
//	STL-like templated tree class.
//
// Copyright (C) 2001-2024 Kasper Peeters <kasper@phi-sci.com>
// Distributed under the GNU General Public License version 3.
//
// Special permission to use tree.hh under the conditions of a 
// different license can be requested from the author.

/** \mainpage tree.hh
    \author   Kasper Peeters
    \version  3.20
    \date     2024-04-12
    \see      http://github.com/kpeeters/tree.hh/

   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. 
*/


#ifndef tree_hh_
#define tree_hh_

#include <cassert>
#include <memory>
#include <stdexcept>
#include <iterator>
#include <set>
#include <queue>
#include <algorithm>
#include <cstddef>
#include <string>

/// 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_();
		tree_node_(const T&);
		tree_node_(T&&);

		tree_node_<T> *parent;
	   tree_node_<T> *first_child, *last_child;
		tree_node_<T> *prev_sibling, *next_sibling;
		T data;
}; 

template<class T>
tree_node_<T>::tree_node_()
	: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0)
	{
	}

template<class T>
tree_node_<T>::tree_node_(const T& val)
	: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0), data(val)
	{
	}

template<class T>
tree_node_<T>::tree_node_(T&& val)
	: parent(0), first_child(0), last_child(0), prev_sibling(0), next_sibling(0), data(val)
	{
	}

// Throw an exception with a stacktrace.

//template <class E>
//void throw_with_trace(const E& e)
//	{
//	throw boost::enable_error_info(e)
//		<< traced(boost::stacktrace::stacktrace());
//	}

class navigation_error : public std::logic_error {
	public:
		navigation_error(const std::string& s) : std::logic_error(s)
			{
//			assert(1==0);
//			std::ostringstream str;
//			std::cerr << boost::stacktrace::stacktrace() << std::endl;
//			str << boost::stacktrace::stacktrace();
//			stacktrace=str.str();
			}

//		virtual const char *what() const noexcept override
//			{
//			return (std::logic_error::what()+std::string("; ")+stacktrace).c_str();
//			}
//
//		std::string stacktrace;
};
		
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();                                         // empty constructor
		tree(const T&);                                 // constructor setting given element as head
		tree(const iterator_base&);
		tree(const tree<T, tree_node_allocator>&);      // copy constructor
		tree(tree<T, tree_node_allocator>&&);           // move constructor
		~tree();
		tree<T,tree_node_allocator>& operator=(const tree<T, tree_node_allocator>&);   // copy assignment
		tree<T,tree_node_allocator>& operator=(tree<T, tree_node_allocator>&&);        // move assignment

      /// 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();
				void         skip_children(bool skip);
				/// 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);

				pre_order_iterator&  next_skip_children();
		};

		/// 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&);

				void swap(fixed_depth_iterator&, fixed_depth_iterator&);
				fixed_depth_iterator& operator=(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 *top_node;
		};

		/// 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&);

				void swap(sibling_iterator&, sibling_iterator&);
				sibling_iterator& operator=(sibling_iterator);
				
				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 *, tree_node *top=0);
            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);
			private:
				tree_node *top_node;
      };

		/// 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 end iterator of the tree.
		post_order_iterator  end_post() const;
		/// Return fixed-depth iterator to the first node at a given depth from the given iterator.
		/// If 'walk_back=true', a depth=0 iterator will be taken from the beginning of the sibling
		/// range, not the current node.
		fixed_depth_iterator begin_fixed(const iterator_base&, unsigned int, bool walk_back=true) const;
		/// Return fixed-depth end iterator.
		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 end iterator.
		breadth_first_queued_iterator end_breadth_first() const;
		/// Return sibling iterator to the first child of given node.
		static sibling_iterator     begin(const iterator_base&);
		/// Return sibling end iterator for children of given node.
		static sibling_iterator     end(const iterator_base&);
      /// Return leaf iterator to the first leaf of the tree.
      leaf_iterator   begin_leaf() const;
      /// Return leaf end iterator for entire tree.
      leaf_iterator   end_leaf() const;
      /// Return leaf iterator to the first leaf of the subtree at the given node.
      leaf_iterator   begin_leaf(const iterator_base& top) const;
      /// Return leaf end iterator for the subtree at the given node.
      leaf_iterator   end_leaf(const iterator_base& top) const;

		typedef std::vector<int> path_t;
		/// Return a path (to be taken from the 'top' node) corresponding to a node in the tree.
		/// The first integer in path_t is the number of steps you need to go 'right' in the sibling
		/// chain (so 0 if we go straight to the children).
		path_t          path_from_iterator(const iterator_base& iter, const iterator_base& top) const;
		/// Return an iterator given a path from the 'top' node.
		iterator        iterator_from_path(const path_t&, const iterator_base& top) const;
				
