// ==========================================================================
//                 SeqAn - The Library for Sequence Analysis
// ==========================================================================
// Copyright (c) 2006-2016, Knut Reinert, FU Berlin
// Copyright (c) 2013 NVIDIA Corporation
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
//     * Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//     * Redistributions in binary form must reproduce the above copyright
//       notice, this list of conditions and the following disclaimer in the
//       documentation and/or other materials provided with the distribution.
//     * Neither the name of Knut Reinert or the FU Berlin nor the names of
//       its contributors may be used to endorse or promote products derived
//       from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL KNUT REINERT OR THE FU BERLIN BE LIABLE
// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
// DAMAGE.
//
// ==========================================================================
// Author: David Weese <david.weese@fu-berlin.de>
// ==========================================================================

#ifndef SEQAN_HEADER_INDEX_ESA_STREE_H
#define SEQAN_HEADER_INDEX_ESA_STREE_H

namespace seqan
{

template <typename TText, typename TSpec>
SEQAN_CONCEPT_IMPL((Index<TText, IndexEsa<TSpec> >), (StringTreeConcept));

template <typename TText, typename TSpec>
SEQAN_CONCEPT_IMPL((Index<TText, IndexEsa<TSpec> > const), (StringTreeConcept));

/*!
 * @class VSTreeIterator VSTree Iterator
 * @extends Iter
 * @headerfile <seqan/index.h>
 *
 * @brief Abstract iterator for string trees, where string trees are trees constructed from a string.
 *
 * @signature template <typename TContainer, typename TSpec>
 *            class Iter<TContainer, VSTree<TSpec> >;
 *
 * @tparam TSpec      The specialization type.
 * @tparam TContainer Type of the container that can be iterated.  Types: @link IndexDfi @endlink,
 *                    @link IndexEsa @endlink, @link IndexWotd @endlink, @link FMIndex @endlink
 *
 * This iterator is a pointer to a node in the string tree of a given text. Depending on the index this can either be a
 * suffix or prefix tree/trie.  Every node can uniquely be mapped to an interval of suffices or prefixes.
 *
 * Default virtual string tree iterators depending on the @link Index @endlink
 *
 * <table border="1">
 * <tr>
 *   <td>IndexSa</td>
 *   <td>Virtual suffix trie iterator</td>
 * </tr>
 * <tr>
 *   <td>IndexEsa</td>
 *   <td>Virtual suffix tree iterator</td>
 * </tr>
 * <tr>
 *   <td>IndexWotd</td>
 *   <td>Virtual suffix tree iterator</td>
 * </tr>
 * <tr>
 *   <td>IndexDfi</td>
 *   <td>Virtual suffix tree iterator</td>
 * </tr>
 * <tr>
 *   <td>FMIndex</td>
 *   <td>Virtual prefix trie iterator</td>
 * </tr>
 * </table>
 *
 * @section Examples
 *
 * This code shows how an index can be used with iterators to achieve a pre-order tree like traversal
 * in DFS of the text "tobeornottobe". In order to do so a Top-Down History iterator is used.
 *
 * @include demos/dox/index/iterator.cpp
 *
 * @code{.output}
 *
 * be
 * beornottobe
 * e
 * eornottobe
 * nottobe
 * o
 * obe
 * obeornottobe
 * ornottobe
 * ottobe
 * rnottobe
 * t
 * tobe
 * tobeornottobe
 * ttobe
 */

    template < typename TIndex, typename TSpec >
    struct Value< Iter< TIndex, VSTree<TSpec> > > {
        typedef typename VertexDescriptor<TIndex>::Type Type;
    };

    template < typename TIndex, typename TSpec >
    struct Size< Iter< TIndex, VSTree<TSpec> > > {
        typedef typename Size<TIndex>::Type Type;
    };

    template < typename TIndex, typename TSpec >
    struct Position< Iter< TIndex, VSTree<TSpec> > > {
        typedef typename Position<TIndex>::Type Type;
    };

/*!
 * @mfn VSTreeIterator#EdgeLabel
 * @headerfile <seqan/index.h>
 * @brief Type of a string representing the characters of edges.
 *
 * @signature EdgeLabel<TSpec>::Type;
 *
 * @tparam TSpec Tag to specify the object of which the type of the edge labels is requested.
 *
 * @return Type of a string representing the characters of edges.
 */
    template < typename TSpec >
    struct EdgeLabel {};

    template < typename TIndex, typename TSpec >
    struct EdgeLabel< Iter< TIndex, VSTree<TSpec> > > {
        typedef typename InfixOnValue< typename Fibre<TIndex, FibreText>::Type const >::Type Type;
    };

/*!
 * @class TopDownIterator Top Down Iterator
 * @extends VSTreeIterator
 * @headerfile <seqan/index.h>
 *
 * @brief Iterator for virtual trees/tries that can go down and right beginning from the root.
 *
 * @signature template <typename TIndex, typename TSpec>
 *            class Iter<TContainer, VSTree< TopDown<TSpec> > >;
 *
 * @tparam TSpec The specialization type.
 * @tparam TIndex Type of the container that can be iterated. Types: @link IndexDfi @endlink, @link IndexEsa @endlink,
 *                @link IndexWotd @endlink, @link FMIndex @endlink, @link IndexSa @endlink
 *
 * If not copy-constructed the @link TopDownIterator @endlink starts in the root node of the virtual tree/trie.
 *
 * @note Instead of using the class Iter directly we recommend to use the result of the metafunction
 *       Iterator&t;TContainer, TopDown&lt;TSpec&gt; &gt;::Type (which is Iter&lt;TContainer,
 *       VSTree&lt;TopDown&lt;TSpec&gt; &gt; &gt;).
 */
/*!
 * @fn TopDownIterator::Iterator
 * @brief Constructor
 *
 * @signature Iter::Iter(index[, vertexDesc]);
 * @signature Iter::Iter(iterator);
 *
 * @param[in] index An index object.
 * @param[in] iterator Another TopDown iterator. (copy constructor) Types: TopDown
 *                    Iterator, TopDownHistory Iterator
 * @param[in] vertexDesc The vertex descriptor of a node the iterator should start
 *                       in. The iterator starts in the root node by default.
 *
 * If not copy-constructed the @link TopDownIterator @endlink starts in the
 * root node of the virtual tree.
 */

    template < typename TIndex, class TSpec >
    class Iter< TIndex, VSTree< TopDown<TSpec> > >
    {
    public:

        typedef typename VertexDescriptor<TIndex>::Type    TVertexDesc;
        typedef Iter                                    iterator;

        TIndex const    *index;        // container of all necessary tables
        TVertexDesc        vDesc;        // current interval in suffix array and
                                    // right border of parent interval (needed in goRight)

        // pseudo history stack (to go up at most one node)
        TVertexDesc        _parentDesc;

//____________________________________________________________________________

       
        Iter() : index() {}

       
        Iter(TIndex &_index):
            index(&_index)
        {
            _indexRequireTopDownIteration(_index);
            goRoot(*this);
        }

       
        Iter(TIndex &_index, MinimalCtor):
            index(&_index),
            vDesc(MinimalCtor()),
            _parentDesc(MinimalCtor()) {}

        // NOTE(esiragusa): _parentDesc is unitialized
       
        Iter(TIndex &_index, TVertexDesc const &_vDesc):
            index(&_index),
            vDesc(_vDesc)
        {
            _indexRequireTopDownIteration(_index);
        }

        template <typename TSpec2>
       
        Iter(Iter<TIndex, VSTree<TopDown<TSpec2> > > const &_origin):
            index(&container(_origin)),
            vDesc(value(_origin)),
            _parentDesc(nodeUp(_origin)) {}

//____________________________________________________________________________

        template <typename TSpec2>
        inline Iter const &
        operator = (Iter<TIndex, VSTree<TopDown<TSpec2> > > const &_origin)
        {
            index = &container(_origin);
            vDesc = value(_origin);
            _parentDesc = nodeUp(_origin);
            return *this;
        }
    };


/*!
 * @class TopDownHistoryIterator Top Down History Iterator
 * @implements ForwardIteratorConcept
 * @extends TopDownIterator
 * @headerfile <seqan/index.h>
 *
 * @brief String tree iterator that can go down, right, and up. Supports depth-
 *        first search.
 *
 * @signature template <typename TIndex, typename TSpec>
 *            class Iter<TIndex, VSTree<TopDown<ParentLinks<TSpec> > > >;
 *
 * @tparam TSpec Specifies the depth-first search mode.  Types: @link DfsOrder @endlink
 * @tparam TIndex Type of the container that can be iterated. Types: @link IndexDfi @endlink, @link IndexEsa @endlink,
 *                @link IndexWotd @endlink, @link FMIndex @endlink, @link IndexSa @endlink
 *
 * @note Instead of using the class Iter directly we recommend to use the result of the metafunction
 *       Iterator&lt;TContainer, TopDown&lt;ParentLinks&lt;TSpec&gt; &gt; &gt;::Type (which is Iter&lt;TContainer,
 *       VSTree&lt;ParentLinks&lt;TopDown&lt;TSpec&gt; &gt; &gt; &gt;).
 *
 * If not copy-constructed the @link TopDownHistoryIterator @endlink starts in the root node of the string tree.
 * Depending on the depth-first search mode the root is not the first DFS node. To go to the first DFS node use @link
 * VSTreeIterator#goBegin @endlink.
 *
 * @section Example
 *
 * @link DemoConstraintIterator @endlink
 */
/*!
 * @fn TopDownHistoryIterator::Iterator
 * @brief Constructor
 *
 * @signature Iter::Iter(index);
 * @signature Iter::Iter(iterator);
 *
 * @param[in] index    An index object.
 * @param[in] iterator Another TopDownHistory iterator. (copy constructor) Types:
 *                     TopDownHistory Iterator
 *
 * If not copy-constructed the @link TopDownHistoryIterator @endlink starts in
 * the root node of the string tree.
 */

    template < typename TVSTreeIter >
    struct HistoryStackEntry_;

    template <typename TSize>
    struct HistoryStackEsa_
    {
        Pair<TSize> range;        // current SA interval of hits

        inline
        HistoryStackEsa_() {}

        template <typename TSize_>
        inline
        HistoryStackEsa_(Pair<TSize_> const &_range): range(_range) {}
    };

    template < typename TIndex, typename TSpec >
    struct HistoryStackEntry_< Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > >
    {
        typedef HistoryStackEsa_<typename Size<TIndex>::Type>    Type;
    };

    template <typename TVSTreeIter>
    struct HistoryStack_;

    template <typename TIndex, typename TSpec>
    struct HistoryStack_<Iter<TIndex, VSTree<TSpec> > >
    {
        typedef Iter<TIndex, VSTree<TSpec> >                        TIter_;
        typedef String<typename HistoryStackEntry_<TIter_>::Type>   Type;

//        typedef String<typename HistoryStackEntry_<TIter_>::Type, Block<> > Type;
    };

    template < typename TIndex, class TSpec >
    class Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > >:
        public Iter< TIndex, VSTree< TopDown<> > >
    {
    public:

        typedef Iter< TIndex, VSTree< TopDown<> > >        TBase;
        typedef    typename HistoryStack_<Iter>::Type      TStack;
        typedef Iter                                    iterator;

        TStack            history;    // contains all previously visited intervals (allows one to go up)

//____________________________________________________________________________

       
        Iter() :
            TBase()
        {}

       
        Iter(TIndex &_index):
            TBase(_index) {}

       
        Iter(TIndex &_index, MinimalCtor):
            TBase(_index, MinimalCtor()) {}

       
        Iter(Iter const &_origin):
            TBase((TBase const &)_origin),
            history(_origin.history) {}

//____________________________________________________________________________

        inline
        Iter const &
        operator = (Iter const &_origin)
        {
            *(TBase*)(this) = _origin;
            history = _origin.history;
            return *this;
        }
    };

//    //TODO(weese): define concepts somewhere else
//    SEQAN_CONCEPT(ParentLinksConcepts,(T))
//    {
//        SEQAN_CONCEPT_USAGE(ParentLinksConcepts)
//        {
//            goUp(a);
//        }
//    private:
//        T a;
//    };
//
//    template <typename TIndex, class TSpec>
//    SEQAN_CONCEPT_IMPL((ParentLinksConcepts), Iter<TIndex,VSTree<TopDown<ParentLinks<TSpec> > > >);

