->prev_sibling;
   if(current_to->next_sibling==0) {
      if(current_to->parent!=0)
         current_to->parent->last_child=tmp;
      }
   else {
      current_to->next_sibling->prev_sibling=tmp;
      }
   tmp->next_sibling=current_to->next_sibling;
   tmp->parent=current_to->parent;
   kp::destructor(&current_to->data);
   alloc_.deallocate(current_to,1);
   current_to=tmp;
   
   // only at this stage can we fix 'last'
   tree_node *last=from.node->next_sibling;

   pre_order_iterator toit=tmp;
   // copy all children
   do {
      assert(current_from!=0);
      if(current_from->first_child != 0) {
         current_from=current_from->first_child;
         toit=append_child(toit, current_from->data);
         }
      else {
         while(current_from->next_sibling==0 && current_from!=start_from) {
            current_from=current_from->parent;
            toit=parent(toit);
            assert(current_from!=0);
            }
         current_from=current_from->next_sibling;
         if(current_from!=last) {
            toit=append_child(parent(toit), current_from->data);
            }
         }
      } while(current_from!=last);

   return current_to;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::replace(
   sibling_iterator orig_begin, 
   sibling_iterator orig_end, 
   sibling_iterator new_begin, 
   sibling_iterator new_end)
   {
   tree_node *orig_first=orig_begin.node;
   tree_node *new_first=new_begin.node;
   tree_node *orig_last=orig_first;
   while((++orig_begin)!=orig_end)
      orig_last=orig_last->next_sibling;
   tree_node *new_last=new_first;
   while((++new_begin)!=new_end)
      new_last=new_last->next_sibling;

   // insert all siblings in new_first..new_last before orig_first
   bool first=true;
   pre_order_iterator ret;
   while(1==1) {
      pre_order_iterator tt=insert_subtree(pre_order_iterator(orig_first), pre_order_iterator(new_first));
      if(first) {
         ret=tt;
         first=false;
         }
      if(new_first==new_last)
         break;
      new_first=new_first->next_sibling;
      }

   // erase old range of siblings
   bool last=false;
   tree_node *next=orig_first;
   while(1==1) {
      if(next==orig_last) 
         last=true;
      next=next->next_sibling;
      erase((pre_order_iterator)orig_first);
      if(last) 
         break;
      orig_first=next;
      }
   return ret;
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::flatten(iter position)
   {
   if(position.node->first_child==0)
      return position;

   tree_node *tmp=position.node->first_child;
   while(tmp) {
      tmp->parent=position.node->parent;
      tmp=tmp->next_sibling;
      } 
   if(position.node->next_sibling) {
      position.node->last_child->next_sibling=position.node->next_sibling;
      position.node->next_sibling->prev_sibling=position.node->last_child;
      }
   else {
      position.node->parent->last_child=position.node->last_child;
      }
   position.node->next_sibling=position.node->first_child;
   position.node->next_sibling->prev_sibling=position.node;
   position.node->first_child=0;
   position.node->last_child=0;

   return position;
   }


template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::reparent(iter position, sibling_iterator begin, sibling_iterator end)
   {
   tree_node *first=begin.node;
   tree_node *last=first;

   assert(first!=position.node);
   
   if(begin==end) return begin;
   // determine last node
   while((++begin)!=end) {
      last=last->next_sibling;
      }
   // move subtree
   if(first->prev_sibling==0) {
      first->parent->first_child=last->next_sibling;
      }
   else {
      first->prev_sibling->next_sibling=last->next_sibling;
      }
   if(last->next_sibling==0) {
      last->parent->last_child=first->prev_sibling;
      }
   else {
      last->next_sibling->prev_sibling=first->prev_sibling;
      }
   if(position.node->first_child==0) {
      position.node->first_child=first;
      position.node->last_child=last;
      first->prev_sibling=0;
      }
   else {
      position.node->last_child->next_sibling=first;
      first->prev_sibling=position.node->last_child;
      position.node->last_child=last;
      }
   last->next_sibling=0;

   tree_node *pos=first;
   while(1==1) {
      pos->parent=position.node;
      if(pos==last) break;
      pos=pos->next_sibling;
      }