		/// Return iterator to the parent of a node. Throws a `navigation_error` if the node
		/// does not have a parent.
		template<typename	iter> static iter parent(iter);
		/// Return iterator to the previous sibling of a node.
		template<typename iter> static iter previous_sibling(iter);
		/// Return iterator to the next sibling of a node.
		template<typename iter> static iter next_sibling(iter);
		/// 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&);
		/// Erase all siblings to the right of the iterator.
		void     erase_right_siblings(const iterator_base&);
		/// Erase all siblings to the left of the iterator.
		void     erase_left_siblings(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 append_child(iter position, T&& x);
		template<typename iter> iter prepend_child(iter position, const T& x);
		template<typename iter> iter prepend_child(iter position, 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);
		pre_order_iterator set_head(T&& x);
		/// Insert node as previous sibling of node pointed to by position.
		template<typename iter> iter insert(iter position, const T& x);
		template<typename iter> iter insert(iter position, T&& x);
		/// Specialisation of previous member.
		sibling_iterator insert(sibling_iterator position, const T& x);
		sibling_iterator insert(sibling_iterator position, T&& x);
		/// Insert node (with children) pointed to by subtree as previous sibling of node pointed to by position.
		/// Does not change the subtree itself (use move_in or move_in_below for that).
		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);
		template<typename iter> iter insert_after(iter position, 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 (plus subtree) a child of the new node.
		template<typename iter> iter wrap(iter position, const T& x);
		/// Replace the range of sibling nodes (plus subtrees), making these children of the new node.
		template<typename iter> iter wrap(iter from, iter to, 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);

		/// Extract the subtree starting at the indicated node, removing it from the original tree.
		tree                         move_out(iterator);
		/// Inverse of take_out: inserts the given tree as previous sibling of indicated node by a 
		/// move operation, that is, the given tree becomes empty. Returns iterator to the top node.
		template<typename iter> iter move_in(iter, tree&);
		/// As above, but now make the tree the last child of the indicated node.
		template<typename iter> iter move_in_below(iter, tree&);
		/// As above, but now make the tree the nth child of the indicated node (if possible).
		template<typename iter> iter move_in_as_nth_child(iter, size_t, tree&);

		/// 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);
		/// As above, but using two trees with a single top node at the 'to' and 'from' positions.
		void     merge(iterator to, iterator from, bool duplicate_leaves);
		/// 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). The iterators will remain valid and keep 
		/// pointing to the same nodes, which now sit at different locations in the tree.
	   void     swap(iterator, iterator);
		
		/// Count the total number of nodes.
		size_t   size() const;
		/// Count the total number of nodes below the indicated node (plus one).
		size_t   size(const iterator_base&) const;
		/// Check if tree is empty.
		bool     empty() const;
		/// Compute the depth to the root or to a fixed other iterator.
		static int depth(const iterator_base&);
		static int depth(const iterator_base&, const iterator_base&);
		/// Compute the depth to the root, counting all levels for which predicate returns true.
		template<class Predicate>
		static int depth(const iterator_base&, Predicate p);
		/// Compute the depth distance between two nodes, counting all levels for which predicate returns true.
		template<class Predicate>
		static int distance(const iterator_base& top, const iterator_base& bottom, Predicate p);
		/// Determine the maximal depth of the tree. An empty tree has max_depth=-1.
		int      max_depth() const;
		/// Determine the maximal depth of the tree with top node at the given position.
		int      max_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 siblings (left and right) of node at iterator. Total nodes at this level is +1.
		unsigned int number_of_siblings(const iterator_base&) const;
		/// Determine whether node at position is in the subtrees with indicated top node.
   	bool     is_in_subtree(const iterator_base& position, const iterator_base& top) 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 whether the iterator is one of the 'head' nodes at the top level, i.e. has no parent.
		static   bool is_head(const iterator_base&);
		/// Find the lowest common ancestor of two nodes, that is, the deepest node such that
		/// both nodes are descendants of it.
		iterator lowest_common_ancestor(const iterator_base&, 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.
		static sibling_iterator child(const iterator_base& position, unsigned int);
		/// Return iterator to the sibling indicated by index
		sibling_iterator sibling(const iterator_base& position, unsigned int) const;  				
		