/*!
 * @class BottomUpIterator Bottom Up Iterator
 * @implements ForwardIteratorConcept
 * @extends VSTreeIterator
 * @headerfile <seqan/index.h>
 * @brief Iterator for an efficient postorder depth-first search in a virtual string tree.
 *
 * @signature template <typename TIndex, typename TSpec>
 *            class Iter<TContainer, VSTree< BottomUp<TSpec> > >;
 *
 * @tparam TSpec The specialization type.
 * @tparam TIndex Type of the container that can be iterated.
 *
 * @note Instead of using the class Iter directly we recommend to use the result of the metafunction
 *       Iterator&lt;TContainer, BottomUp&lt;TSpec&gt; &gt;::Type (which is Iter&lt;TContainer,
 *       VSTree&lt;BottomUp&lt;TSpec&gt; &gt; &gt;).
 */

/*!
 * @fn BottomUpIterator::Iter
 * @brief Constructor
 *
 * @signature Iter::Iter(index);
 * @signature Iter::Iter(iterator);
 *
 * @param[in] index    An index object.
 * @param[in] iterator A Bottom Up Iterator.
 *
 * If not copy-constructed the @link BottomUpIterator @endlink starts in the first DFS node, which is the left-most leaf
 * of the virtual string tree.
 */

    template < typename TIndex, typename TSpec >
    struct HistoryStackEntry_< Iter< TIndex, VSTree< BottomUp<TSpec> > > >
    {
        typedef HistoryStackEsa_<typename Size<TIndex>::Type>    Type;
    };

    template < typename TIndex, typename TSpec >
    class Iter< TIndex, VSTree< BottomUp<TSpec> > >
    {
    public:

        typedef typename VertexDescriptor<TIndex>::Type    TVertexDesc;
        typedef typename Size<TIndex>::Type                TSize;
        typedef    typename HistoryStack_<Iter>::Type      TStack;
        typedef Iter                                    iterator;

        TIndex    const    *index;            // container of all necessary tables
        TVertexDesc        vDesc;            // current interval in suffix array and
                                        // right border of parent interval (unused here)
        TSize            lValue;            // current l-value
        TStack            history;        // contains all left borders of current l-intervals (== left borders of history intervals)

//____________________________________________________________________________

        Iter() :
            index(),
            lValue(0)
        {}

        Iter(TIndex &_index):
            index(&_index),
            vDesc(MinimalCtor()),
            lValue(0)
        {
            _indexRequireBottomUpIteration(_index);
            goBegin(*this);
        }

        Iter(TIndex &_index, MinimalCtor):
            index(&_index),
            vDesc(MinimalCtor()),
            lValue(0) {}

        Iter(Iter const &_origin):
            index(&container(_origin)),
            vDesc(value(_origin)),
            lValue(_dfsLcp(_origin)),
            history(_origin.history) {}

//____________________________________________________________________________

        inline Iter const &
        operator = (Iter const &_origin)
        {
            index = &container(_origin);
            vDesc = _origin.vDesc;
            lValue = _origin.lValue;
            history = _origin.history;
            return *this;
        }
    };


    //////////////////////////////////////////////////////////////////////////////
    // Iterator wrappers
    //////////////////////////////////////////////////////////////////////////////

/*!
 * @mfn StringTreeConcept#Iterator
 * @headerfile <seqan/index.h>
 * @brief Returns the type of an iterator to traverse the nodes of a string tree.
 *
 * @signature Iterator<TIndex, TSpec>::Type;
 *
 * @tparam TIndex The index type.
 * @tparam TSpec The spec type of a @link VSTreeIterator @endlink, e.g. @link TopDownIterator TopDown<>@endlink or @link BottomUpIterator BottomUp<>@endlink.
 *
 * @return Type The resulting string tree iterator type.
 */

    template <typename TObject, typename TSpec>
    struct Iterator< TObject, BottomUp<TSpec> > {
        typedef Iter< TObject, VSTree< BottomUp<TSpec> > > Type;
    };

    template <typename TObject, typename TSpec>
    struct Iterator< TObject, TopDown<TSpec> > {
        typedef Iter< TObject, VSTree< TopDown<TSpec> > > Type;
    };




    template < typename TIndex, typename TSpec >
    inline void _dumpHistoryStack(Iter<TIndex, VSTree<TSpec> > &it) {
        for(typename Size<TIndex>::Type i = 0; i < length(it.history); ++i)
            std::cerr << it.history[i].range << '\t';
        std::cerr << value(it) << std::endl;
    }

    template <typename TText, typename TSpec>
    inline void
    _dump(Index<TText, IndexEsa<TSpec> > &index)
    {
        std::cout << "  SA" << std::endl;
        for(unsigned i=0; i < length(indexSA(index)); ++i)
            std::cout << i << ":  " << indexSA(index)[i] << "  " << suffix(indexText(index), indexSA(index)[i]) << std::endl;

        std::cout << std::endl << "  LCP" << std::endl;
        for(unsigned i=0; i < length(indexLcp(index)); ++i)
            std::cout << i << ":  " << indexLcp(index)[i] << std::endl;

        std::cout << std::endl << "  Childtab" << std::endl;
        for(unsigned i=0; i < length(indexChildtab(index)); ++i)
            std::cout << i << ":  " << indexChildtab(index)[i] << std::endl;

        std::cout << std::endl;
    }


//////////////////////////////////////////////////////////////////////////////

    template < typename TIndex, typename TSpec >
    inline bool _dfsReversedOrder(Iter<TIndex, VSTree< BottomUp<TSpec> > > &it) {
        return lcpAt(_dfsRange(it).i2 - 1, container(it)) > back(it.history).range.i2;
    }

    // standard push/pop handlers of lcp-dfs-traversal
    template < typename TIndex, typename TSpec, typename TSize >
    inline void _dfsOnPop(Iter<TIndex, VSTree< BottomUp<TSpec> > > &it, TSize const) {
        _dfsRange(it).i1 = back(it.history).range.i1;
        _dfsLcp(it) = back(it.history).range.i2;
        eraseBack(it.history);
    }

    template < typename TIndex, typename TSpec, typename TElement >
    inline void _dfsOnPush(Iter<TIndex, VSTree< BottomUp<TSpec> > > &it, TElement const &e) {
        appendValue(it.history, e);
    }

    template < typename TIndex, typename TSpec >
    inline void _dfsOnLeaf(Iter<TIndex, VSTree< BottomUp<TSpec> > > &it) {
        _setSizeInval(_dfsLcp(it));
    }


//////////////////////////////////////////////////////////////////////////////
// postorder bottom up iterator (dfs)

    template < typename TIndex, typename TSpec, typename THideEmptyEdges >
    inline void goNextImpl(
        Iter<TIndex, VSTree< BottomUp<TSpec> > > &it,
        VSTreeIteratorTraits<Postorder_, THideEmptyEdges> const)
    {
        typedef Iter<TIndex, VSTree< BottomUp<TSpec> > >    TIter;
        typedef typename Size<TIndex>::Type                 TSize;
        typedef typename HistoryStackEntry_<TIter>::Type    TStackEntry;

        TIndex const &index = container(it);
        do {
            // postorder dfs via lcp-table
            if (isRoot(it)) {
                _dfsClear(it);
                return;
            }

            if (_dfsRange(it).i2)
            {
                TStackEntry    _top_ = back(it.history);
                TSize        lcp_i = lcpAt(_dfsRange(it).i2 - 1, index);

                if (lcp_i < _top_.range.i2) {
                    _dfsOnPop(it, lcp_i);
                    if (nodePredicate(it)) return;
                    else continue;
                }

                if (lcp_i > _top_.range.i2) {
                    _top_.range.i1 = _dfsRange(it).i1;
                    _top_.range.i2 = lcp_i;
                    _dfsOnPush(it, _top_);
                }

    // innerer Knoten:
    // wenn kein Pop, aber Push -> begehe mind. 2. Teilbaum irgendeines Vorfahrs
    // wenn kein Pop, kein Push -> verlasse mind. zweites Kindblatt
    // wenn Pop, aber kein Push -> verlasse Wurzel des mind. 2.Teilbaums
    // wenn Pop und Push        -> verlasse ersten Teilbaum (sieht Vater zum ersten Mal und pusht jenen)

    // wenn nach Pop ein Pop folgen wuerde    -> Vater ist Top of Stack
    // wenn nach Pop ein Push folgen wuerde    -> Vater erst beim Push auf Stack (-> zwischenspeichern)
            }

            // last lcp entry (== 0) causes removal of toplevel interval
            if ((_dfsRange(it).i1 = _dfsRange(it).i2++) == length(index)) {
                _dfsOnPop(it, 0);
                _dfsRange(it).i2 = _dfsRange(it).i1;
            } else {
                // skip $ leafs (empty edges)
                if (THideEmptyEdges::VALUE &&
                    suffixLength(saAt(_dfsRange(it).i1, index), index) == lcpAt(_dfsRange(it).i1, index))
                    continue;

                _dfsOnLeaf(it);
    // Blatt:
    // wenn danach kein Pop, aber Push -> Vater wird erst noch gepusht
    // wenn danach Pop                   -> Vater ist Top des Stack
            }
            if (nodePredicate(it)) return;
        } while (true);
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#repLength
 * @headerfile <seqan/index.h>
 * @brief Returns the length of the substring representing the path from root to <tt>iterator</tt> node.
 *
 * @signature TSize repLength(iterator);
 *
 * @param[in] iterator An iterator of a string tree. Types: @link VSTreeIterator @endlink
 *
 * @return TSize The length of the sequence returned by @link VSTreeIterator#representative
 *               @endlink The return type is the result of the metafunction @link Size @endlink of the underlying
 *               index.
 *
 * @link DemoMummy @endlink
 * @link DemoSupermaximalRepeats @endlink
 * @link DemoMaximalUniqueMatches @endlink
 */
    template < typename TIndex, typename TSpec >
    inline typename Size<TIndex>::Type
    repLength(Iter< TIndex, VSTree<BottomUp<TSpec> > > const &it)
    {
        typename Size<TIndex>::Type lcp;
        if (!_isSizeInval(lcp = it.lValue))
            return lcp;
        else
            return suffixLength(getOccurrence(it), container(it));
    }


    template < typename TIndex, typename TSize >
    inline typename Size<TIndex>::Type
    repLength(TIndex const &index, VertexEsa<TSize> const &vDesc)
    {
        if (_isLeaf(vDesc)) return suffixLength(saAt(vDesc.range.i1, index), index);
        if (_isRoot(vDesc)) return 0;

        // get l-value of suffix array range
        TSize lval = _getUp(vDesc.range.i2, index);
        if (!(vDesc.range.i1 < lval && lval < vDesc.range.i2))
            lval = _getDown(vDesc.range.i1, index);

        // retrieve the longest-common-prefix length of suffices in range
        return lcpAt(lval - 1, index);
    }

    template < typename TIndex, typename TSpec >
    inline typename Size<TIndex>::Type
    repLength(Iter< TIndex, VSTree<TopDown<TSpec> > > const &it)
    {
        return repLength(container(it), value(it));
    }

//////////////////////////////////////////////////////////////////////////////

/*!
 * @fn TopDownHistoryIterator#nodeDepth
 *
 * @headerfile <seqan/index.h>
 *
 * @brief Returns the zero-based node depth of the <tt>iterator</tt> node.
 *
 * @signature TSize nodeDepth(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TSize The length of the path from root to <tt>iterator</tt> node,
 *               e.g. 0 is returned for the root node. The type of the result
 *               is the result of the metafunction @link Size @endlink of the underlying index.
 */

    template < typename TIndex, typename TSpec >
    inline typename Size<TIndex>::Type
    nodeDepth(Iter< TIndex, VSTree<TopDown<ParentLinks<TSpec> > > > const &it)
    {
        return length(it.history);
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn TopDownIterator#parentRepLength
 * @headerfile <seqan/index.h>
 * @brief Returns the length of the substring representing the path from root to <tt>iterator</tt>'s parent node.
 *
 * @signature TSize parentRepLength(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TReturn The length of the sequence returned by @link VSTreeIterator#representative @endlink of the parent node. The result
 *                 type is the resultof the metafunction @link Size @endlink of the underlying index.
 */

    template < typename TIndex, typename TSpec >
    inline typename Size<TIndex>::Type
    parentRepLength(Iter< TIndex, VSTree<TopDown<TSpec> > > const &it)
    {
        return repLength(container(it), nodeUp(it));
    }