   return first;
   }

template <class T, class tree_node_allocator>
template <typename iter> iter tree<T, tree_node_allocator>::reparent(iter position, iter from)
   {
   if(from.node->first_child==0) return position;
   return reparent(position, from.node->first_child, end(from));
   }

template <class T, class tree_node_allocator>
template <typename iter> iter tree<T, tree_node_allocator>::wrap(iter position, const T& x)
   {
   assert(position.node!=0);
   sibling_iterator fr=position, to=position;
   ++to;
   iter ret = insert(position, x);
   reparent(ret, fr, to);
   return ret;
   }

template <class T, class tree_node_allocator>
template <typename iter> iter tree<T, tree_node_allocator>::move_after(iter target, iter source)
   {
   tree_node *dst=target.node;
   tree_node *src=source.node;
   assert(dst);
   assert(src);

   if(dst==src) return source;
   if(dst->next_sibling)
      if(dst->next_sibling==src) // already in the right spot
         return source;

   // take src out of the tree
   if(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;
   else                     src->parent->first_child=src->next_sibling;
   if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;
   else                     src->parent->last_child=src->prev_sibling;

   // connect it to the new point
   if(dst->next_sibling!=0) dst->next_sibling->prev_sibling=src;
   else                     dst->parent->last_child=src;
   src->next_sibling=dst->next_sibling;
   dst->next_sibling=src;
   src->prev_sibling=dst;
   src->parent=dst->parent;
   return src;
   }

template <class T, class tree_node_allocator>
template <typename iter> iter tree<T, tree_node_allocator>::move_before(iter target, iter source)
   {
   tree_node *dst=target.node;
   tree_node *src=source.node;
   assert(dst);
   assert(src);

   if(dst==src) return source;
   if(dst->prev_sibling)
      if(dst->prev_sibling==src) // already in the right spot
         return source;

   // take src out of the tree
   if(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;
   else                     src->parent->first_child=src->next_sibling;
   if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;
   else                     src->parent->last_child=src->prev_sibling;

   // connect it to the new point
   if(dst->prev_sibling!=0) dst->prev_sibling->next_sibling=src;
   else                     dst->parent->first_child=src;
   src->prev_sibling=dst->prev_sibling;
   dst->prev_sibling=src;
   src->next_sibling=dst;
   src->parent=dst->parent;
   return src;
   }

// specialisation for sibling_iterators
template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::move_before(sibling_iterator target, 
                                                                                         sibling_iterator source)
   {
   tree_node *dst=target.node;
   tree_node *src=source.node;
   tree_node *dst_prev_sibling;
   if(dst==0) { // must then be an end iterator
      dst_prev_sibling=target.parent_->last_child;
      assert(dst_prev_sibling);
      }
   else dst_prev_sibling=dst->prev_sibling;
   assert(src);

   if(dst==src) return source;
   if(dst_prev_sibling)
      if(dst_prev_sibling==src) // already in the right spot
         return source;

   // take src out of the tree
   if(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;
   else                     src->parent->first_child=src->next_sibling;
   if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;
   else                     src->parent->last_child=src->prev_sibling;

   // connect it to the new point
   if(dst_prev_sibling!=0) dst_prev_sibling->next_sibling=src;
   else                    target.parent_->first_child=src;
   src->prev_sibling=dst_prev_sibling;
   if(dst) {
      dst->prev_sibling=src;
      src->parent=dst->parent;
      }
   src->next_sibling=dst;
   return src;
   }

template <class T, class tree_node_allocator>
template <typename iter> iter tree<T, tree_node_allocator>::move_ontop(iter target, iter source)
   {
   tree_node *dst=target.node;
   tree_node *src=source.node;
   assert(dst);
   assert(src);

   if(dst==src) return source;

   // remember connection points
   tree_node *b_prev_sibling=dst->prev_sibling;
   tree_node *b_next_sibling=dst->next_sibling;
   tree_node *b_parent=dst->parent;

   // remove target
   erase(target);

   // take src out of the tree
   if(src->prev_sibling!=0) src->prev_sibling->next_sibling=src->next_sibling;
   else                     src->parent->first_child=src->next_sibling;
   if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;
   else                     src->parent->last_child=src->prev_sibling;