		/// For debugging only: verify internal consistency by inspecting all pointers in the tree
		/// (which will also trigger a valgrind error in case something got corrupted).
		void debug_verify_consistency() 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) const
					{
					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(tree<T, tree_node_allocator>&& x) 
	{
	head_initialise_();
	if(x.head->next_sibling!=x.feet) { // move tree if non-empty only
		head->next_sibling=x.head->next_sibling;
		feet->prev_sibling=x.feet->prev_sibling;
		x.head->next_sibling->prev_sibling=head;
		x.feet->prev_sibling->next_sibling=feet;
		x.head->next_sibling=x.feet;
		x.feet->prev_sibling=x.head;
		}
	}

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();
	std::allocator_traits<decltype(alloc_)>::destroy(alloc_, head);
	std::allocator_traits<decltype(alloc_)>::destroy(alloc_, feet);
	std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, head, 1);
	std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, feet, 1);
	}

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::head_initialise_() 
   { 
   head = std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
   feet = std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, head, tree_node_<T>());
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, feet, tree_node_<T>());	

   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>
tree<T,tree_node_allocator>& tree<T, tree_node_allocator>::operator=(const tree<T, tree_node_allocator>& other)
	{
	if(this != &other)
		copy_(other);
	return *this;
	}

template <class T, class tree_node_allocator>
tree<T,tree_node_allocator>& tree<T, tree_node_allocator>::operator=(tree<T, tree_node_allocator>&& x)
	{
	if(this != &x) {
		clear(); // clear any existing data.
		
		head->next_sibling=x.head->next_sibling;
		feet->prev_sibling=x.feet->prev_sibling;
		x.head->next_sibling->prev_sibling=head;
		x.feet->prev_sibling->next_sibling=feet;
		x.head->next_sibling=x.feet;
		x.feet->prev_sibling=x.head;
		}
	return *this;
	}

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));
		std::allocator_traits<decltype(alloc_)>::destroy(alloc_, prev);
		std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, prev, 1);
		}
	it.node->first_child=0;
	it.node->last_child=0;
//	std::cout << "exit" << std::endl;
	}

template<class T, class tree_node_allocator> 
void tree<T, tree_node_allocator>::erase_right_siblings(const iterator_base& it)
	{
	if(it.node==0) return;

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

	while(cur!=0) {
		prev=cur;
		cur=cur->next_sibling;
		erase_children(pre_order_iterator(prev));
		std::allocator_traits<decltype(alloc_)>::destroy(alloc_, prev);
		std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, prev, 1);
		}
	it.node->next_sibling=0;
	if(it.node->parent!=0)
		it.node->parent->last_child=it.node;
	}

template<class T, class tree_node_allocator> 
void tree<T, tree_node_allocator>::erase_left_siblings(const iterator_base& it)
	{
	if(it.node==0) return;

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

	while(cur!=0) {
		prev=cur;
		cur=cur->prev_sibling;
		erase_children(pre_order_iterator(prev));
		std::allocator_traits<decltype(alloc_)>::destroy(alloc_, prev);
		std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, prev, 1);
		}
	it.node->prev_sibling=0;
	if(it.node->parent!=0)
		it.node->parent->first_child=it.node;
	}