//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn TopDownIterator#emptyParentEdge
 * @headerfile <seqan/index.h>
 * @brief Returns <tt>true</tt> iff the edge label from the <tt>iterator</tt>
 *        node to its parent is empty.
 *
 * @signature bool emptyParentEdge(iterator);
 *
 * @param[in] iterator An iterator of a string tree. Types: @link TopDownIterator @endlink
 *
 * @return bool <tt>true</tt> if @link TopDownIterator#parentEdgeLength @endlink<tt> returns 0, otherwise </tt>false$.
 */

    template < typename TIndex, typename TSpec >
    inline bool
    emptyParentEdge(Iter< TIndex, VSTree<TopDown<TSpec> > > const &it)
    {
        // the following is more efficient than
        // return parentEdgeLength(it) == 0;
        TIndex const &index = container(it);
        typename SAValue<TIndex>::Type pos = getOccurrence(it);
        return getSeqOffset(pos, stringSetLimits(index)) + parentRepLength(it)
            == sequenceLength(getSeqNo(pos, stringSetLimits(index)), index);
    }


//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn TopDownHistoryIterator#lca
 * @headerfile <seqan/index.h>
 * @brief Returns the last common ancestor of two tree nodes.
 *
 * @signature bool lca(a, b, result);
 *
 * @param[in]  a      The first node. Types: @link TopDownHistoryIterator @endlink
 * @param[in]  b      The second node. Types: @link TopDownHistoryIterator @endlink
 * @param[out] result A reference to the resulting lca node. Types: @link TopDownHistoryIterator @endlink
 *
 * @return TReturn <tt>false</tt> if the lca of <tt>a</tt> and <tt>b</tt> is the root node, otherwise <tt>true</tt>.
 */

    template < typename TIndex, class TSpec1, class TSpec2 >
    inline bool lca(
        Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec1> > > > &a,
        Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec2> > > > &b,
        Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec1> > > > &_lca)
    {
        typedef Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec1> > > > TIter;
        typename TIter::TStack::const_iterator iA;
        typename TIter::TStack::const_iterator iB;

        typedef typename Size<TIndex>::Type TSize;

        typename HistoryStackEntry_<TIter>::Type hA, hB;

        // push current intervals
        hA = value(a).range;
        hB = value(b).range;
        appendValue(a.history, hA);
        appendValue(b.history, hB);

        TSize s = min(length(a.history), length(b.history)), i0 = 0;

        while (s) {
            TSize m = s / 2;
            iA = begin(a.history, Standard()) + i0 + m;
            iB = begin(b.history, Standard()) + i0 + m;
            if ((*iA).range == (*iB).range) {
                i0 += m + 1;
                s -= m + 1;
            } else
                s = m;
        }

        _lca.history = prefix(a.history, i0);

        // pop current intervals
        eraseBack(a.history);
        eraseBack(b.history);
        goUp(_lca);

        return i0;
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn TopDownHistoryIterator#lcp
 * @headerfile <seqan/index.h>
 * @brief Returns the length of the longest-common-prefix of two suffix tree
 *        nodes.
 *
 * @signature TSize lcp(a, b);
 *
 * @param[in] a The first node. Types: @link TopDownHistoryIterator @endlink
 * @param[in] b The second node. Types: @link TopDownHistoryIterator @endlink
 *
 * @return TSize The lcp-length of <tt>a</tt> and <tt>b</tt>. The type of the result is the result of the metafunction
 *               @link Size @endlink of the @link Index @endlink of the iterator
 */
    // return the lcp of a and b by seeking the lca of them
    template < typename TIndex, class TSpec1, class TSpec2 >
    inline typename Size<TIndex>::Type lcp(
        Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec1> > > > &a,
        Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec2> > > > &b)
    {
        typedef Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec1> > > > TIter;
        typename TIter::TStack::const_iterator iA;
        typename TIter::TStack::const_iterator iB;

        typedef typename Size<TIndex>::Type TSize;

        typename HistoryStackEntry_<TIter>::Type hA, hB;

        // push current intervals
        hA = value(a).range;
        hB = value(b).range;
        appendValue(a.history, hA);
        appendValue(b.history, hB);

        TSize s = min(length(a.history), length(b.history)), i0 = 0;

        while (s) {
            TSize m = s / 2;
            iA = begin(a.history, Standard()) + i0 + m;
            iB = begin(b.history, Standard()) + i0 + m;
            if ((*iA).range == (*iB).range) {
                i0 += m + 1;
                s -= m + 1;
            } else
                s = m;
        }

        TSize _lcp = (i0 > 0)? repLength(container(a), TDesc(a.history[i0 - 1], 0)): 0;

        // pop current intervals
        eraseBack(a.history);
        eraseBack(b.history);

        return _lcp;
    }

//////////////////////////////////////////////////////////////////////////////
    template < typename TIndex, class TSpec >
    inline TIndex const &
    container(Iter< TIndex, VSTree<TSpec> > const &it) {
        return *it.index;
    }

    template < typename TIndex, class TSpec >
    inline TIndex &
    container(Iter< TIndex, VSTree<TSpec> > &it) {
        return *const_cast<TIndex*>(it.index);
    }


//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#value
 * @headerfile <seqan/index.h>
 * @brief Returns a vertex descriptor of the current node.
 *
 * @signature TDesc value(iterator);
 *
 * @param[in] iterator An iterator of a string tree. Types: @link VSTreeIterator @endlink
 *
 * @return TDesc An object of type @link StringTreeConcept#VertexDescriptor @endlink that
 *               uniquely identifies the current node. The vertex descriptor can be used to
 *               store node specific values in an @link PropertyMapConcept @endlink.
 */

/*!
 * @fn VSTreeIterator#assignProperty
 * @brief Assigns a property to an item in the property map.
 * @signature void assignProperty(pm, value(iterator), val)
 * @param[in,out] pm        An @link PropertyMapConcept @endlink.
 * @param[in]     iterator  An iterator of a string tree. Types: @link VSTreeIterator @endlink
 * @param[in]     val       The new value, where the type of the new value must match the value type of the property map.
*/

/*!
 * @fn VSTreeIterator#property
 * @brief Accesses the property of an item in the property map.
 * @signature TRef property(pm, value(iterator))
 * @param[in,out] pm        An @link PropertyMapConcept @endlink.
 * @param[in]     iterator  An iterator of a string tree. Types: @link VSTreeIterator @endlink
 * @return TRef Reference to the item in the property map of type @link Reference @endlink.
 */

/*!
 * @fn VSTreeIterator#getProperty
 * @brief Get method for an item's property.
 * @signature TValue getProperty(pm, value(iterator))
 * @param[in,out] pm        An @link PropertyMapConcept @endlink.
 * @param[in]     iterator  An iterator of a string tree. Types: @link VSTreeIterator @endlink
 * @return TValue Reference to the item in the property map of type @link GetValue @endlink.
 */

    template < typename TIndex, class TSpec >
    inline typename VertexDescriptor<TIndex>::Type &
    value(Iter< TIndex, VSTree<TSpec> > &it) {
        return it.vDesc;
    }

    template < typename TIndex, class TSpec >
    inline typename VertexDescriptor<TIndex>::Type const &
    value(Iter< TIndex, VSTree<TSpec> > const &it) {
        return it.vDesc;
    }

//////////////////////////////////////////////////////////////////////////////
// property map interface

/*!
 * @fn StringTreeConcept#resizeVertexMap
 * @headerfile <seqan/index.h>
 * @brief Initializes a vertex map.
 *
 * @signature void resizeVertexMap(pm, index);
 *
 * @param[in,out] pm    An External Property Map.
 * @param[in]     index An index with a string tree interface. Types: @link IndexEsa @endlink, @link IndexWotd @endlink
 */
    template < typename TText, typename TSpec, typename TPropertyMap >
    inline void
    resizeVertexMap(
        TPropertyMap & pm,
        Index<TText, TSpec> const & index)
    {
        resize(pm, 2 * length(index), Generous());
    }
/* // different interface compared to resizeVertexMap(graph, ...)
    template < typename TText, typename TSpec, typename TPropertyMap, typename TProperty >
    inline void
    resizeVertexMap(
        Index<TText, TSpec> const& index,
        TPropertyMap & pm,
        TProperty const & prop)
    {
        resize(pm, 2 * length(index), prop, Generous());
    }
*/
    template < typename TSize >
    inline typename Id< VertexEsa<TSize> const >::Type
    _getId(VertexEsa<TSize> const &desc)
    {
        TSize i2 = getValueI2(desc.range);
        if (_isSizeInval(i2) || i2 == desc.parentRight)
            // desc is the right-most child -> use left interval border
            return 2 * getValueI1(desc.range);
        else
            // desc is not the right-most child -> use right interval border
            // ensure that it doesn't collide with the left borders
            return 2 * getValueI2(desc.range) - 1;
    }

    template < typename TSize >
    inline typename Id< VertexEsa<TSize> >::Type
    _getId(VertexEsa<TSize> &desc)
    {
        return _getId(const_cast<VertexEsa<TSize> const &>(desc));
    }


//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#getOccurrence
 * @headerfile <seqan/index.h>
 * @brief Returns an occurrence of the @link VSTreeIterator#representative @endlink substring in the index text.
 *
 * @signature TSAValue getOccurrence(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TSAValue A position where the @link VSTreeIterator#representative @endlink of <tt>iterator</tt> occurs in
 *         the text.  The return type is the result of the metafunction @link SAValue @endlink of the index type of
 *         the iterator.
 */

    template < typename TIndex, class TSpec >
    inline typename SAValue<TIndex>::Type
    getOccurrence(Iter< TIndex, VSTree<TSpec> > const &it)
    {
        return saAt(value(it).range.i1, container(it));
    }


//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#countOccurrences
 * @headerfile <seqan/index.h>
 * @brief Returns the number of occurrences of @link VSTreeIterator#representative @endlink
 *        substring in the index text.
 *
 * @signature TSize countOccurrences(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TSize The number of positions where the @link VSTreeIterator#representative @endlink of <tt>iterator</tt> occurs in the
 *               text. The return type is the result of the metafunction @link Size @endlink of the index type of the
 *               iterator.

 * The necessary index tables are built on-demand via @link Index#indexRequire @endlink if index is not <tt>const</tt>.
 *
 * @section Examples
 *
 * @include demos/dox/index/counting.cpp
 *
 * The result is as follows:
 *
 * @include demos/dox/index/counting.cpp.stdout
 */

    template < typename TIndex, class TSpec >
    inline typename Size<TIndex>::Type
    countOccurrences(Iter< TIndex, VSTree<TSpec> > const &it)
    {
        if (_isSizeInval(value(it).range.i2))
            return length(indexSA(container(it))) - value(it).range.i1;
        else
            return value(it).range.i2 - value(it).range.i1;
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#range
 * @headerfile <seqan/index.h>
 * @brief Returns the suffix array interval borders of occurrences of @link VSTreeIterator#representative @endlink substring in the
 *        index text.
 *
 * @signature TPair range(iterator);
 *
 * @param[in] iterator An iterator of a string tree/trie.
 *
 * @return TPair All positions where a substring occurs in the text are stored in a contiguous range of the suffix
 *               array. <tt>range</tt> returns begin and end position of this range for occurrences of @link
 *               VSTreeIterator#representative @endlink. The type is @link Pair @endlink<@link Size @endlink< <tt>TIndex<tt> > >
 *               with TIndex being the index type of the iterator.
 *
 * The necessary index tables are built on-demand via @link Index#indexRequire @endlink if index is not <tt>const</tt>.
 */
    template < typename TText, typename TSpec, typename TDesc >
    inline Pair<typename Size<Index<TText, TSpec> >::Type>
    range(Index<TText, TSpec> const &index, TDesc const &desc)
    {
        if (_isSizeInval(desc.range.i2))
            return Pair<typename Size<Index<TText, TSpec> >::Type>(desc.range.i1, length(indexSA(index)));
        else
            return desc.range;
    }