   // connect it to the new point
   if(b_prev_sibling!=0) b_prev_sibling->next_sibling=src;
   else                  b_parent->first_child=src;
   if(b_next_sibling!=0) b_next_sibling->prev_sibling=src;
   else                  b_parent->last_child=src;
   src->prev_sibling=b_prev_sibling;
   src->next_sibling=b_next_sibling;
   src->parent=b_parent;
   return src;
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::merge(sibling_iterator to1,   sibling_iterator to2,
                                          sibling_iterator from1, sibling_iterator from2,
                                          bool duplicate_leaves)
   {
   sibling_iterator fnd;
   while(from1!=from2) {
      if((fnd=std::find(to1, to2, (*from1))) != to2) { // element found
         if(from1.begin()==from1.end()) { // full depth reached
            if(duplicate_leaves)
               append_child(parent(to1), (*from1));
            }
         else { // descend further
            merge(fnd.begin(), fnd.end(), from1.begin(), from1.end(), duplicate_leaves);
            }
         }
      else { // element missing
         insert_subtree(to2, from1);
         }
      ++from1;
      }
   }


template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::sort(sibling_iterator from, sibling_iterator to, bool deep)
   {
   std::less<T> comp;
   sort(from, to, comp, deep);
   }

template <class T, class tree_node_allocator>
template <class StrictWeakOrdering>
void tree<T, tree_node_allocator>::sort(sibling_iterator from, sibling_iterator to, 
                                        StrictWeakOrdering comp, bool deep)
   {
   if(from==to) return;
   // make list of sorted nodes
   // CHECK: if multiset stores equivalent nodes in the order in which they
   // are inserted, then this routine should be called 'stable_sort'.
   std::multiset<tree_node *, compare_nodes<StrictWeakOrdering> > nodes(comp);
   sibling_iterator it=from, it2=to;
   while(it != to) {
      nodes.insert(it.node);
      ++it;
      }
   // reassemble
   --it2;

   // prev and next are the nodes before and after the sorted range
   tree_node *prev=from.node->prev_sibling;
   tree_node *next=it2.node->next_sibling;
   typename std::multiset<tree_node *, compare_nodes<StrictWeakOrdering> >::iterator nit=nodes.begin(), eit=nodes.end();
   if(prev==0) {
      if((*nit)->parent!=0) // to catch "sorting the head" situations, when there is no parent
         (*nit)->parent->first_child=(*nit);
      }
   else prev->next_sibling=(*nit);

   --eit;
   while(nit!=eit) {
      (*nit)->prev_sibling=prev;
      if(prev)
         prev->next_sibling=(*nit);
      prev=(*nit);
      ++nit;
      }
   // prev now points to the last-but-one node in the sorted range
   if(prev)
      prev->next_sibling=(*eit);

   // eit points to the last node in the sorted range.
   (*eit)->next_sibling=next;
   (*eit)->prev_sibling=prev; // missed in the loop above
   if(next==0) {
      if((*eit)->parent!=0) // to catch "sorting the head" situations, when there is no parent
         (*eit)->parent->last_child=(*eit);
      }
   else next->prev_sibling=(*eit);

   if(deep) {  // sort the children of each node too
      sibling_iterator bcs(*nodes.begin());
      sibling_iterator ecs(*eit);
      ++ecs;
      while(bcs!=ecs) {
         sort(begin(bcs), end(bcs), comp, deep);
         ++bcs;
         }
      }
   }

template <class T, class tree_node_allocator>
template <typename iter>
bool tree<T, tree_node_allocator>::equal(const iter& one_, const iter& two, const iter& three_) const
   {
   std::equal_to<T> comp;
   return equal(one_, two, three_, comp);
   }

template <class T, class tree_node_allocator>
template <typename iter>
bool tree<T, tree_node_allocator>::equal_subtree(const iter& one_, const iter& two_) const
   {
   std::equal_to<T> comp;
   return equal_subtree(one_, two_, comp);
   }

template <class T, class tree_node_allocator>
template <typename iter, class BinaryPredicate>
bool tree<T, tree_node_allocator>::equal(const iter& one_, const iter& two, const iter& three_, BinaryPredicate fun) const
   {
   pre_order_iterator one(one_), three(three_);