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;
		}

	std::allocator_traits<decltype(alloc_)>::destroy(alloc_, cur);
	std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, 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, bool walk_back) const
	{
	typename tree<T, tree_node_allocator>::fixed_depth_iterator ret;
	ret.top_node=pos.node;

	tree_node *tmp=pos.node;
	unsigned int curdepth=0;
	while(curdepth<dp) { // go down one level
		while(tmp->first_child==0) {
			if(tmp->next_sibling==0) {
				// try to walk up and then right again
				do {
					if(tmp==ret.top_node)
					   throw std::range_error("tree: begin_fixed out of range");
					tmp=tmp->parent;
               if(tmp==0) 
					   throw std::range_error("tree: begin_fixed out of range");
               --curdepth;
				   } while(tmp->next_sibling==0);
				}
			tmp=tmp->next_sibling;
			}
		tmp=tmp->first_child;
		++curdepth;
		}

	// Now walk back to the first sibling in this range.
	if(walk_back)
	while(tmp->prev_sibling!=0)
		tmp=tmp->prev_sibling;	
	
	ret.node=tmp;
	return ret;
	}

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: use is_valid() as a temporary workaround 
	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) 
	{
	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) 
	{
	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>
typename tree<T, tree_node_allocator>::path_t tree<T, tree_node_allocator>::path_from_iterator(const iterator_base& iter, const iterator_base& top) const
	{
	path_t path;
	tree_node *walk=iter.node;
		
	do {
		if(path.size()>0)
			walk=walk->parent;
		int num=0;
		while(walk!=top.node && walk->prev_sibling!=0 && walk->prev_sibling!=head) {
			++num;
			walk=walk->prev_sibling;
			}
		path.push_back(num);
		}
	while(walk->parent!=0 && walk!=top.node);

	std::reverse(path.begin(), path.end());
	return path;
	}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::iterator_from_path(const path_t& path, const iterator_base& top) const
	{
	iterator it=top;
	tree_node *walk=it.node;

	for(size_t step=0; step<path.size(); ++step) {
		if(step>0)
			walk=walk->first_child;
		if(walk==0)
			throw std::range_error("tree::iterator_from_path: no more nodes at step "+std::to_string(step));

		for(int i=0; i<path[step]; ++i) {
			walk=walk->next_sibling;
			if(walk==0)
				throw std::range_error("tree::iterator_from_path: out of siblings at step "+std::to_string(step));
			}
		}
	it.node=walk;
	return it;
	}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::begin_leaf(const iterator_base& top) const
   {
	tree_node *tmp=top.node;
	while(tmp->first_child)
		 tmp=tmp->first_child;
   return leaf_iterator(tmp, top.node);
   }

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::leaf_iterator tree<T, tree_node_allocator>::end_leaf(const iterator_base& top) const
   {
   return leaf_iterator(top.node, top.node);
   }

template <class T, class tree_node_allocator>
template <typename iter>
iter tree<T, tree_node_allocator>::parent(iter position) 
	{
	if(position.node==0)
		throw navigation_error("tree: attempt to navigate from null iterator.");
	 
	if(position.node->parent==0) 
		throw navigation_error("tree: attempt to navigate up past head node.");

	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) 
	{
	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) 
	{
	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
	{
	// We make use of a temporary fixed_depth iterator to implement this.

	typename tree<T, tree_node_allocator>::fixed_depth_iterator tmp(position.node);

	++tmp;
	return iter(tmp);

	//	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!=feet);
	assert(position.node);

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, tree_node_<T>());
	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!=feet);
	assert(position.node);

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, tree_node_<T>());
	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!=feet);
	assert(position.node);

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, 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>::append_child(iter position, T&& x)
	{
	assert(position.node!=head);
	assert(position.node!=feet);
	assert(position.node);

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp); // Here is where the move semantics kick in
	std::swap(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!=feet);
	assert(position.node);

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, 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>::prepend_child(iter position, T&& x)
	{
	assert(position.node!=head);
	assert(position.node!=feet);
	assert(position.node);

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);
	std::swap(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!=feet);
	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!=feet);
	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!=feet);
	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!=feet);
	assert(position.node);

	if(from==to) return from; // should return end of tree?

	iter ret;
	do {
		--to;
		ret=insert_subtree(position.begin(), to);
		}
	while(to!=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>
typename tree<T, tree_node_allocator>::pre_order_iterator tree<T, tree_node_allocator>::set_head(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.
		}
	assert(position.node!=head); // Cannot insert before head.