    template < typename TIndex, typename TSpec >
    inline Pair<typename Size<TIndex>::Type>
    range(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        if (_isSizeInval(value(it).range.i2))
            return Pair<typename Size<TIndex>::Type>(value(it).range.i1, length(indexSA(container(it))));
        else
            return value(it).range;
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#getOccurrences
 * @headerfile <seqan/index.h>
 * @brief Returns all occurrences of the @link VSTreeIterator#representative @endlink substring in the index text.
 *
 * @signature TInfix getOccurrences(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TInfix All positions where the @link VSTreeIterator#representative @endlink of <tt>iterator</tt> occurs in the text.
 *                Type @link SegmentableConcept#Infix @endlink&lt;@link Fibre @endlink&lt;TIndex, FibreSA&gt;::Type&gt;.
 *
 * The necessary index tables are built on-demand via @link Index#indexRequire @endlink if index is not <tt>const</tt>.
 *
 * @section Example
 *
 * @link DemoMummy @endlink
 * @link DemoSupermaximalRepeats @endlink
 * @link DemoMaximalUniqueMatches @endlink
 *
 * @see VSTreeIterator#isUnique
 * @see VSTreeIterator#getFrequency
 * @see VSTreeIterator#isPartiallyLeftExtensible
 * @see VSTreeIterator#isLeftMaximal
 * @see orderOccurrences
 */

    template < typename TIndex, class TSpec >
    inline typename Infix< typename Fibre<TIndex, FibreSA>::Type const >::Type
    getOccurrences(Iter< TIndex, VSTree<TSpec> > const &it)
    {
        if (_isSizeInval(value(it).range.i2))
            return infix(indexSA(container(it)), value(it).range.i1, length(indexSA(container(it))));
        else
            return infix(indexSA(container(it)), value(it).range.i1, value(it).range.i2);
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#alignment
 * @brief Returns an alignment of the occurrences of the @link VSTreeIterator#representative @endlink substring in the index text.
 * @note Internal function.
 *
 * @signature TAlign alignment(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TAlign A local alignment corresponding to the seed of the <tt>iterator<tt>.
 *
 * The function @link VSTreeIterator#representative @endlink must uniquely occur in every sequence (e.g. in Mums),
 * otherwise the seed returned is one many. The return type is a @link Align @endlink object.
 */

    template < typename TString, typename TSSetSpec, typename TIndexSpec, class TSpec >
    inline Align<TString, ArrayGaps>
    alignment(Iter< Index< StringSet<TString, TSSetSpec>, TIndexSpec >, VSTree<TSpec> > &it)
    {
        typedef Index< StringSet<TString, TSSetSpec>, TIndexSpec > TIndex;
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type TOccs;
        typedef typename Iterator<TOccs, Standard>::Type TIter;

        Align<TString, ArrayGaps> align;
        TIndex &index = container(it);
        resize(rows(align), length(indexText(index)));    // resize alignment to number of sequences
        TOccs occs = getOccurrences(it);
        typename Size<TIndex>::Type repLen = repLength(it);
        TIter occ = begin(occs, Standard()), occEnd = end(occs, Standard());
        while (occ != occEnd) {
            typename Size<TIndex>::Type seqNo = getSeqNo(*occ, stringSetLimits((TIndex const&)index));
            typename Size<TIndex>::Type seqOfs = getSeqOffset(*occ, stringSetLimits((TIndex const&)index));
            setSource(row(align, seqNo), value(indexText(index), seqNo), seqOfs, seqOfs + repLen);
            ++occ;
        }
        return align;
    }
/*
    template < typename TString, typename TConcSpec, typename TIndexSpec, class TSpec >
    inline typename Align<TString const, ArrayGaps>
    alignment(Iter< Index< StringSet<TString, Owner<ConcatDirect<TConcSpec> > >, TIndexSpec >, VSTree<TSpec> > const &it)
    {
        typedef Index< StringSet<TString, Owner<ConcatDirect<TConcSpec> > >, TIndexSpec > TIndex;
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type TOccs;
        typedef typename Iterator<TOccs, Standard>::Type TIter;

        Align<TString const, ArrayGaps> align;
        TIndex const &index = container(it);
        resize(rows(align), length(indexText(index)));    // resize alignment to number of sequences
        TOccs occs = getOccurrences(it);
        typename Size<TIndex>::Type repLen = repLength(it);
        TIter occ = begin(occs, Standard()), occEnd = end(occs, Standard());
        while (occ != occEnd) {
            typename Size<TIndex>::Type seqNo = getSeqNo(*occ, stringSetLimits(index));
            typename Size<TIndex>::Type globOfs = posGlobalize(*occ, stringSetLimits(index));
            setSource(row(align, seqNo), concat(indexText(index)), globOfs, globOfs + repLen);
            ++occ;
        }
        return align;
    }
*/
    template < typename TString, typename TConcSpec, typename TIndexSpec, class TSpec >
    inline Align<TString, ArrayGaps>
    alignment(Iter< Index< StringSet<TString, Owner<ConcatDirect<TConcSpec> > >, TIndexSpec >, VSTree<TSpec> > &it)
    {
        typedef Index< StringSet<TString, Owner<ConcatDirect<TConcSpec> > >, TIndexSpec > TIndex;
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type TOccs;
        typedef typename Iterator<TOccs, Standard>::Type TIter;

        Align<TString, ArrayGaps> align;
        TIndex &index = container(it);
        resize(rows(align), length(indexText(index)));    // resize alignment to number of sequences
        TOccs occs = getOccurrences(it);
        typename Size<TIndex>::Type repLen = repLength(it);
        TIter occ = begin(occs, Standard()), occEnd = end(occs, Standard());
        while (occ != occEnd) {
            typename Size<TIndex>::Type seqNo = getSeqNo(*occ, stringSetLimits((TIndex const&)index));
            typename Size<TIndex>::Type globOfs = posGlobalize(*occ, stringSetLimits((TIndex const&)index));
            setSource(row(align, seqNo), concat(indexText(index)), globOfs, globOfs + repLen);
            ++occ;
        }
        return align;
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#getOccurrencesBwt
 * @headerfile <seqan/index.h>
 * @brief Returns the characters left beside all occurrence of the @link
 *        VSTreeIterator#representative @endlink substring in the index text.
 *
 * @signature TReturn getOccurrencesBwt(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree.
 *
 * @return TReturn All positions where the @link VSTreeIterator#representative @endlink of
 *                 <tt>iterator</tt> occurs in the text.
 *
 *                 If <tt>iterator</tt>'s container type is <tt>TIndex</tt> the return type is
 *                 <tt>Infix<Fibre<TIndex, EsaBwt>::Type const>::Type</tt>.
 */
    template < typename TIndex, class TSpec >
    inline typename Infix< typename Fibre<TIndex, EsaBwt>::Type const >::Type
    getOccurrencesBwt(Iter< TIndex, VSTree<TSpec> > const &it)
    {
        if (_isSizeInval(value(it).range.i2))
            return infix(indexBwt(container(it)), value(it).range.i1, length(indexSA(container(it))));
        else
            return infix(indexBwt(container(it)), value(it).range.i1, value(it).range.i2);
    }

//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#representative
 * @headerfile <seqan/index.h>
 * @brief Returns a substring representing the path from root to <tt>iterator</tt> node.
 *
 * @signature TInfix representative(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TInfix Infix&lt;TSting&gt; An @link InfixSegment @endlink of the text of an index. The type is <tt>Infix&lt;Fibre&lt;TIndex, FibreText&gt;::Type&gt;::Type</tt>.
 *
 * @section Examples
 *
 * @link DemoMummy @endlink
 * @link DemoSupermaximalRepeats @endlink
 * @link DemoConstraintIterator @endlink
 * @link DemoMaximalRepeats @endlink
 * @link DemoMaximalUniqueMatches @endlink
 */

    template < typename TIndex, class TSpec >
    inline typename InfixOnValue< typename Fibre<TIndex, FibreText>::Type const >::Type
    representative(Iter< TIndex, VSTree<TSpec> > const &it)
    {
        return infixWithLength(indexText(container(it)), getOccurrence(it), repLength(it));
    }


//////////////////////////////////////////////////////////////////////////////
/*!
 * @fn VSTreeIterator#countChildren
 * @headerfile <seqan/index.h>
 * @brief Count the number of children of a tree node.
 *
 * @signature TSize countChildren(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TSize The number of children of a tree node. The type is the result of @link Size @endlink of the index type
 *               of the iterator.
 *
 * @section Examples
 *
 * @code{.cpp}
 * // this code is in seqan/index/index_esa_stree.h
 *
 *  typedef Index< String<char> > TMyIndex;
 *  TMyIndex myIndex(myString);
 *
 *  Iterator< TMyIndex, TopDown<ParentLinks<PreorderEmptyEdges> > >::Type tdIterator(myIndex);
 *  Size<TMyIndex>::Type count;
 *
 *  while (!atEnd(tdIterator)) {
 *  // We print out the representatives of all nodes that have more than 3 children and the number of occurrences.
 *  count = countChildren(tdIterator);
 *  if (count >= 3)
 *  {
 *      std::cout << "Representative " << representative(tdIterator) << " has " <<  count << " children  and " << countOccurrences(tdIterator) << " Occurrences " << std::endl;
 *
 *      ++tdIterator;
 *  }
 * @endcode
 *
 * @link DemoIndexCountChildren @endlink
 */
    template < typename TIndex, typename TSpec >
    inline typename Size<TIndex>::Type
    countChildren(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        typedef Iter<TIndex, VSTree<TSpec> >                    TIter;
        typedef typename GetVSTreeIteratorTraits<TIter>::Type    TTraits;

        Iter<TIndex, VSTree<TopDown<TTraits> > > temp(it);
        typename Size<TIndex>::Type numChildren = 0;
        if (goDown(temp))
        {
            ++numChildren;
            while (goRight(temp)) ++numChildren;
        }
        return numChildren;
    }

    template < typename TText, typename TIndexSpec, typename TSpec >
    inline typename Size<Index<TText, IndexEsa<TIndexSpec> > >::Type
    countChildren(Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree<TSpec> > const &it)
    {
        typedef Index<TText, IndexEsa<TIndexSpec> >            TIndex;
        typedef Iter<TIndex, VSTree<TSpec> >                    TIter;
        typedef typename GetVSTreeIteratorTraits<TIter>::Type    TTraits;
        typedef typename TTraits::HideEmptyEdges                THideEmptyEdges;

        if (_isLeaf(it, EmptyEdges())) return 0;

        typedef typename Size<TIndex>::Type TSize;
        TIndex const &index = container(it);
        TSize lcp = repLength(it);
        TSize result = (isRoot(it))? 0: 1;

        // check if child has an empty edge (same representative as its parent)
        typename SAValue<TIndex>::Type pos = getOccurrence(it);
        if (THideEmptyEdges::VALUE && getSeqOffset(pos, stringSetLimits(index)) + lcp == sequenceLength(getSeqNo(pos, stringSetLimits(index)), index))
            --result;    // if so, don't count

        // get l-Value between first and second child
        TSize i = _getUp(value(it).range.i2, index);
        if (!(value(it).range.i1 < i && i < value(it).range.i2))
            i = _getDown(value(it).range.i1, index);

        if (THideEmptyEdges::VALUE)
        {
            // only count children with non-empty parent edges (different representative than its parent)
            pos = saAt(i, index);
            if (getSeqOffset(pos, stringSetLimits(index)) + lcp != sequenceLength(getSeqNo(pos, stringSetLimits(index)), index))
                ++result;
        } else
            ++result;

        // try to get next l-Value
        while (_isNextl(i, index))
        {
            i = _getNextl(i, index);
            if (THideEmptyEdges::VALUE)
            {
                // only count children with non-empty parent edges (different representative than its parent)
                pos = saAt(i, index);
                if (getSeqOffset(pos, stringSetLimits(index)) + lcp != sequenceLength(getSeqNo(pos, stringSetLimits(index)), index))
                    ++result;
            } else
                ++result;
        }
        return result;
    }

    // get the interval of SA of the subtree under the edge beginning with character c
    template < typename TText, class TIndexSpec, class TSpec, typename TValue >
    inline bool
    _getNodeByChar(
        Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree<TSpec> > const &it,
        TValue c,
        typename VertexDescriptor< Index<TText, IndexEsa<TIndexSpec> > >::Type &childDesc)
    {
        typedef Index<TText, IndexEsa<TIndexSpec> >        TIndex;
        typedef typename Size<TIndex>::Type                    TSize;
        typedef typename Fibre<TIndex, EsaSA>::Type const  TSA;
        typedef typename Value<TSA>::Type                   TSAValue;

        if (_isLeaf(it, EmptyEdges())) return false;