// if(one==two && is_valid(three) && three.number_of_children()!=0)
//    return false;
   while(one!=two && is_valid(three)) {
      if(!fun(*one,*three))
         return false;
      if(one.number_of_children()!=three.number_of_children()) 
         return false;
      ++one;
      ++three;
      }
   return true;
   }

template <class T, class tree_node_allocator>
template <typename iter, class BinaryPredicate>
bool tree<T, tree_node_allocator>::equal_subtree(const iter& one_, const iter& two_, BinaryPredicate fun) const
   {
   pre_order_iterator one(one_), two(two_);

   if(!fun(*one,*two)) return false;
   if(number_of_children(one)!=number_of_children(two)) return false;
   return equal(begin(one),end(one),begin(two),fun);
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator> tree<T, tree_node_allocator>::subtree(sibling_iterator from, sibling_iterator to) const
   {
   tree tmp;
   tmp.set_head(value_type());
   tmp.replace(tmp.begin(), tmp.end(), from, to);
   return tmp;
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::subtree(tree& tmp, sibling_iterator from, sibling_iterator to) const
   {
   tmp.set_head(value_type());
   tmp.replace(tmp.begin(), tmp.end(), from, to);
   }

template <class T, class tree_node_allocator>
int tree<T, tree_node_allocator>::size() const
   {
   int i=0;
   pre_order_iterator it=begin(), eit=end();
   while(it!=eit) {
      ++i;
      ++it;
      }
   return i;
   }

template <class T, class tree_node_allocator>
int tree<T, tree_node_allocator>::size(const iterator_base& top) const
   {
   int i=0;
   pre_order_iterator it=top, eit=top;
   eit.skip_children();
   ++eit;
   while(it!=eit) {
      ++i;
      ++it;
      }
   return i;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::empty() const
   {
   pre_order_iterator it=begin(), eit=end();
   return (it==eit);
   }

template <class T, class tree_node_allocator>
int tree<T, tree_node_allocator>::depth(const iterator_base& it) const
   {
   tree_node* pos=it.node;
   assert(pos!=0);
   int ret=0;
   while(pos->parent!=0) {
      pos=pos->parent;
      ++ret;
      }
   return ret;
   }

template <class T, class tree_node_allocator>
unsigned int tree<T, tree_node_allocator>::number_of_children(const iterator_base& it) 
   {
   tree_node *pos=it.node->first_child;
   if(pos==0) return 0;
   
   unsigned int ret=1;
//   while(pos!=it.node->last_child) {
//      ++ret;
//      pos=pos->next_sibling;
//      }
   while((pos=pos->next_sibling))
      ++ret;
   return ret;
   }

template <class T, class tree_node_allocator>
unsigned int tree<T, tree_node_allocator>::number_of_siblings(const iterator_base& it) const
   {
   tree_node *pos=it.node;
   unsigned int ret=0;
   // count forward
   while(pos->next_sibling && 
         pos->next_sibling!=head &&
         pos->next_sibling!=feet) {
      ++ret;
      pos=pos->next_sibling;
      }
   // count backward
   pos=it.node;
   while(pos->prev_sibling && 
         pos->prev_sibling!=head &&
         pos->prev_sibling!=feet) {
      ++ret;
      pos=pos->prev_sibling;
      }
   
   return ret;
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::swap(sibling_iterator it)
   {
   tree_node *nxt=it.node->next_sibling;
   if(nxt) {
      if(it.node->prev_sibling)
         it.node->prev_sibling->next_sibling=nxt;
      else
         it.node->parent->first_child=nxt;
      nxt->prev_sibling=it.node->prev_sibling;
      tree_node *nxtnxt=nxt->next_sibling;
      if(nxtnxt)
         nxtnxt->prev_sibling=it.node;
      else
         it.node->parent->last_child=it.node;
      nxt->next_sibling=it.node;
      it.node->prev_sibling=nxt;
      it.node->next_sibling=nxtnxt;
      }
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::swap(iterator one, iterator two)
   {
   // if one and two are adjacent siblings, use the sibling swap
   if(one.node->next_sibling==two.node) swap(one);
   else if(two.node->next_sibling==one.node) swap(two);
   else {
      tree_node *nxt1=one.node->next_sibling;
      tree_node *nxt2=two.node->next_sibling;
      tree_node *pre1=one.node->prev_sibling;
      tree_node *pre2=two.node->prev_sibling;
      tree_node *par1=one.node->parent;
      tree_node *par2=two.node->parent;