	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, 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>
template <class iter>
iter tree<T, tree_node_allocator>::insert(iter position, 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=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);
	std::swap(tmp->data, x); // Move semantics
	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=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, 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>
typename tree<T, tree_node_allocator>::sibling_iterator tree<T, tree_node_allocator>::insert(sibling_iterator position, T&& x)
	{
	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);
	std::swap(tmp->data, x); // Move semantics

	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=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, 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_after(iter position, T&& x)
	{
	tree_node *tmp=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp);
	std::swap(tmp->data, x); // move semantics
	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);
	position.node->data=x;
//	alloc_.destroy(position.node);
//	alloc_.construct(position.node, 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=std::allocator_traits<decltype(alloc_)>::allocate(alloc_, 1, 0);
	std::allocator_traits<decltype(alloc_)>::construct(alloc_, tmp, (*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);
	std::allocator_traits<decltype(alloc_)>::destroy(alloc_, current_to);
	std::allocator_traits<decltype(alloc_)>::deallocate(alloc_, 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;
   for(;;) {
		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>::wrap(iter from, iter to, const T& x)
	{
	assert(from.node!=0);
	iter ret = insert(from, x);
	reparent(ret, from, 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;
		}
	else {
		src->parent=dst_prev_sibling->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;

//	if(dst==src->prev_sibling) {
//
//		}

	// 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 {
		assert(src->parent!=0);
		src->parent->first_child=src->next_sibling;
		}
	if(src->next_sibling!=0) src->next_sibling->prev_sibling=src->prev_sibling;
	else {
		assert(src->parent!=0);
		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 {
		assert(b_parent!=0);
		b_parent->first_child=src;
		}
	if(b_next_sibling!=0) b_next_sibling->prev_sibling=src;
	else {
		assert(b_parent!=0);
		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>
tree<T, tree_node_allocator> tree<T, tree_node_allocator>::move_out(iterator source)
	{
	tree ret;

	// Move source node into the 'ret' tree.
	ret.head->next_sibling = source.node;
	ret.feet->prev_sibling = source.node;

	// Close the links in the current tree.
	if(source.node->prev_sibling!=0) 
		source.node->prev_sibling->next_sibling = source.node->next_sibling;

	if(source.node->next_sibling!=0) 
		source.node->next_sibling->prev_sibling = source.node->prev_sibling;

	// If the moved-out node was a first or last child of
	// the parent, adjust those links.
	if(source.node->parent->first_child==source.node) { 
		if(source.node->next_sibling!=0)
			source.node->parent->first_child=source.node->next_sibling;
		else
			source.node->parent->first_child=0;
		}
	if(source.node->parent->last_child==source.node) { 
		if(source.node->prev_sibling!=0)
			source.node->parent->last_child=source.node->prev_sibling;
		else
			source.node->parent->last_child=0;
		}
	source.node->parent=0;
	
	// Fix source prev/next links.
	source.node->prev_sibling = ret.head;
	source.node->next_sibling = ret.feet;

	return ret; // A good compiler will move this, not copy.
	}

template <class T, class tree_node_allocator>
template<typename iter> iter tree<T, tree_node_allocator>::move_in(iter loc, tree& other)
	{
	if(other.head->next_sibling==other.feet) return loc; // other tree is empty

	tree_node *other_first_head = other.head->next_sibling;
	tree_node *other_last_head  = other.feet->prev_sibling;

	sibling_iterator prev(loc);
	--prev;
	
	prev.node->next_sibling = other_first_head;
	loc.node->prev_sibling  = other_last_head;
	other_first_head->prev_sibling = prev.node;
	other_last_head->next_sibling  = loc.node;

	// Adjust parent pointers.
	tree_node *walk=other_first_head;
	while(true) {
		walk->parent=loc.node->parent;
		if(walk==other_last_head)
			break;
		walk=walk->next_sibling;
		}