        Pair<TSize> child(value(it).range.i1, _getUp(value(it).range.i2, container(it)));
        if (!(value(it).range.i1 < child.i2 && child.i2 < value(it).range.i2))
            child.i2 = _getDown(value(it).range.i1, container(it));

        TSize _lcp = lcpAt(child.i2 - 1, container(it));
        TIndex const &index = container(it);
        TText const &text = indexText(index);

        TSAValue pos = saAt(child.i1, container(it));
        if (posAddAndCheck(pos, _lcp, text) && (textAt(pos, container(it)) == c))
        {
            childDesc.range = child;
            childDesc.parentRight = value(it).range.i2;
            return true;
        }
        child.i1 = child.i2;
        while (_isNextl(child.i2, container(it)))
        {
            child.i2 = _getNextl(child.i2, container(it));
            pos = saAt(child.i1, container(it));
            if (posAddAndCheck(pos, _lcp, text) && (textAt(pos, container(it)) == c))
            {
                childDesc.range = child;
                childDesc.parentRight = value(it).range.i2;
                return true;
            }
            child.i1 = child.i2;
        }

        if (!isRoot(it)) {
            pos = saAt(child.i1, container(it));
            if (posAddAndCheck(pos, _lcp, text) && (textAt(pos, container(it)) == c))
            {
                childDesc.range.i1 = child.i1;
                childDesc.range.i2 = childDesc.parentRight = value(it).range.i2;
                return true;
            }
        }
        return false;
    }


//TODO(singer): Why only bottom-up???
/*!
 * @fn VSTreeIterator#nodePredicate
 * @headerfile <seqan/index.h>
 * @brief If <tt>false</tt> this node will be skipped during the bottom-up traversal.
 *
 * @signature bool nodePredicate(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return bool Returns whether or not the node will be skipped.
 *
 * @see DemoConstraintIterator
 */

    template < typename TIndex, class TSpec >
    inline bool
    nodePredicate(Iter<TIndex, TSpec> &)
    {
        return true;
    }


/*!
 * @fn VSTreeIterator#nodeHullPredicate
 * @headerfile <seqan/index.h>
 * @brief If <tt>false</tt> this node and its subtree is concealed.
 *
 * @signature bool nodeHullPredicate(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return bool Returns whether or not a subtree is concealed.
 *
 * @link DemoConstraintIterator @endlink
 */

    template < typename TIndex, class TSpec >
    inline bool
    nodeHullPredicate(Iter<TIndex, TSpec> &)
    {
        return true;
    }

//____________________________________________________________________________

/*!
 * @fn VSTreeIterator#goRoot
 * @headerfile <seqan/index.h>
 * @brief Move iterator to the root node.
 *
 * @signature void goRoot(iterator);
 *
 * @param[in,out] iterator An iterator of a suffix tree.
 */

    template < typename TText, typename TIndexSpec, class TSpec >
    inline void goRoot(Iter<Index<TText, TIndexSpec>, VSTree<TSpec> > &it)
    {
        _historyClear(it);
        clear(it);                            // start in root node with range (0,infty)
        if (!empty(indexSA(container(it))))
            _setSizeInval(value(it).range.i2);    // infty is equivalent to length(index) and faster to compare
    }

//____________________________________________________________________________

//TODO(singer): The summary is not entirely true!!!
/*!
 * @fn StringTreeConcept#begin
 * @headerfile <seqan/index.h>
 * @brief Returns an iterator pointing to the root node of a string tree index.
 *
 * @signature TIterator begin(index, tag);
 *
 * @param[in] index An index that implements the @link StringTreeConcept @endlink.  Types: @link IndexEsa @endlink, @link IndexDfi @endlink,
 *                  @link IndexWotd @endlink, @link FMIndex @endlink.
 * @param[in] tag   The specialisation of the iterator to be returned by the function.
 *                  Types: @link VSTreeIterator @endlink
 *
 * @return TIterator Returns an iterator pointing to the root node of the virtual string tree of the index. The type is
 *                   the result of <tt>Iterator<Index<TText, TIndexSpec>, TSpec >::Type</tt>
 *
 * @section Examples
 *
 * The following example shows the usage of the @link StringTreeConcept#begin @endlink function. Note that in the first case @link StringTreeConcept#begin @endlink
 * returns an iterator pointing to the root node, while in the second case @link StringTreeConcept#begin @endlink returns a pointer to the
 * left most node.
 *
 * @include demos/dox/index/begin_atEnd_representative.cpp
 *
 * The output is as follows:
 *
 * @include demos/dox/index/begin_atEnd_representative.cpp.stdout
 */
    template < typename TText, typename TIndexSpec, class TSpec >
    inline typename Iterator<Index<TText, TIndexSpec>, TSpec >::Type
    begin(Index<TText, TIndexSpec> &index, TSpec const)
    {
        typedef Iter<Index<TText, TIndexSpec>, VSTree<TSpec> >    TIter;
        typedef typename GetVSTreeIteratorTraits<TIter>::Type    TTraits;

        typename Iterator<Index<TText, TIndexSpec>, TSpec>::Type it(index);

        SEQAN_IF_CONSTEXPR (IsSameType<typename TTraits::DfsOrder, Postorder_>::VALUE) {
            while (goDown(it)) ;
        }

        return it;
    }

    template < typename TText, typename TIndexSpec, class TSpec >
    inline typename Iterator<Index<TText, TIndexSpec>, BottomUp<TSpec> >::Type
    begin(Index<TText, TIndexSpec> &index, BottomUp<TSpec> const)
    {
        return typename Iterator<Index<TText, TIndexSpec>, BottomUp<TSpec> >::Type(index);
    }
/*!
 * @fn VSTreeIterator#goBegin
 * @headerfile <seqan/index.h>
 * @brief Iterates to the first position of a container.
 *
 * @signature void goBegin(iterator);
 *
 * @param[in,out] iterator Object that iterates through
 *
 * This function is equivalent to <tt>iterator = begin(container)</tt>.
 *
 * @see StringTreeConcept#begin
 */

/*!
 * @fn BottomUpIterator#goBegin
 * @headerfile <seqan/index.h>
 * @brief Iterates to the first position of a container.
 *
 * @signature void goBegin(iterator);
 *
 * @param[in,out] iterator Object that iterates through.
 *
 * This function is equivalent to <tt>iterator = begin(container)</tt>.
 *
 * @see StringTreeConcept#begin
 */
    template < typename TText, typename TIndexSpec, class TSpec >
    inline void goBegin(Iter<Index<TText, TIndexSpec>, VSTree<TSpec> > &it)
    {
        typedef Iter<Index<TText, TIndexSpec>, VSTree<TSpec> >    TIter;
        typedef typename GetVSTreeIteratorTraits<TIter>::Type    TTraits;
        typedef typename TTraits::HideEmptyEdges                THideEmptyEdges;

        goRoot(it);

        SEQAN_IF_CONSTEXPR (IsSameType<typename TTraits::DfsOrder, Postorder_>::VALUE) {
            while (goDown(it)) ;
            return;
        }

        // if root doesn't suffice predicate, do a dfs-step
        if ((THideEmptyEdges::VALUE && emptyParentEdge(it)) || !nodeHullPredicate(it))
            goNext(it);
    }

    template < typename TText, typename TIndexSpec, class TSpec >
    inline void goBegin(Iter<Index<TText, IndexEsa<TIndexSpec> >, VSTree< BottomUp<TSpec> > > &it)
    {
        typedef Index<TText, IndexEsa<TIndexSpec> >        TIndex;
        typedef Iter<TIndex, VSTree< BottomUp<TSpec> > >    TIter;
        //typedef typename VertexDescriptor<TIndex>::Type        TVertexDesc;
        typedef typename Size<TIndex>::Type                    TSize;
        typedef    Pair<TSize>                                    TStackEntry;

        _dfsClear(it);
        clear(it);                            // start in root node with range (0,infty)
        if (!empty(indexSA(container(it)))) {
            _dfsOnPush(it, TStackEntry(0,0));
            goNextImpl(it, typename GetVSTreeIteratorTraits< TIter >::Type());
        }
    }

//____________________________________________________________________________

// TODO(singer) ask Dave
    template < typename TText, typename TIndexSpec, class TSpec >
    inline typename Iterator<Index<TText, TIndexSpec>, TSpec >::Type
    end(Index<TText, TIndexSpec> &index, TSpec const)
    {
        return typename Iterator<
            Index<TText, TIndexSpec>,
            TSpec
        >::Type (index, MinimalCtor());
    }

// TODO(singer) ask Dave
    template < typename TText, typename TIndexSpec, class TSpec >
    inline void goEnd(Iter<Index<TText, IndexEsa<TIndexSpec> >, VSTree<TSpec> > &it)
    {
        _historyClear(it);
        clear(it);
    }

    template < typename TText, typename TIndexSpec, class TSpec >
    inline void goEnd(Iter<Index<TText, IndexEsa<TIndexSpec> >, VSTree< BottomUp<TSpec> > > &it)
    {
        _dfsClear(it);
        clear(it);
    }

//____________________________________________________________________________

// TODO(singer) ask Dave
// TODO(holtgrew): Dave needs to update this.
/*!
 * @fn VSTreeIterator#goNext
 * @brief Go to next tree node.
 *
 * @signature void goNext(it);
 *
 * @param[in,out] it VSTreeIterator to advance.
 */

    template < typename TIndex, typename TSpec >
    inline void goNext(Iter<TIndex, VSTree<TSpec> > &it) {
        goNext(it, typename GetVSTreeIteratorTraits< Iter<TIndex, VSTree<TSpec> > >::Type());
    }

    template < typename TIndex, typename TSpec, typename TTraits >
    inline void goNext(Iter<TIndex, VSTree<TSpec> > &it, TTraits const traits) {
        goNextImpl(it, traits);
    }

    template < typename TIndex, typename TSpec >
    inline void goNextRight(Iter<TIndex, VSTree<TSpec> > &it) {
        goNextRight(it, typename GetVSTreeIteratorTraits< Iter<TIndex, VSTree<TSpec> > >::Type());
    }

    template < typename TIndex, typename TSpec, typename TTraits >
    inline void goNextRight(Iter<TIndex, VSTree<TSpec> > &it, TTraits const traits) {
        goNextRightImpl(it, traits);
    }

    template < typename TIndex, typename TSpec >
    inline void goNextUp(Iter<TIndex, VSTree<TSpec> > &it) {
        goNextUp(it, typename GetVSTreeIteratorTraits< Iter<TIndex, VSTree<TSpec> > >::Type());
    }

    template < typename TIndex, typename TSpec, typename TTraits >
    inline void goNextUp(Iter<TIndex, VSTree<TSpec> > &it, TTraits const traits) {
        goNextUpImpl(it, traits);
    }


//TODO(singer): The lcp stuff needs to be adapted
/*!
 * @fn TopDownIterator#goDown
 * @headerfile <seqan/index.h>
 * @brief Iterates down one edge or a path in a tree.
 *
 * @signature bool goDown(iterator);
 * @signature bool goDown(iterator, char);
 * @signature bool goDown(iterator, text[, lcp]);
 *
 * @param[in] char <tt>iterator</tt> goes down the edge beginning with <tt>char</tt>.
 * @param[in] text <tt>iterator</tt> goes down the path representing <tt>text</tt>.  If <tt>text</tt> ends within
 *                 an edge, <tt>iterator</tt> will point to the child-end of this edge.
 * @param[in] lcp  A reference of a size type. When <tt>goDown</tt> returns, <tt>lcp</tt> contains the length of the
 *                 longest-common-prefix of <tt>text</tt> and a path beginning at the <tt>iterator</tt> node.
 *                 Types: @link String @endlink, @link Segment @endlink
 * @param[in] iterator
 *                 An iterator of a tree.
 *
 * @return bool <tt>true</tt> if the edge or path to go down exists, otherwise <tt>false</tt>.
 *
 * <tt>goDown(iterator)</tt> goes down the leftmost edge in the tree, i.e. the edge beginning with the lexicographically
 * smallest character.
 *
 * @section Example
 *
 * The following code shows a simple example how the function @link TopDownIterator#goDown @endlink is used.
 *
 * @include demos/dox/index/begin_range_goDown_representative_repLength.cpp
 *
 * @code{.output}
 * The string ISSI occurs 2 times in MISSISSIPPI and has 4 characters.
 * The string ISSI occurs 2 times in MISSISSIPPI and has 4 characters.
 * @endcode
 */
    //////////////////////////////////////////////////////////////////////////////
    // unified history stack access for goDown(..)

    template < typename TIndex, class TSpec >
    inline void
    _historyClear(Iter< TIndex, VSTree<TSpec> > &) {}


    template < typename TIndex, class TSpec >
    inline void
    _historyClear(Iter< TIndex, VSTree< TopDown<TSpec> > > &it)
    {
        it._parentDesc = value(it);
    }

    template < typename TIndex, class TSpec >
    inline void
    _historyClear(Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it)
    {
        clear(it.history);
    }
/*
    template < typename TText, class TIndexSpec, class TSpec >
    inline void
    _historyPush(Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree<TSpec> > &it)
    {
        value(it).parentRight = value(it).range.i2;
    }
*/    template < typename TText, class TIndexSpec, class TSpec >
    inline void
    _historyPush(Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown<TSpec> > > &it)
    {
        it._parentDesc = value(it);
        value(it).parentRight = value(it).range.i2;
    }
    template < typename TText, class TIndexSpec, class TSpec >
    inline void
    _historyPush(Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown< ParentLinks<TSpec> > > > &it)
    {
        typedef Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown< ParentLinks<TSpec> > > > TIter;
        typename HistoryStackEntry_<TIter>::Type h;
        h.range = value(it).range;

        value(it).parentRight = value(it).range.i2;
        appendValue(it.history, h);
    }


    // standard down/right/up handlers of top-down-traversal
    template < typename TIndex, typename TSpec >
    inline void _onGoDown(Iter<TIndex, VSTree< TopDown<TSpec> > > &) {}

    template < typename TIndex, typename TSpec >
    inline void _onGoRight(Iter<TIndex, VSTree< TopDown<TSpec> > > &) {}

    template < typename TIndex, typename TSpec >
    inline void _onGoUp(Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &) {}


    //////////////////////////////////////////////////////////////////////////////
    // goDown

    // go down the leftmost edge (including empty $-edges)
    template < typename TText, class TIndexSpec, class TSpec, typename TDfsOrder >
    inline bool _goDown(
        Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown<TSpec> > > &it,
        VSTreeIteratorTraits<TDfsOrder, False> const)
    {
        typedef Index<TText, IndexEsa<TIndexSpec> >    TIndex;

        if (_isLeaf(it, EmptyEdges())) return false;
        _historyPush(it);

        TIndex const &index = container(it);

        typename Size<TIndex>::Type lval = _getUp(value(it).range.i2, index);
        if (!(value(it).range.i1 < lval && lval < value(it).range.i2))
            lval = _getDown(value(it).range.i1, index);
        value(it).range.i2 = lval;
        return true;
    }

    template <typename TIterator>
    struct IsParentLinks_: public False {};

    template <typename TIndex, typename TSpec>
    struct IsParentLinks_< Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > >: public True {};


    template <typename TIndex, typename TSpec, typename TVertexDesc>
    inline void
    _setParentNodeDescriptor(Iter<TIndex, VSTree< TopDown<TSpec> > > &it,
                             TVertexDesc const &desc)
    {
        it._parentDesc = desc;
    }

    template <typename TIndex, typename TSpec, typename TVertexDesc>
    inline void
    _setParentNodeDescriptor(Iter<TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &,
                             TVertexDesc const &)
    {
    }

    // go down the leftmost edge (skip empty $-edges)
    template < typename TText, class TIndexSpec, class TSpec, typename TDfsOrder >
    inline bool _goDown(
        Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown<TSpec> > > &it,
        VSTreeIteratorTraits<TDfsOrder, True> const)
    {
        typedef Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown<TSpec> > >   TIter;
        typedef Index<TText, IndexEsa<TIndexSpec> >                                     TIndex;
        typedef typename VertexDescriptor<TIndex>::Type                                 TVertexDesc;

        if (_isLeaf(it, HideEmptyEdges())) return false;

        // save parent descriptor if we need to restore it
        TVertexDesc oldParentDesc;
        if (!IsParentLinks_<TIter>::VALUE)
            oldParentDesc = nodeUp(it);

        _historyPush(it);

        TIndex const &index = container(it);

        typename Size<TIndex>::Type rangeLeft = value(it).range.i1;
        typename Size<TIndex>::Type lval = _getUp(value(it).range.i2, index);
        if (!(rangeLeft < lval && lval < value(it).range.i2))
            lval = _getDown(rangeLeft, index);

        // skip the all empty edges
        typename Size<TIndex>::Type lcp = lcpAt(lval - 1, index);
        while (suffixLength(saAt(rangeLeft, index), index) <= lcp)
            ++rangeLeft;

        // if we skipped some empty edges, get the next l-value to set range.i2
        if (value(it).range.i1 != rangeLeft)
        {
            value(it).range.i1 = rangeLeft;
            if (_isNextl(rangeLeft, index))
                lval = _getNextl(rangeLeft, index);
            else
                lval = value(it).parentRight;
        }
        value(it).range.i2 = lval;

        if (!nodeHullPredicate(it))
        {
            if (!goRight(it))
            {
                _goUp(it);
                _setParentNodeDescriptor(it, oldParentDesc);
                return false;
            }
        }
        return true;
    }

    // go down the leftmost edge
    template < typename TIndex, class TSpec >
    inline bool goDown(Iter< TIndex, VSTree< TopDown<TSpec> > > &it) {
        if (_goDown(it, typename GetVSTreeIteratorTraits< Iter<TIndex, VSTree< TopDown<TSpec> > > >::Type())) {
            _onGoDown(it);
            return true;
        } else
            return false;
    }


    //////////////////////////////////////////////////////////////////////////////
    // goDown a specific edge (chosen by the first character)

    // go down the edge beginning with c (returns false iff this edge doesn't exists)
    template < typename TIndex, class TSpec, typename TValue >
    inline bool _goDownChar(Iter< TIndex, VSTree< TopDown<TSpec> > > &it, TValue c)
    {
        typename VertexDescriptor<TIndex>::Type nodeDesc;
        if (_getNodeByChar(it, c, nodeDesc)) {
            _historyPush(it);
            value(it) = nodeDesc;
            return true;
        }
        return false;
    }

    // go down the path corresponding to pattern
    // lcp is the longest prefix of pattern and path
    template < typename TIndex, typename TSpec, typename TString, typename TSize >
    inline bool
    _goDownString(
        Iter< TIndex, VSTree< TopDown<TSpec> > > &node,
        TString const &pattern,
        TSize &lcp)
    {
        typedef typename Fibre<TIndex, FibreText>::Type const        TText;
        typedef typename InfixOnValue<TText>::Type                   TInfix;
        typedef typename Iterator<TInfix, Standard>::Type            IText;
        typedef typename Iterator<TString const, Standard>::Type    IPattern;

        IPattern p_begin = begin(pattern, Standard()), p_end = end(pattern, Standard());
        IText t_begin, t_end;

        if (p_begin == p_end) {
            lcp = 0;
            return true;
        }

        TSize parentRepLen = repLength(node);
        // go down the edge beginning with a pattern character
        while (_goDownChar(node, *p_begin))
        {
            TInfix t = representative(node);
            t_begin = begin(t, Standard()) + parentRepLen;
            t_end = end(t, Standard());

            while (t_begin != t_end && p_begin != p_end)
            {
                // compare each character along the edge
                if (*p_begin != *t_begin) {
                    lcp = p_begin - begin(pattern, Standard());
                    return false;
                }
                ++t_begin;
                ++p_begin;
            }

            // was the whole pattern found?
            if (p_begin == p_end) {
                lcp = length(pattern);
                return true;
            }
            parentRepLen = length(t);
        }
        lcp = p_begin - begin(pattern, Standard());
        return false;
    }

    template < typename TIndex, typename TSpec, typename TObject >
    inline bool
    _goDownObject(
        Iter< TIndex, VSTree< TopDown<TSpec> > > &it,
        TObject const &obj,
        False)
    {
        return _goDownChar(it, obj);
    }

    template < typename TIndex, typename TSpec, typename TObject >
    inline bool
    _goDownObject(
        Iter< TIndex, VSTree< TopDown<TSpec> > > &it,
        TObject const &obj,
        True)
    {
        typename Size<TIndex>::Type dummy;
        return _goDownString(it, obj, dummy);
    }


    // public interface for goDown(it, ...)
    template < typename TIndex, typename TSpec, typename TObject >
    inline bool
    goDown(
        Iter< TIndex, VSTree< TopDown<TSpec> > > &it,
        TObject const &obj)
    {
        return _goDownObject(it, obj, typename IsSequence<TObject>::Type());
    }

    template < typename TIndex, typename TSpec, typename TString, typename TSize >
    inline bool
    goDown(
        Iter< TIndex, VSTree< TopDown<TSpec> > > &it,
        TString const &pattern,
        TSize &lcp)
    {
        return _goDownString(it, pattern, lcp);
    }


/*!
 * @fn TopDownHistoryIterator#goUp
 * @headerfile <seqan/index.h>
 * @brief Iterates up one edge to the parent in a tree/trie.
 *
 * @signature bool goUp(iterator);
 *
 * @param[in,out] iterator An iterator of a string tree/trie.
 *
 * @return bool <tt>true</tt> if the iterator could be moved, otherwise <tt>false</tt>.
 *
 * @section Example
 *
 * The following code shows how the function @link TopDownHistoryIterator#goUp @endlink is used.
 *
 * @include demos/dox/index/iterator.cpp
 *
 * @code{.output}
 * be
 * beornottobe
 * e
 * eornottobe
 * nottobe
 * o
 * obe
 * obeornottobe
 * ornottobe
 * ottobe
 * rnottobe
 * t
 * tobe
 * tobeornottobe
 * ttobe
 *
 * @endcode
 */
    // go up one edge (returns false if in root node)
    // can be used at most once, as no history stack is available
    template < typename TIndex, class TSpec >
    inline bool
    _goUp(Iter< TIndex, VSTree< TopDown<TSpec> > > &it)
    {
        if (!isRoot(it)) {
            value(it) = it._parentDesc;
            return true;
        }
        return false;
    }

    // go up one edge (returns false if in root node)
    template < typename TIndex, class TSpec >
    inline bool
    _goUp(Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it)
    {
        if (!empty(it.history)) {
            value(it).range = back(it.history).range;
            eraseBack(it.history);
            if (!empty(it.history))
                value(it).parentRight = back(it.history).range.i2;    // copy right boundary of parent's range
            return true;
        }
        return false;
    }

    // go up one edge
    template < typename TIndex, class TSpec >
    inline bool goUp(Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it) {
        if (_goUp(it)) {
            _onGoUp(it);
            return true;
        } else
            return false;
    }

/*!
 * @fn TopDownIterator#nodeUp
 * @headerfile <seqan/index.h>
 * @brief Returns the vertex descriptor of the parent node.
 *
 * @signature TVertexDiscriptor nodeUp(iterator);
 *
 * @param[in,out] iterator An iterator of a string tree/trie.
 *
 * @return TVertexDescriptor The vertex descriptor of the parent node. The type is @link VertexDescriptor @endlink of TIndex. If
 *                           <tt>iterator</tt> points at the root node, the vertex descriptor of it is returned.
 */

    // return vertex descriptor of parent's node
    template < typename TIndex, class TSpec >
    inline typename VertexDescriptor<TIndex>::Type
    nodeUp(Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > const &it)
    {
        if (!empty(it.history))
        {
            typename Size<TIndex>::Type parentRight = 0;
            if (length(it.history) >= 2)
                parentRight = backPrev(it.history).range.i2;
            return typename VertexDescriptor<TIndex>::Type(back(it.history).range, parentRight);
        } else
            return value(it);
    }

    // nodeUp adaption for non-history iterators
    // ATTENTION: Do not call nodeUp after a goDown that returned false (or after _goUp)!
    template < typename TIndex, class TSpec >
    inline typename VertexDescriptor<TIndex>::Type const &
    nodeUp(Iter< TIndex, VSTree< TopDown<TSpec> > > const &it)
    {
        return it._parentDesc;
    }

/*!
 * @fn TopDownIterator#goRight
 * @headerfile <seqan/index.h>
 * @brief Iterates to the next sibling in a tree.
 *
 * @signature bool goRight(iterator);
 *
 * @param[in,out] iterator An iterator of a string tree.
 *
 * @return bool <tt>true</tt> if the iterator could be moved, otherwise <tt>false</tt>.
 */
    // go right to the lexic. next sibling
    template < typename TText, class TIndexSpec, class TSpec, typename TDfsOrder, typename THideEmptyEdges >
    inline bool _goRight(
        Iter< Index<TText, IndexEsa<TIndexSpec> >, VSTree< TopDown<TSpec> > > &it,
        VSTreeIteratorTraits<TDfsOrder, THideEmptyEdges> const)
    {
        typedef Index<TText, IndexEsa<TIndexSpec> > TIndex;

        if (isRoot(it)) return false;

        typename Size<TIndex>::Type right = value(it).parentRight;
        if (_isSizeInval(right)) right = length(indexSA(container(it)));

        do {
            if (value(it).range.i2 == right)                // not the right-most child?
                return false;

            if (_isNextl(value(it).range.i2, container(it)))
            {
                value(it).range.i1 = value(it).range.i2;    // go right
                value(it).range.i2 = _getNextl(value(it).range.i2, container(it));
            } else {
                value(it).range.i1 = value(it).range.i2;    // now it is the right-most child
                value(it).range.i2 = value(it).parentRight;
            }

        } while ((THideEmptyEdges::VALUE && emptyParentEdge(it)) || !nodeHullPredicate(it));
        return true;
    }

    // go down the leftmost edge
    template < typename TIndex, class TSpec >
    inline bool goRight(Iter< TIndex, VSTree< TopDown<TSpec> > > &it) {
        if (_goRight(it, typename GetVSTreeIteratorTraits< Iter<TIndex, VSTree< TopDown<TSpec> > > >::Type())) {
            _onGoRight(it);
            return true;
        } else
            return false;
    }

/*!
 * @fn TopDownIterator#parentEdgeLength
 * @headerfile <seqan/index.h>
 * @brief Returns the length of the edge from the <tt>iterator</tt> node to its parent.
 *
 * @signature TSize parentEdgeLength(iterator);
 *
 * @param[in,out] iterator An iterator of a string tree.
 *
 * @return TSize The returned value is equal to <tt>length(parentEdgeLabel(iterator))</tt> and its type is the result of
 *               the metafunction @link Size @endlink of the underlying index.
 */
    template < typename TIndex, class TSpec >
    inline typename Size< TIndex >::Type
    parentEdgeLength(Iter< TIndex, VSTree< TopDown<TSpec> > > const &it)
    {
        return repLength(it) - parentRepLength(it);
    }

/*!
 * @fn TopDownIterator#parentEdgeLabel
 * @headerfile <seqan/index.h>
 * @brief Returns a substring representing the edge from an <tt>iterator</tt> node to its parent.
 *
 * @signature TEdgeLabel parentEdgeLabel(iterator);
 *
 * @param[in] iterator An iterator of a string tree/trie.
 *
 * @return TEdgeLabel Returns a substring representing the edge from an <tt>iterator</tt> node to its parent.
 *                    and its type is the result of the metafunction @link VSTreeIterator#EdgeLabel @endlink of the iterator.
 */

    template < typename TIndex, class TSpec >
    inline typename EdgeLabel< Iter< TIndex, VSTree<TSpec> > >::Type
    parentEdgeLabel(Iter< TIndex, VSTree< TopDown<TSpec> > > const &it)
    {
        return infixWithLength(
            indexText(container(it)),
            posAdd(getOccurrence(it), parentRepLength(it)),
            parentEdgeLength(it));
    }

//TODO(singer): EsaRawText
/*!
 * @fn TopDownIterator#parentEdgeFirstChar
 * @headerfile <seqan/index.h>
 * @brief Returns the first character of the edge from an <tt>iterator</tt> node to its parent.
 *
 * @signature TValue parentEdgeFirstChar(iterator);
 *
 * @param[in] iterator An iterator of a string tree.
 *
 * @return TValue A single character of type <tt>Value&lt;TIndex&gt;::Type</tt> which is identical to
 *                 <tt>Value&lt;Fibre&lt;TIndex, EsaRawText&gt;::Type&gt;::Type</tt>.
 */

    template < typename TIndex, class TSpec >
    inline typename Value<TIndex>::Type
    parentEdgeFirstChar(Iter< TIndex, VSTree<TSpec> > const &it)
    {
        return infixWithLength(
            indexText(container(it)),
            posAdd(getOccurrence(it), parentRepLength(it)),
            1)[0];
    }

    template < typename TIndex, class TSpec >
    inline void _clear(Iter<TIndex, VSTree<TSpec> > &it)
    {
        value(it) = typename VertexDescriptor<TIndex>::Type(MinimalCtor());
    }

    template < typename TIndex, class TSpec >
    inline void clear(Iter<TIndex, VSTree<TSpec> > &it)
    {
        _clear(it);
    }

    template < typename TIndex, class TSpec >
    inline void _dfsClear(Iter<TIndex, VSTree<TSpec> > &it)
    {
        clear(it.history);
    }


    //////////////////////////////////////////////////////////////////////////////
    // dfs traversal for ParentLink iterators

    template < typename TIndex, typename TSpec, typename THideEmptyEdges >
    inline void goNextImpl(
        Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it,
        VSTreeIteratorTraits<Preorder_, THideEmptyEdges> const)
    {
        // preorder dfs
        do {
            if (!goDown(it) && !goRight(it))
                while (goUp(it) && !goRight(it)) {}
            if (isRoot(it)) {
                clear(it);
                return;
            }
        } while (!nodePredicate(it));
    }

    template < typename TIndex, typename TSpec, typename THideEmptyEdges >
    inline void goNextRightImpl(
        Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it,
        VSTreeIteratorTraits<Preorder_, THideEmptyEdges> const tag)
    {
        // preorder dfs
        if (!goRight(it))
            while (goUp(it) && !goRight(it)) {}
        if (isRoot(it)) {
            clear(it);
            return;
        }
        if (!nodePredicate(it))
            goNextImpl(it, tag);
    }

    template < typename TIndex, typename TSpec, typename THideEmptyEdges >
    inline void goNextUpImpl(
        Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it,
        VSTreeIteratorTraits<Preorder_, THideEmptyEdges> const tag)
    {
        // preorder dfs
        while (goUp(it) && !goRight(it)) {}
        if (isRoot(it)) {
            clear(it);
            return;
        }
        if (!nodePredicate(it))
            goNextImpl(it, tag);
    }




    template < typename TIndex, typename TSpec, typename THideEmptyEdges >
    inline void goNextImpl(
        Iter< TIndex, VSTree< TopDown< ParentLinks<TSpec> > > > &it,
        VSTreeIteratorTraits<Postorder_, THideEmptyEdges> const)
    {
        // postorder dfs
        do {
            if (goRight(it))
                while (goDown(it)) ;
            else
                if (!goUp(it)) {
                    clear(it);
                    return;
                }
        } while (!nodePredicate(it));
    }

    //////////////////////////////////////////////////////////////////////////////
    // boolean functions

    template < typename TIndex, class TSpec >
    inline bool eof(Iter<TIndex, VSTree<TSpec> > &it)
    {
        return !value(it).range.i2;
    }

    template < typename TIndex, class TSpec >
    inline bool eof(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return !value(it).range.i2;
    }

    template < typename TIndex, class TSpec >
    inline bool empty(Iter<TIndex, VSTree<TSpec> > &it)
    {
        return !value(it).range.i2;
    }

    template < typename TIndex, class TSpec >
    inline bool empty(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return !value(it).range.i2;
    }

//..concept:Concept.ContainerConcept
/*!
 * @fn VSTreeIterator#atEnd
 * @headerfile <seqan/index.h>
 * @brief Determines whether an virtual string tree iterator is at the end position.
 *
 * @signature bool atEnd(iterator);
 *
 * @param[in] iterator An iterator.
 *
 * @return bool <tt>true</tt> if <tt>iterator</tt> points behind the last item of the container, otherwise
 *              <tt>false</tt>.
 *
 * @section Examples
 *
 * The following example shows the usage of the @link VSTreeIterator#atEnd @endlink function.
 *
 * @include demos/dox/index/begin_atEnd_representative.cpp
 *
 * @code{.output}
 * A
 * AA
 * ATAA
 * TA
 * TAA
 * TATAA
 * --------------------------------
 * AA
 * ATAA
 * A
 * TAA
 * TATAA
 * TA
 *
 */

/*!
 * @fn BottomUp#atEnd
 * @headerfile <seqan/index.h>
 * @brief Determines whether an virtual string tree iterator is at the end position.
 *
 * @signature bool atEnd(iterator);
 *
 * @param[in] iterator An iterator.
 *
 * @return bool <tt>true</tt> if <tt>iterator</tt> points behind the last item of the container, otherwise
 *              <tt>false</tt>.
 *
 * @section Examples
 *
 * The following example shows the usage of the @link BottomUp#atEnd @endlink function.
 *
 * @include demos/dox/index/begin_atEnd_representative.cpp
 *
 * @code{.output}
 * A
 * AA
 * ATAA
 * TA
 * TAA
 * TATAA
 * --------------------------------
 * AA
 * ATAA
 * A
 * TAA
 * TATAA
 * TA
 *
 */

    template < typename TIndex, class TSpec >
    inline bool atEnd(Iter<TIndex, VSTree<TSpec> > &it)
    {
        return !value(it).range.i2;
    }

    template < typename TIndex, class TSpec >
    inline bool atEnd(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return !value(it).range.i2;
    }

/*!
 * @fn VSTreeIterator#isRoot
 * @headerfile <seqan/index.h>
 * @brief Test whether a tree iterator points to the root node.
 *
 * @signature bool isRoot(iterator);
 *
 * @param[in] iterator An iterator of a tree.
 *
 * @return bool <tt>true</tt> if <tt>iterator</tt> points to the root of the tree, otherwise <tt>false</tt>.
 *
 * @section Example
 *
 * The following example shows the usage of the @Function.isRoot@ function.
 *
 * @include demos/dox/index/begin_atEnd_representative_bottomUp.cpp
 *
 * code{.output}
 * output:AA
 * ATAA
 * A
 * TAA
 * TATAA
 * TA
 * @endcode
 */
    template < typename TIndex, class TSpec >
    inline bool isRoot(Iter<TIndex, VSTree< BottomUp<TSpec> > > const &it)
    {
        return empty(it.history);
    }

    template < typename TIndex, class TSpec >
    inline bool isRoot(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return _isRoot(value(it));
    }

    template < typename TSize >
    inline bool _isRoot(VertexEsa<TSize> const &value)
    {
//IOREV _notio_
        return _isSizeInval(value.range.i2);
    }

//TODO(singer): Note the case for trie or FM Index
/*!
 * @fn VSTreeIterator#isRightTerminal
 * @headerfile <seqan/index.h>
 * @brief Test whether iterator points to a suffix.
 *
 * @signature bool isRightTerminal(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree.
 *
 * @return bool <tt>true</tt> if <tt>iterator</tt> points to the node representing a suffix, otherwise
 *              <tt>false</tt>.
 *
 * Every leaf is also a right terminal (see @link VSTreeIterator#isLeaf @endlink), but not vice versa.
 */

    template < typename TIndex, class TSpec >
    inline bool isRightTerminal(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        // do we reach a leaf in a suffix tree with trailing '$'
        typename SAValue<TIndex>::Type pos = getOccurrence(it);
        TIndex const &index = container(it);
        typename StringSetLimits<typename Host<TIndex>::Type const>::Type &limits = stringSetLimits(index);

        return (getSeqOffset(pos, limits) + repLength(it)
            == sequenceLength(getSeqNo(pos, limits), index));
    }

/*!
 * @fn VSTreeIterator#isLeftMaximal
 * @headerfile <seqan/index.h>
 * @brief Test whether the occurrences of an iterator's @link VSTreeIterator#representative @endlink mutually differ in the character
 *        left of the hits.
 *
 * @signature bool isLeftMaximal(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree.
 *
 * @return bool <tt>true</tt> if there are at least two different characters left of the occurrences, otherwise
 *              <tt>false</tt>.
 *
 * @see VSTreeIterator#getOccurrences
 */

    template < typename TIndex, class TSpec >
    inline bool isLeftMaximal(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type    TOccs;
        typedef typename Infix< typename Fibre<TIndex, EsaBwt>::Type const >::Type    TOccsBWT;
        typedef typename Value< typename Fibre<TIndex, EsaBwt>::Type const >::Type    TValue;

        typedef typename Iterator<TOccs, Standard>::Type    TIter;
        typedef typename Iterator<TOccsBWT, Standard>::Type TIterBWT;

        TIndex const &index = container(it);
        typename StringSetLimits<typename Host<TIndex>::Type const>::Type &limits = stringSetLimits(index);

        TOccs occs = getOccurrences(it);
        TOccsBWT bwts = getOccurrencesBwt(it);

        TIter oc = begin(occs, Standard()), ocEnd = end(occs, Standard());
        TIterBWT bw = begin(bwts, Standard());

        if (oc == ocEnd) return true;
        if (posAtFirstLocal(*oc, limits)) return true;

        TValue seen = *bw;
        ++oc;
        ++bw;
        if (oc == ocEnd) return true;

        do {
            if (posAtFirstLocal(*oc, limits)) return true;
            if (seen != *bw) return true;
            ++oc;
            ++bw;
        } while (oc != ocEnd);

        return false;
    }

/*!
 * @fn VSTreeIterator#isPartiallyLeftExtensible
 * @headerfile <seqan/index.h>
 * @brief Test whether the characters left of the two occurrences of @link VSTreeIterator#representative @endlink are equal.
 *
 * @signature bool isPartiallyLeftExtensible(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree.
 *
 * @return bool <tt>true</tt> if there are at least two different characters left of the occurrences, otherwise
 *              <tt>false</tt>.
 *
 * @see VSTreeIterator#getOccurrences
 */
    template < typename TIndex, class TSpec, typename TSet >
    inline bool isPartiallyLeftExtensible(Iter<TIndex, VSTree<TSpec> > const &it, TSet &charSet)
    {
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type    TOccs;
        typedef typename Infix< typename Fibre<TIndex, EsaBwt>::Type const >::Type    TOccsBWT;
        typedef typename Value< typename Fibre<TIndex, EsaBwt>::Type const >::Type    TValue;

        typedef typename Iterator<TOccs, Standard>::Type    TIter;
        typedef typename Iterator<TOccsBWT, Standard>::Type TIterBWT;

        TIndex const &index = container(it);
        typename StringSetLimits<typename Host<TIndex>::Type const>::Type &limits = stringSetLimits(index);

        clear(charSet);

        TOccs occs = getOccurrences(it);
        TOccsBWT bwts = getOccurrencesBwt(it);

        TIter oc = begin(occs, Standard()), ocEnd = end(occs, Standard());
        TIterBWT bw = begin(bwts, Standard());

        while (oc != ocEnd) {
            if (!posAtFirstLocal(*oc, limits)) {
                TValue c = *bw;
                if (in(c, charSet)) return true;
                insert(c, charSet);
            }
            ++oc;
            ++bw;
        }

        return false;
    }

    template < typename TIndex, class TSpec >
    inline bool isPartiallyLeftExtensible(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        typename Set<typename Value<TIndex>::Type>::Type set;
        return isPartiallyLeftExtensible(it, set);
    }

/*!
 * @fn VSTreeIterator#isUnique
 * @headerfile <seqan/index.h>
 * @brief Test whether the @link VSTreeIterator#representative @endlink occurs only once in every sequence.
 *
 * @signature bool isUnique(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree.
 *
 * @return bool <tt>true</tt> if there are at least two different characters left of the occurrences, otherwise
 *              <tt>false</tt>.
 *
 * @see VSTreeIterator#getOccurrences
 */

    template < typename TIndex, class TSpec, typename TSet >
    inline bool isUnique(Iter<TIndex, VSTree<TSpec> > const &it, TSet &set)
    {
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type TOccs;
        typedef typename Iterator<TOccs, Standard>::Type TIter;
        typedef typename Size<TIndex>::Type TSize;

        TIndex const &index = container(it);

        clear(set);

        TOccs occs = getOccurrences(it);
        TIter oc = begin(occs, Standard()), ocEnd = end(occs, Standard());

        while (oc != ocEnd) {
            TSize seqNo = getSeqNo(*oc, stringSetLimits(index));
            if (in(seqNo, set)) return false;
            insert(seqNo, set);
            ++oc;
        }

        return true;
    }

    template < typename TIndex, class TSpec >
    inline bool isUnique(Iter<TIndex, VSTree<TSpec> > const &it) {
        VectorSet_<
            typename Size<TIndex>::Type,
            Alloc<>
        > set(countSequences(container(it)));
        return isUnique(it, set);
    }

/*!
 * @fn VSTreeIterator#getFrequency
 * @headerfile <seqan/index.h>
 * @brief Returns the number of sequences, which contain the @link
 *        VSTreeIterator#representative @endlink as a substring.
 *
 * @signature int getFrequency(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree. Types: @link VSTreeIterator @endlink
 *
 * @return int The number of different sequences containing the @link VSTreeIterator#representative @endlink.
 *
 * @section Example
 *
 * The following code how @link VSTreeIterator#getFrequency @endlink is used. Note that the result of alternative 1 and 2 is the same,
 * however alternative one copies a string which requires more memory.
 *
 * @include demos/dox/index/getOccurrences_getFrequency_range_getFibre.cpp
 *
 * @code{.output}
 * SSI occurs in 2 sequences.
 * Hit in sequence 0 at position 5
 * Hit in sequence 1 at position 4
 * Hit in sequence 0 at position 2
 * ----------------------------
 * Hit in sequence 0 at position 5
 * Hit in sequence 1 at position 4
 * Hit in sequence 0 at position 2
 * @endcode
 * @see VSTreeIterator#getOccurrences
 */

    template < typename TIndex, class TSpec, typename TSet >
    inline typename Size<TIndex>::Type
    getFrequency(Iter<TIndex, VSTree<TSpec> > const &it, TSet &set)
    {
        typedef typename Infix< typename Fibre<TIndex, EsaSA>::Type const >::Type TOccs;
        typedef typename Iterator<TOccs, Standard>::Type TIter;
        typedef typename Size<TIndex>::Type TSize;

        TIndex const &index = container(it);

        clear(set);

        TOccs occs = getOccurrences(it);
        TIter oc = begin(occs, Standard()), ocEnd = end(occs, Standard());

        int counter = 0;
        while (oc != ocEnd) {
            TSize seqNo = getSeqNo(*oc, stringSetLimits(index));
            if (!in(seqNo, set)) {
                ++counter;
                insert(seqNo, set);
            }
            ++oc;
        }

        return counter;
    }

    template < typename TIndex, class TSpec >
    inline typename Size<TIndex>::Type
    getFrequency(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        VectorSet_<
            typename Size<TIndex>::Type,
            Alloc<>
        > set(countSequences(container(it)));
        return getFrequency(it, set);
    }

/*!
 * @fn VSTreeIterator#childrenAreLeaves
 * @headerfile <seqan/index.h>
 * @brief Test whether iterator points to a node with only leaf-children.
 *
 * @signature bool childrenAreLeaves(iterator);
 *
 * @param[in] iterator An iterator of a suffix tree.
 *
 * @return bool <tt>true</tt> if <tt>iterator</tt> points to an inner node of the tree, whose children are leaves.
 *              Otherwise it is <tt>false</tt>.
 */
    template < typename TIndex, class TSpec >
    inline bool childrenAreLeaves(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return countChildren(it) == countOccurrences(it);
    }

/*!
 * @fn VSTreeIterator#isLeaf
 * @headerfile <seqan/index.h>
 * @brief Test whether a tree iterator points to a leaf.
 *
 * @signature bool isLeaf(iterator);
 *
 * @param[in] iterator An iterator of a tree.
 *
 * @return bool <tt>true</tt> if <tt>iterator</tt> points to a leaf of the tree, otherwise <tt>false</tt>.
 *
 * @link DemoIndexCountChildren @endlink
 */
    template < typename TSize >
    inline bool _isLeaf(VertexEsa<TSize> const &vDesc)
    {
//IOREV _notio_
        // is this a leaf?
        return vDesc.range.i1 + 1 >= vDesc.range.i2;
    }

    // is this a leaf? (including empty $-edges)
    template < typename TIndex, class TSpec, typename TDfsOrder >
    inline bool _isLeaf(
        Iter<TIndex, VSTree<TSpec> > const &it,
        VSTreeIteratorTraits<TDfsOrder, False> const)
    {
        return _isLeaf(value(it));
    }


    template <typename TIndex, typename TSpec>
    inline typename SAValue<TIndex>::Type
    _lastOccurrence(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return back(getOccurrences(it));
    }

    template <typename TText, typename TIndexSpec, typename TSpec>
    inline typename SAValue<Index<TText, IndexEsa<TIndexSpec> > >::Type
    _lastOccurrence(Iter<Index<TText, IndexEsa<TIndexSpec> >, VSTree<TSpec> > const &it)
    {
        if (_isSizeInval(value(it).range.i2))
            return back(indexSA(container(it)));
        else
            return saAt(value(it).range.i2 - 1, container(it));
    }

    // is this a leaf? (hide empty $-edges)
    template < typename TIndex, class TSpec, typename TDfsOrder >
    inline bool _isLeaf(Iter<TIndex, VSTree<TSpec> > const &it, VSTreeIteratorTraits<TDfsOrder, True> const)
    {
        typedef typename SAValue<TIndex>::Type  TOcc;

        if (_isLeaf(value(it))) return true;

        TIndex const &index = container(it);

        // get representative length (see repLength)
        typename Size<TIndex>::Type lcp = repLength(it);

        // if the last suffix in the interval is larger than the lcp,
        // not all outgoing edges are empty (uses lex. sorting)
        TOcc oc = _lastOccurrence(it);
        return getSeqOffset(oc, stringSetLimits(index)) + lcp == sequenceLength(getSeqNo(oc, stringSetLimits(index)), index);
    }

    template < typename TIndex, class TSpec >
    inline bool isLeaf(Iter<TIndex, VSTree<TSpec> > const &it)
    {
        return _isLeaf(it, typename GetVSTreeIteratorTraits< Iter<TIndex, VSTree<TSpec> > >::Type());
    }

    //////////////////////////////////////////////////////////////////////////////
    // (more or less) internal functions for accessing the childtab

    template < typename TSize, typename TIndex >
    inline bool _isNextl(TSize i, TIndex const &index)
    {
//IOREV _notio_
        if (i >= length(index)) return false;
        TSize j = childAt(i, index);
        return (j > i) && lcpAt(j - 1, index) == lcpAt(i - 1, index);
    }

    template < typename TSize, typename TIndex >
    inline bool _isUp(TSize i, TIndex const &index)
    {
//IOREV _notio_
        if (i >= length(index)) return false;
        TSize j = childAt(i, index);
        return (j <= i) && lcpAt(j - 1, index) > lcpAt(i - 1, index);
    }

    template < typename TSize, typename TIndex >
    inline TSize _getNextl(TSize i, TIndex const &index)
    {
        return childAt(i, index);
    }

    template < typename TSize, typename TIndex >
    inline TSize _getUp(TSize i, TIndex const &index)
    {
        if (!_isSizeInval(i))
            return childAt(i - 1, index);
        else
            return childAt(0, index);
    }

    template < typename TSize, typename TIndex >
    inline TSize _getDown(TSize i, TIndex const &index)
    {
        return childAt(i, index);
    }


    //////////////////////////////////////////////////////////////////////////////
    // depth-first search

    template < typename TIndex, class TSpec >
    inline Pair<typename Size<TIndex>::Type> &
    _dfsRange(Iter< TIndex, VSTree< BottomUp<TSpec> > > &it)
    {
        return value(it).range;
    }

    template < typename TIndex, class TSpec >
    inline Pair<typename Size<TIndex>::Type> const &
    _dfsRange(Iter< TIndex, VSTree< BottomUp<TSpec> > > const &it)
    {
        return value(it).range;
    }

    template < typename TIndex, class TSpec >
    inline typename Size<TIndex>::Type & _dfsLcp(Iter< TIndex, VSTree< BottomUp<TSpec> > > &it)
    {
        return it.lValue;
    }

    template < typename TIndex, class TSpec >
    inline typename Size<TIndex>::Type _dfsLcp(Iter< TIndex, VSTree< BottomUp<TSpec> > > const &it)
    {
        return it.lValue;
    }


}

#endif