      // reconnect
      one.node->parent=par2;
      one.node->next_sibling=nxt2;
      if(nxt2) nxt2->prev_sibling=one.node;
      else     par2->last_child=one.node;
      one.node->prev_sibling=pre2;
      if(pre2) pre2->next_sibling=one.node;
      else     par2->first_child=one.node;    

      two.node->parent=par1;
      two.node->next_sibling=nxt1;
      if(nxt1) nxt1->prev_sibling=two.node;
      else     par1->last_child=two.node;
      two.node->prev_sibling=pre1;
      if(pre1) pre1->next_sibling=two.node;
      else     par1->first_child=two.node;
      }
   }

// template <class BinaryPredicate>
// tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::find_subtree(
//    sibling_iterator subfrom, sibling_iterator subto, iterator from, iterator to, 
//    BinaryPredicate fun) const
//    {
//    assert(1==0); // this routine is not finished yet.
//    while(from!=to) {
//       if(fun(*subfrom, *from)) {
//          
//          }
//       }
//    return to;
//    }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::is_in_subtree(const iterator_base& it, const iterator_base& begin, 
                                                 const iterator_base& end) const
   {
   // FIXME: this should be optimised.
   pre_order_iterator tmp=begin;
   while(tmp!=end) {
      if(tmp==it) return true;
      ++tmp;
      }
   return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::is_valid(const iterator_base& it) const
   {
   if(it.node==0 || it.node==feet || it.node==head) return false;
   else return true;
   }

template <class T, class tree_node_allocator>
unsigned int tree<T, tree_node_allocator>::index(sibling_iterator it) const
   {
   unsigned int ind=0;
   if(it.node->parent==0) {
      while(it.node->prev_sibling!=head) {
         it.node=it.node->prev_sibling;
         ++ind;
         }
      }
   else {
      while(it.node->prev_sibling!=0) {
         it.node=it.node->prev_sibling;
         ++ind;
         }
      }
   return ind;
   }


template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::child(const iterator_base& it, unsigned int num) const
   {
   tree_node *tmp=it.node->first_child;
   while(num--) {
      assert(tmp!=0);
      tmp=tmp->next_sibling;
      }
   return tmp;
   }




// Iterator base

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::iterator_base::iterator_base()
   : node(0), skip_current_children_(false)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::iterator_base::iterator_base(tree_node *tn)
   : node(tn), skip_current_children_(false)
   {
   }

template <class T, class tree_node_allocator>
T& tree<T, tree_node_allocator>::iterator_base::operator*() const
   {
   return node->data;
   }

template <class T, class tree_node_allocator>
T* tree<T, tree_node_allocator>::iterator_base::operator->() const
   {
   return &(node->data);
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::post_order_iterator::operator!=(const post_order_iterator& other) const
   {
   if(other.node!=this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::post_order_iterator::operator==(const post_order_iterator& other) const
   {
   if(other.node==this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::pre_order_iterator::operator!=(const pre_order_iterator& other) const
   {
   if(other.node!=this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::pre_order_iterator::operator==(const pre_order_iterator& other) const
   {
   if(other.node==this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::sibling_iterator::operator!=(const sibling_iterator& other) const
   {
   if(other.node!=this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::sibling_iterator::operator==(const sibling_iterator& other) const
   {
   if(other.node==this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::leaf_iterator::operator!=(const leaf_iterator& other) const
   {
   if(other.node!=this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::leaf_iterator::operator==(const leaf_iterator& other) const
   {
   if(other.node==this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::iterator_base::begin() const
   {
   if(node->first_child==0) 
      return end();

   sibling_iterator ret(node->first_child);
   ret.parent_=this->node;
   return ret;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::iterator_base::end() const
   {
   sibling_iterator ret(0);
   ret.parent_=node;
   return ret;
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::iterator_base::skip_children()
   {
   skip_current_children_=true;
   }

template <class T, class tree_node_allocator>
unsigned int tree<T, tree_node_allocator>::iterator_base::number_of_children() const
   {
   tree_node *pos=node->first_child;
   if(pos==0) return 0;
   
   unsigned int ret=1;
   while(pos!=node->last_child) {
      ++ret;
      pos=pos->next_sibling;
      }
   return ret;
   }



// Pre-order iterator

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator() 
   : iterator_base(0)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(tree_node *tn)
   : iterator_base(tn)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(const iterator_base &other)
   : iterator_base(other.node)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::pre_order_iterator::pre_order_iterator(const sibling_iterator& other)
   : iterator_base(other.node)
   {
   if(this->node==0) {
      if(other.range_last()!=0)
         this->node=other.range_last();
      else 
         this->node=other.parent_;
      this->skip_children();
      ++(*this);
      }
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator++()
   {
   assert(this->node!=0);
   if(!this->skip_current_children_ && this->node->first_child != 0) {
      this->node=this->node->first_child;
      }
   else {
      this->skip_current_children_=false;
      while(this->node->next_sibling==0) {
         this->node=this->node->parent;
         if(this->node==0)
            return *this;
         }
      this->node=this->node->next_sibling;
      }
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator--()
   {
   assert(this->node!=0);
   if(this->node->prev_sibling) {
      this->node=this->node->prev_sibling;
      while(this->node->last_child)
         this->node=this->node->last_child;
      }
   else {
      this->node=this->node->parent;
      if(this->node==0)
         return *this;
      }
   return *this;
}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::pre_order_iterator::operator++(int n)
   {
   pre_order_iterator copy = *this;
   ++(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::pre_order_iterator::operator--(int n)
{
  pre_order_iterator copy = *this;
  --(*this);
  return copy;
}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator+=(unsigned int num)
   {
   while(num>0) {
      ++(*this);
      --num;
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::pre_order_iterator& tree<T, tree_node_allocator>::pre_order_iterator::operator-=(unsigned int num)
   {
   while(num>0) {
      --(*this);
      --num;
      }
   return (*this);
   }



// Post-order iterator

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::post_order_iterator::post_order_iterator() 
   : iterator_base(0)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(tree_node *tn)
   : iterator_base(tn)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(const iterator_base &other)
   : iterator_base(other.node)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::post_order_iterator::post_order_iterator(const sibling_iterator& other)
   : iterator_base(other.node)
   {
   if(this->node==0) {
      if(other.range_last()!=0)
         this->node=other.range_last();
      else 
         this->node=other.parent_;
      this->skip_children();
      ++(*this);
      }
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator++()
   {
   assert(this->node!=0);
   if(this->node->next_sibling==0) {
      this->node=this->node->parent;
      this->skip_current_children_=false;
      }
   else {
      this->node=this->node->next_sibling;
      if(this->skip_current_children_) {
         this->skip_current_children_=false;
         }
      else {
         while(this->node->first_child)
            this->node=this->node->first_child;
         }
      }
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator--()
   {
   assert(this->node!=0);
   if(this->skip_current_children_ || this->node->last_child==0) {
      this->skip_current_children_=false;
      while(this->node->prev_sibling==0)
         this->node=this->node->parent;
      this->node=this->node->prev_sibling;
      }
   else {
      this->node=this->node->last_child;
      }
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::post_order_iterator::operator++(int)
   {
   post_order_iterator copy = *this;
   ++(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator tree<T, tree_node_allocator>::post_order_iterator::operator--(int)
   {
   post_order_iterator copy = *this;
   --(*this);
   return copy;
   }


template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator+=(unsigned int num)
   {
   while(num>0) {
      ++(*this);
      --num;
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::post_order_iterator& tree<T, tree_node_allocator>::post_order_iterator::operator-=(unsigned int num)
   {
   while(num>0) {
      --(*this);
      --num;
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::post_order_iterator::descend_all()
   {
   assert(this->node!=0);
   while(this->node->first_child)
      this->node=this->node->first_child;
   }


// Breadth-first iterator

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator()
   : iterator_base()
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator(tree_node *tn)
   : iterator_base(tn)
   {
   traversal_queue.push(tn);
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::breadth_first_queued_iterator::breadth_first_queued_iterator(const iterator_base& other)
   : iterator_base(other.node)
   {
   traversal_queue.push(other.node);
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator!=(const breadth_first_queued_iterator& other) const
   {
   if(other.node!=this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator==(const breadth_first_queued_iterator& other) const
   {
   if(other.node==this->node) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::breadth_first_queued_iterator& tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator++()
   {
   assert(this->node!=0);

   // Add child nodes and pop current node
   sibling_iterator sib=this->begin();
   while(sib!=this->end()) {
      traversal_queue.push(sib.node);
      ++sib;
      }
   traversal_queue.pop();
   if(traversal_queue.size()>0)
      this->node=traversal_queue.front();
   else 
      this->node=0;
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::breadth_first_queued_iterator tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator++(int n)
   {
   breadth_first_queued_iterator copy = *this;
   ++(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::breadth_first_queued_iterator& tree<T, tree_node_allocator>::breadth_first_queued_iterator::operator+=(unsigned int num)
   {
   while(num>0) {
      ++(*this);
      --num;
      }
   return (*this);
   }



// Fixed depth iterator

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator()
   : iterator_base()
   {
   set_first_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(tree_node *tn)
   : iterator_base(tn)
   {
   set_first_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const iterator_base& other)
   : iterator_base(other.node)
   {
   set_first_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const sibling_iterator& other)
   : iterator_base(other.node), first_parent_(other.parent_)
   {
   find_leftmost_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(const fixed_depth_iterator& other)
   : iterator_base(other.node), first_parent_(other.first_parent_)
   {
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::fixed_depth_iterator::operator==(const fixed_depth_iterator& other) const
   {
   if(other.node==this->node && other.first_parent_==first_parent_) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
bool tree<T, tree_node_allocator>::fixed_depth_iterator::operator!=(const fixed_depth_iterator& other) const
   {
   if(other.node!=this->node || other.first_parent_!=first_parent_) return true;
   else return false;
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::fixed_depth_iterator::set_first_parent_()
   {
   return; // FIXME: we do not use first_parent_ yet, and it actually needs some serious reworking if
           // it is ever to work at the 'head' level.
   first_parent_=0;
   if(this->node==0) return;
   if(this->node->parent!=0)
      first_parent_=this->node->parent;
   if(first_parent_)
      find_leftmost_parent_();
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::fixed_depth_iterator::find_leftmost_parent_()
   {
   return; // FIXME: see 'set_first_parent()'
   tree_node *tmppar=first_parent_;
   while(tmppar->prev_sibling) {
      tmppar=tmppar->prev_sibling;
      if(tmppar->first_child)
         first_parent_=tmppar;
      }
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator++()
   {
   assert(this->node!=0);

   if(this->node->next_sibling) {
      this->node=this->node->next_sibling;
      }
   else { 
      int relative_depth=0;
      upper:
      do {
         this->node=this->node->parent;
         if(this->node==0) return *this;
         --relative_depth;
         } while(this->node->next_sibling==0);
      lower:
      this->node=this->node->next_sibling;
      while(this->node->first_child==0) {
         if(this->node->next_sibling==0)
            goto upper;
         this->node=this->node->next_sibling;
         if(this->node==0) return *this;
         }
      while(relative_depth<0 && this->node->first_child!=0) {
         this->node=this->node->first_child;
         ++relative_depth;
         }
      if(relative_depth<0) {
         if(this->node->next_sibling==0) goto upper;
         else                          goto lower;
         }
      }
   return *this;

// if(this->node->next_sibling!=0) {
//    this->node=this->node->next_sibling;
//    assert(this->node!=0);
//    if(this->node->parent==0 && this->node->next_sibling==0) // feet element
//       this->node=0;
//    }
// else {
//    tree_node *par=this->node->parent;
//    do {
//       par=par->next_sibling;
//       if(par==0) { // FIXME: need to keep track of this!
//          this->node=0;
//          return *this;
//          }
//       } while(par->first_child==0);
//    this->node=par->first_child;
//    }
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator--()
   {
   assert(this->node!=0);
   if(this->node->prev_sibling!=0) {
      this->node=this->node->prev_sibling;
      assert(this->node!=0);
      if(this->node->parent==0 && this->node->prev_sibling==0) // head element
         this->node=0;
      }
   else {
      tree_node *par=this->node->parent;
      do {
         par=par->prev_sibling;
         if(par==0) { // FIXME: need to keep track of this!
            this->node=0;
            return *this;
            }
         } while(par->last_child==0);
      this->node=par->last_child;
      }
   return *this;
}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::fixed_depth_iterator::operator++(int)
   {
   fixed_depth_iterator copy = *this;
   ++(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator tree<T, tree_node_allocator>::fixed_depth_iterator::operator--(int)
{
  fixed_depth_iterator copy = *this;
  --(*this);
  return copy;
}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator-=(unsigned int num)
   {
   while(num>0) {
      --(*this);
      --(num);
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::fixed_depth_iterator& tree<T, tree_node_allocator>::fixed_depth_iterator::operator+=(unsigned int num)
   {
   while(num>0) {
      ++(*this);
      --(num);
      }
   return *this;
   }

// FIXME: add the other members of fixed_depth_iterator.


// Sibling iterator

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::sibling_iterator::sibling_iterator() 
   : iterator_base()
   {
   set_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(tree_node *tn)
   : iterator_base(tn)
   {
   set_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(const iterator_base& other)
   : iterator_base(other.node)
   {
   set_parent_();
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::sibling_iterator::sibling_iterator(const sibling_iterator& other)
   : iterator_base(other), parent_(other.parent_)
   {
   }

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::sibling_iterator::set_parent_()
   {
   parent_=0;
   if(this->node==0) return;
   if(this->node->parent!=0)
      parent_=this->node->parent;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator++()
   {
   if(this->node)
      this->node=this->node->next_sibling;
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator--()
   {
   if(this->node) this->node=this->node->prev_sibling;
   else {
      assert(parent_);
      this->node=parent_->last_child;
      }
   return *this;
}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling_iterator::operator++(int)
   {
   sibling_iterator copy = *this;
   ++(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::sibling_iterator::operator--(int)
   {
   sibling_iterator copy = *this;
   --(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator+=(unsigned int num)
   {
   while(num>0) {
      ++(*this);
      --num;
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator-=(unsigned int num)
   {
   while(num>0) {
      --(*this);
      --num;
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::tree_node *tree<T, tree_node_allocator>::sibling_iterator::range_first() const
   {
   tree_node *tmp=parent_->first_child;
   return tmp;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::tree_node *tree<T, tree_node_allocator>::sibling_iterator::range_last() const
   {
   return parent_->last_child;
   }

// Leaf iterator

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::leaf_iterator::leaf_iterator() 
   : iterator_base(0)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(tree_node *tn)
   : iterator_base(tn)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const iterator_base &other)
   : iterator_base(other.node)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const sibling_iterator& other)
   : iterator_base(other.node)
   {
   if(this->node==0) {
      if(other.range_last()!=0)
         this->node=other.range_last();
      else 
         this->node=other.parent_;
      ++(*this);
      }
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator++()
   {
   assert(this->node!=0);
   while(this->node->next_sibling==0) {
      if (this->node->parent==0) return *this;
      this->node=this->node->parent;
      }
   this->node=this->node->next_sibling;
   while(this->node->first_child)
      this->node=this->node->first_child;
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator--()
   {
   assert(this->node!=0);
   while (this->node->prev_sibling==0) {
      if (this->node->parent==0) return *this;
      this->node=this->node->parent;
      }
   this->node=this->node->prev_sibling;
   while(this->node->last_child)
      this->node=this->node->last_child;
   return *this;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::leaf_iterator::operator++(int)
   {
   leaf_iterator copy = *this;
   ++(*this);
   return copy;
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::leaf_iterator::operator--(int)
   {
   leaf_iterator copy = *this;
   --(*this);
   return copy;
   }


template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator+=(unsigned int num)
   {
   while(num>0) {
      ++(*this);
      --num;
      }
   return (*this);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator& tree<T, tree_node_allocator>::leaf_iterator::operator-=(unsigned int num)
   {
   while(num>0) {
      --(*this);
      --num;
      }
   return (*this);
   }

#endif

// Local variables:
// default-tab-width: 3
// End:

---