	// Close other tree.
	other.head->next_sibling=other.feet;
	other.feet->prev_sibling=other.head;

	return other_first_head;
	}

template <class T, class tree_node_allocator>
template<typename iter> iter tree<T, tree_node_allocator>::move_in_below(iter loc, tree& other)
	{
	if(other.head->next_sibling==other.feet) return loc; // other tree is empty

	auto n = other.number_of_children(loc);
	return move_in_as_nth_child(loc, n, other);
	}

template <class T, class tree_node_allocator>
template<typename iter> iter tree<T, tree_node_allocator>::move_in_as_nth_child(iter loc, size_t n, tree& other)
	{
	if(other.head->next_sibling==other.feet) return loc; // other tree is empty

	tree_node *other_first_head = other.head->next_sibling;
	tree_node *other_last_head  = other.feet->prev_sibling;

	if(n==0) {
		if(loc.node->first_child==0) {
			loc.node->first_child=other_first_head;
			loc.node->last_child=other_last_head;
			other_last_head->next_sibling=0;
			other_first_head->prev_sibling=0;
			} 
		else {
			loc.node->first_child->prev_sibling=other_last_head;
			other_last_head->next_sibling=loc.node->first_child;
			loc.node->first_child=other_first_head;
			other_first_head->prev_sibling=0;
			}
		}
	else {
		--n;
		tree_node *walk = loc.node->first_child;
		while(true) {
			if(walk==0)
				throw std::range_error("tree: move_in_as_nth_child position out of range");
			if(n==0) 
				break;
			--n;
			walk = walk->next_sibling;
			}
		if(walk->next_sibling==0) 
			loc.node->last_child=other_last_head;
		else 
			walk->next_sibling->prev_sibling=other_last_head;
		other_last_head->next_sibling=walk->next_sibling;
		walk->next_sibling=other_first_head;
		other_first_head->prev_sibling=walk;
		}

	// Adjust parent pointers.
	tree_node *walk=other_first_head;
	while(true) {
		walk->parent=loc.node;
		if(walk==other_last_head)
			break;
		walk=walk->next_sibling;
		}

	// Close other tree.
	other.head->next_sibling=other.feet;
	other.feet->prev_sibling=other.head;

	return other_first_head;
	}


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>::merge(iterator to, iterator from, bool duplicate_leaves)
	{
	sibling_iterator to1(to);
	sibling_iterator to2=to1;
	++to2;
	sibling_iterator from1(from);
	sibling_iterator from2=from1;
	++from2;

	merge(to1, to2, from1, from2, duplicate_leaves);
	}


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
	{
	assert(from!=to); // if from==to, the range is empty, hence no tree to return.

	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
	{
	assert(from!=to); // if from==to, the range is empty, hence no tree to return.

	tmp.set_head(value_type());
	tmp.replace(tmp.begin(), tmp.end(), from, to);
	}

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

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

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

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

template <class T, class tree_node_allocator>
int tree<T, tree_node_allocator>::max_depth() const
	{
	int maxd=-1;
	for(tree_node *it = head->next_sibling; it!=feet; it=it->next_sibling)
		maxd=std::max(maxd, max_depth(it));

	return maxd;
	}


template <class T, class tree_node_allocator>
int tree<T, tree_node_allocator>::max_depth(const iterator_base& pos) const
	{
	tree_node *tmp=pos.node;

	if(tmp==0 || tmp==head || tmp==feet) return -1;

	int curdepth=0, maxdepth=0;
	while(true) { // try to walk the bottom of the tree
		while(tmp->first_child==0) {
			if(tmp==pos.node) return maxdepth;
			if(tmp->next_sibling==0) {
				// try to walk up and then right again
				do {
					tmp=tmp->parent;
               if(tmp==0) return maxdepth;
               --curdepth;
					}
				while(tmp->next_sibling==0);
				}
         if(tmp==pos.node) return maxdepth;
			tmp=tmp->next_sibling;
			}
		tmp=tmp->first_child;
		++curdepth;
		maxdepth=std::max(curdepth, maxdepth);
		} 
	}

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& top) const
   {
	sibling_iterator first=top;
	sibling_iterator last=first;
	++last;
	return is_in_subtree(it, first, last);
	}

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>
bool tree<T, tree_node_allocator>::is_head(const iterator_base& it) 
  	{
	if(it.node->parent==0) return true;
	return false;
	}

template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::iterator tree<T, tree_node_allocator>::lowest_common_ancestor(
	const iterator_base& one, const iterator_base& two) const
	{
	std::set<iterator, iterator_base_less> parents;

	// Walk up from 'one' storing all parents.
	iterator walk=one;
	do {
		walk=parent(walk);
		parents.insert(walk);
		}
	while( walk.node->parent );

	// Walk up from 'two' until we encounter a node in parents.
	walk=two;
	do {
		walk=parent(walk);
		if(parents.find(walk) != parents.end()) break;
		}
	while( walk.node->parent );

	return walk;
	}

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>::sibling(const iterator_base& it, unsigned int num) const
   {
   tree_node *tmp;
   if(it.node->parent==0) {
      tmp=head->next_sibling;
      while(num) {
         tmp = tmp->next_sibling;
         --num;
         }
      }
   else {
      tmp=it.node->parent->first_child;
      while(num) {
         assert(tmp!=0);
         tmp = tmp->next_sibling;
         --num;
         }
      }
   return tmp;
   }
 
template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::debug_verify_consistency() const
	{
	iterator it=begin();
	while(it!=end()) {
		// std::cerr << *it << " (" << it.node << ")" << std::endl;
		if(it.node->parent!=0) {
			if(it.node->prev_sibling==0) 
				assert(it.node->parent->first_child==it.node);
			else 
				assert(it.node->prev_sibling->next_sibling==it.node);
			if(it.node->next_sibling==0) 
				assert(it.node->parent->last_child==it.node);
			else
				assert(it.node->next_sibling->prev_sibling==it.node);
			}
		++it;
		}
	}

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) 
	{
	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 && other.top_node==this->top_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>
void tree<T, tree_node_allocator>::iterator_base::skip_children(bool skip)
   {
   skip_current_children_=skip;
   }

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)
	{
	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::next_skip_children() 
   {
	(*this).skip_children();
	(*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)
{
  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)
	{
	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()
	{
	}

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::fixed_depth_iterator::fixed_depth_iterator(tree_node *tn)
	: iterator_base(tn), top_node(0)
	{
	}

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), top_node(0)
	{
	}

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), top_node(0)
	{
	}

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), top_node(other.top_node)
	{
	}

template <class T, class tree_node_allocator>
void tree<T, tree_node_allocator>::fixed_depth_iterator::swap(fixed_depth_iterator& first, fixed_depth_iterator& second) 
	{
	std::swap(first.node, second.node);
	std::swap(first.skip_current_children_, second.skip_current_children_);
	std::swap(first.top_node, second.top_node);
	}

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=(fixed_depth_iterator other)
	{
	swap(*this, other);
	return *this;
	}
		
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.top_node==top_node) 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.top_node!=top_node) return true;
	else return false;
	}

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 {
			if(this->node==this->top_node) {
				this->node=0; // FIXME: return a proper fixed_depth end iterator once implemented
				return *this;
				}
			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;
	}

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

//
//
//	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;
	}


// 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::swap(sibling_iterator& first, sibling_iterator& second) 
	{
	std::swap(first.node, second.node);
	std::swap(first.skip_current_children_, second.skip_current_children_);
	std::swap(first.parent_, second.parent_);
	}


template <class T, class tree_node_allocator>
typename tree<T, tree_node_allocator>::sibling_iterator& tree<T, tree_node_allocator>::sibling_iterator::operator=(sibling_iterator other)
	{
	swap(*this, other);
	return *this;
	}
		
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), top_node(0)
   {
   }

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

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const iterator_base &other)
   : iterator_base(other.node), top_node(0)
   {
   }

template <class T, class tree_node_allocator>
tree<T, tree_node_allocator>::leaf_iterator::leaf_iterator(const sibling_iterator& other)
   : iterator_base(other.node), top_node(0)
   {
   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);
	if(this->node->first_child!=0) { // current node is no longer leaf (children got added)
		 while(this->node->first_child) 
			  this->node=this->node->first_child;
		 }
	else {
		 while(this->node->next_sibling==0) { 
			  if (this->node->parent==0) return *this;
			  this->node=this->node->parent;
			  if (top_node != 0 && this->node==top_node) return *this;
			  }
		 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;
		if (top_node !=0 && this->node==top_node) return *this; 
		}
	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:
// tab-width: 3
// End:
