// ==========================================================================
//                 SeqAn - The Library for Sequence Analysis
// ==========================================================================
// Copyright (c) 2006-2024, Knut Reinert, FU Berlin
// 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: Rene Rahn <rene.rahn@fu-berlin.de>
// ==========================================================================
// Implements the core of the dp algorithms.
// This is the crucial part of the refactoring of the alignment algorithms.
// It implements - at the moment only a column wise approach - the core
// loop structure for all alignment profiles. We generally differ between an
// unbanded alignment which is very easy, a banded alignment and a special
// case of the banded alignment the Hamming distance, where upper diagonal
// equals lower diagonal.
//
// The unbanded alignment:
// The computation of the unbanded alignment is divided into three parts.
// In the following we refer to a track as the part where the inner loop
// is iterating (in case of column wise navigation a track is equivalent
// to a column).
// First we compute the initial track. Afterwards we continue with all
// inner tracks of the dp matrix and in the end we compute the last track
// separately. This is because all three types have a special property that
// is different from the other track types.
// Each track itself is further divided into three parts, namely the first cell
// the inner cell and the last cell, corresponding to the initial row,
// all inner rows and the last row of a typical dp matrix. This partition of
// the dp matrix allows us to easily change the behavior of different cells
// according to the chosen dp profile at compile time.
// See alignment_dp_meta_info.h to learn about the different meta objects
// that manage the characteristics of each cell of a particular track type.
//
// The banded alignment:
// In the banded alignment we generally divide the dp matrix into the same
// partition as for the unbanded alignment. The only difference is that we,
// additionally add a specific information of how the current track is
// located within the dp matrix. Since we only consider a band we do not
// necessarily span over the full matrix size for a particular column.
// We distinguish between the locations: PartialColumnTop,
// PartialColumnMiddle, PartialColumnBottom and FullColumn (which is the
// default location for unbanded alignments). Each location of the column
// implies a different composition of the cells contained within a
// particular track. Thus, we are able to set different recursion
// directions and tracking informations for each cell independent from the
// runtime. The only difference is that the outer for-loop (iterating over
// the tracks) is split up into three loops. The first loop then only
// iterates over these tracks that are located at the top of the matrix.
// The second for-loop iterates over the tracks that either are of type
// PartialColumnMiddle or FullColumn (wide bands, where the upper diagonal
// begins behind the track where the lower diagonal crosses the last row of
// the dp matrix). And the last for-loop iterates over the tail of the band
// which is located at the PartialColumnBottom.
//
// The Hamming distance:
// In the special case where upper diagonal equals lower diagonal we only
// have to parse one diagonal of the matrix so we have a special
// implementation for that, though it works for all dp profiles.
//
// Restricitons:
// At the moment we have implemented a restriction such that not all bands
// are accepted. If the dp profile consists of the standard global alignment
// algorithm (NeedlemanWunsch or Gotoh), the band is required to go through
// the sink and the source of the dp matrix. If this is not given the
// alignment algorithm is aborted and the score std::numeric_limits<TScoreValue>::min()
// is returned.
// There are no further restrictions.
//
// GapCosts:
// Another detail of the new module is the selection of the gap functions,
// which is also now part of the compile time configuration. Whenever an
// algorithm is implemented it would automatically work for both gap
// functions (linear gaps and affine gaps).
//
// Navigation:
// It is possible to a certain degree to change the behavior of how to parse
// through the dp matrix. Using the new navigators one can implement
// different behaviors for different matrices. At the moment we only support
// column wise navigation for full and sparse score matrices and for full
// traceback matrices. Another detail of this navigators comes into account,
// when we want to compute only the score. We actually create a navigator
// for the dp matrix but implemented it this way that it gets never actually
// called when the traceback is disabled. Thus we do not store the traceback
// matrix if it is not necessary.
//
// Traceback:
// The traceback is now implemented as a single function that is used by all
// alignment profiles. Here we prefer the diagonal direction before the
// vertical before the horizontal direction.
// All tracebacks are first stored within the String<TraceSegment> object
// and afterwards, when the traceback is finished adapted to its given
// target object such as Align, Graph, Fragments, etc.
//
// Tracing:
// We use now an object called DPScout to keep track of the maximal score.
// This object scouts for the best value and can be overloaded to implement
// different strategies of how the score should be traced. Togehter with
// the meta_info file it only traces thus cells that are allowed to be
// traced given the current dp profile. Since this is also a compile time
// property we do not need to track every cell for the global alignment,
// while we do in the local alignment.
//
// Structure:
// The sequences within the matrix are marked as horizontal and vertical
// sequence to determine there orientation within the matrix.
// ==========================================================================

#ifndef SEQAN_INCLUDE_SEQAN_ALIGN_DP_ALGORITHM_IMPL_H_
#define SEQAN_INCLUDE_SEQAN_ALIGN_DP_ALGORITHM_IMPL_H_

namespace seqan2 {

// ============================================================================
// Forwards
// ============================================================================

// ============================================================================
// Tags, Classes, Enums
// ============================================================================

// ============================================================================
// Metafunctions
// ============================================================================

// ============================================================================
// Functions
// ============================================================================

// ----------------------------------------------------------------------------
// Function prepareAlign()
// ----------------------------------------------------------------------------

template<typename TSequence, typename TAlignSpec>
inline void
prepareAlign(StringSet<Align<TSequence, TAlignSpec> > & align,
             TSequence const & strH,
             StringSet<TSequence> const & setV)
{
    size_t numAlignments = length(setV);

    SEQAN_ASSERT_EQ(length(align), 0u);
    SEQAN_ASSERT_GT(numAlignments, 0u);

    resize(align, numAlignments);
    for(size_t i = 0; i < numAlignments; ++i)
    {
        resize(rows(align[i]), 2);
        assignSource(row(align[i], 0), strH);
        assignSource(row(align[i], 1), setV[i]);
    }
}

// ----------------------------------------------------------------------------
// Function _checkBandProperties()
// ----------------------------------------------------------------------------

// Checks whether the chosen band fits the dp profile.
template <typename TSequenceH, typename TSequenceV, typename TAlignmentProfile>
inline bool _checkBandProperties(TSequenceH const & /*seqH*/,
                                 TSequenceV const & /*seqV*/,
                                 DPBandConfig<BandOff> const & /*band*/,
                                 TAlignmentProfile const & /*alignProfile*/)
{
    return true;
}

template <typename TSequenceH, typename TSequenceV, typename TAlignmentProfile>
inline bool _checkBandProperties(TSequenceH const & seqH,
                                 TSequenceV const & seqV,
                                 DPBandConfig<BandOn> const & band,
                                 TAlignmentProfile const & /*alignProfile*/)
{
    typedef typename MakeSigned<typename Size<TSequenceH>::Type>::Type TSignedSize;

    // Check if the intersection between band and DP matrix is empty.
    if (upperDiagonal(band) < (0 - static_cast<TSignedSize>(length(seqV))) ||
        lowerDiagonal(band) > static_cast<TSignedSize>(length(seqH)))
    {
        return false;
    }

    // If the band begins before the beginning of the horizontal sequence
    // then check if free end-gaps are enabled at the beginning of the vertical sequence.
    if (upperDiagonal(band) < 0 && !IsFreeEndGap_<TAlignmentProfile, DPFirstColumn>::VALUE)
        return false;

    // If the band begins before the beginning of the vertical sequence
    // then check if free end-gaps are enabled at the beginning of the horizontal sequence.
    if (lowerDiagonal(band) > 0 && !IsFreeEndGap_<TAlignmentProfile, DPFirstRow>::VALUE)
        return false;

    // If the band ends behind the end of the vertical sequence
    // then check if free end-gaps are enabled at the end of the horizontal sequence.
    if (upperDiagonal(band) + static_cast<TSignedSize>(length(seqV)) < static_cast<TSignedSize>(length(seqH)) &&
        !IsFreeEndGap_<TAlignmentProfile, DPLastRow>::VALUE)
    {
        return false;
    }

    // If the band ends behind the end of the horizontal sequence
    // then check if free end-gaps are enabled at the end of the vertical sequence.
    if (lowerDiagonal(band) + static_cast<TSignedSize>(length(seqV)) > static_cast<TSignedSize>(length(seqH)) &&
        !IsFreeEndGap_<TAlignmentProfile, DPLastColumn>::VALUE)
    {
        return false;
    }

    return true;
}

// ----------------------------------------------------------------------------
// Function _invalidDPSettings()
// ----------------------------------------------------------------------------


// Checks if the settings for the dp algorithm are valid.
// Returns true if they are valid, false otherwise.
template <typename TSequenceH, typename TSequenceV, typename TBand, typename TAlignmentProfile>
inline bool _isValidDPSettings(TSequenceH const & seqH,
                               TSequenceV const & seqV,
                               TBand const & band,
                               TAlignmentProfile const & alignProfile)
{
    // Check if the sequences are empty.
    if (empty(seqH) || empty(seqV))
    {
        return false;
    }

    return _checkBandProperties(seqH, seqV, band, alignProfile);
}

// ----------------------------------------------------------------------------
// Function _isBandEnabled()
// ----------------------------------------------------------------------------

// Returns true if a band is selected, otherwise false.
template <typename TBandSpec>
inline bool
_isBandEnabled(DPBandConfig<TBandSpec> const & /*band*/)
{
    return IsSameType<TBandSpec, BandOn>::VALUE;
}

// ----------------------------------------------------------------------------
// Function _computeCell()
// ----------------------------------------------------------------------------

// Computes the score and tracks it if enabled.
template <typename TDPScout,
          typename TTraceMatrixNavigator,
          typename TDPCell,
          typename TSequenceHValue, typename TSequenceVValue, typename TScoringScheme, typename TColumnDescriptor,
          typename TCellDescriptor, typename TDPProfile>
inline void
_computeCell(TDPScout & scout,
             TTraceMatrixNavigator & traceMatrixNavigator,
             TDPCell & current,
             TDPCell & diagonal,
             TDPCell const & horizontal,
             TDPCell & vertical,
             TSequenceHValue const & seqHVal,
             TSequenceVValue const & seqVVal,
             TScoringScheme const & scoringScheme,
             TColumnDescriptor const &,
             TCellDescriptor const &,   // One of FirstCell, InnerCell or LastCell.
             TDPProfile const &)
{
    typedef DPMetaColumn_<TDPProfile, TColumnDescriptor> TMetaColumn;

    assignValue(traceMatrixNavigator,
                _computeScore(current, diagonal, horizontal, vertical, seqHVal, seqVVal, scoringScheme,
                              typename RecursionDirection_<TMetaColumn, TCellDescriptor>::Type(),
                              TDPProfile()));

    if (TrackingEnabled_<TMetaColumn, TCellDescriptor>::VALUE)
    {
        typedef typename LastColumnEnabled_<TDPProfile, TColumnDescriptor>::Type TIsLastColumn;
        typedef typename LastRowEnabled_<TDPProfile, TCellDescriptor, TColumnDescriptor>::Type TIsLastRow;

        // TODO(rrahn): Refactor to set vertical score only when max is updated.
        if (IsTracebackEnabled_<TDPProfile>::VALUE)
        {
            _setVerticalScoreOfCell(current, _verticalScoreOfCell(vertical));
        }
        _scoutBestScore(scout, current, traceMatrixNavigator,
                        TIsLastColumn(), TIsLastRow());
    }
}

// ----------------------------------------------------------------------------
// Function _precomputeScoreMatrixOffset()
// ----------------------------------------------------------------------------

// Default fallback if scoring scheme is not a matrix.
template <typename TSeqValue,
          typename TScoringScheme>
inline TSeqValue const &
_precomputeScoreMatrixOffset(TSeqValue const & seqVal,
                             TScoringScheme const & /*score*/)
{
    return seqVal;
}

// ----------------------------------------------------------------------------
// Function _computeTrack()
// ----------------------------------------------------------------------------

template <typename TDPScout,
          typename TDPScoreMatrixNavigator,
          typename TDPTraceMatrixNavigator,
          typename TSeqHValue,
          typename TSeqVValue,
          typename TSeqVIterator,
          typename TScoringScheme,
          typename TDPCell,
          typename TColumnDescriptor,
          typename TDPProfile>
inline void
_computeTrack(TDPScout & scout,
              TDPScoreMatrixNavigator & dpScoreMatrixNavigator,
              TDPTraceMatrixNavigator & dpTraceMatrixNavigator,
              TSeqHValue const & seqHValue,
              TSeqVValue const & seqVValue,
              TSeqVIterator const & seqBegin,
              TSeqVIterator const & seqEnd,
              TScoringScheme const & scoringScheme,
              TDPCell & cacheDiag,
              TDPCell & cacheVert,
              TColumnDescriptor const &,
              TDPProfile const &)
{
    _goNextCell(dpScoreMatrixNavigator, TColumnDescriptor(), FirstCell());
    _goNextCell(dpTraceMatrixNavigator, TColumnDescriptor(), FirstCell());

    _preInitCacheDiagonal(cacheDiag, dpScoreMatrixNavigator, TColumnDescriptor());

    // Precompute the row of the scoring matrix for future look-ups.
    TSeqHValue tmpSeqH = _precomputeScoreMatrixOffset(seqHValue, scoringScheme);

    // Initilaize SIMD version with multiple end points.
    _preInitScoutVertical(scout, coordinate(dpTraceMatrixNavigator, +DPMatrixDimension_::VERTICAL));

    // Compute the first cell.
    _computeCell(scout,
                 dpTraceMatrixNavigator,
                 value(dpScoreMatrixNavigator),
                           cacheDiag,
                           previousCellHorizontal(dpScoreMatrixNavigator),
                           cacheVert,
                 tmpSeqH,
                 seqVValue,
                 scoringScheme,
                 TColumnDescriptor(), FirstCell(), TDPProfile());

    TSeqVIterator iter = seqBegin;
#ifdef __INTEL_LLVM_COMPILER // It works with c++20 and c++23, though.
    asm ("" : : "m"(iter)); // Kindly request IntelLLVM (2024.1.2) to not optimize iter away.
#endif
    for (; iter != seqEnd - 1; ++iter)
    {
        _goNextCell(dpScoreMatrixNavigator, TColumnDescriptor(), InnerCell());
        _goNextCell(dpTraceMatrixNavigator, TColumnDescriptor(), InnerCell());

        _incVerticalPos(scout);
        // Compute the inner cell.
        if (SEQAN_UNLIKELY(_reachedVerticalEndPoint(scout, iter)))
        {
            _computeCell(scout,
                         dpTraceMatrixNavigator,
                         value(dpScoreMatrixNavigator),
                         cacheDiag,
                         previousCellHorizontal(dpScoreMatrixNavigator),
                         cacheVert,
                         tmpSeqH, sequenceEntryForScore(scoringScheme, container(iter), position(iter)),
                         scoringScheme, TColumnDescriptor(), LastCell(), TDPProfile());
            _nextVerticalEndPos(scout);
        }
        else
        {
            _computeCell(scout,
                         dpTraceMatrixNavigator,
                         value(dpScoreMatrixNavigator),
                         cacheDiag,
                         previousCellHorizontal(dpScoreMatrixNavigator),
                         cacheVert,
                         tmpSeqH, sequenceEntryForScore(scoringScheme, container(iter), position(iter)),
                         scoringScheme, TColumnDescriptor(), InnerCell(), TDPProfile());
        }
    }
    _goNextCell(dpScoreMatrixNavigator, TColumnDescriptor(), LastCell());
    _goNextCell(dpTraceMatrixNavigator, TColumnDescriptor(), LastCell());
    _incVerticalPos(scout);
    _computeCell(scout,
                 dpTraceMatrixNavigator,
                 value(dpScoreMatrixNavigator),
                           cacheDiag,
                           previousCellHorizontal(dpScoreMatrixNavigator),
                           cacheVert,
                 tmpSeqH,
                 sequenceEntryForScore(scoringScheme, container(iter), position(iter)),
                 scoringScheme,
                 TColumnDescriptor(), LastCell(), TDPProfile());
}

template <typename TDPScout,
          typename TDPScoreMatrixNavigator,
          typename TDPTraceMatrixNavigator,
          typename TSeqHValue,
          typename TSeqVValue,
          typename TSeqVIterator,
          typename TScoringScheme,
          typename TColumnDescriptor,
          typename TDPProfile>
inline void
_computeTrack(TDPScout & scout,
              TDPScoreMatrixNavigator & dpScoreMatrixNavigator,
              TDPTraceMatrixNavigator & dpTraceMatrixNavigator,
              TSeqHValue const & seqHValue,
              TSeqVValue const & seqVValue,
              TSeqVIterator const & seqBegin,
              TSeqVIterator const & seqEnd,
              TScoringScheme const & scoringScheme,
              TColumnDescriptor const &,
              TDPProfile const &)
{
    using TDPCell = std::decay_t<decltype(value(dpScoreMatrixNavigator))>;

    TDPCell cacheDiag;
    TDPCell cacheVert;
    _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator, seqHValue, seqVValue, seqBegin, seqEnd,
                  scoringScheme, cacheDiag, cacheVert, TColumnDescriptor{}, TDPProfile{});
}

// ----------------------------------------------------------------------------
// Function _computeUnbandedAlignmentHelperTerminate()
// ----------------------------------------------------------------------------

template <typename TDPCell, typename TSpec>
inline bool //TODO(C++11) constexpr
_computeAlignmentHelperCheckTerminate(DPScout_<TDPCell, TSpec > const & /**/)
{
    return false;
}

template <typename TDPCell, typename TSpec>
inline bool
_computeAlignmentHelperCheckTerminate(DPScout_<TDPCell,Terminator_<TSpec> > const & s)
{
    return _terminationCriteriumIsMet(s);
}

// ----------------------------------------------------------------------------
// Function _computeUnbandedAlignment()
// ----------------------------------------------------------------------------

// Computes the standard DP-algorithm.
template <typename TDPScout,
          typename TDPScoreMatrixNavigator,
          typename TDPTraceMatrixNavigator,
          typename TSequenceH,
          typename TSequenceV,
          typename TScoringScheme,
          typename TBand,
          typename TAlignmentAlgo, typename TGapCosts, typename TTraceFlag, typename TExecPolicy>
inline void
_computeAlignmentImpl(TDPScout & scout,
                      TDPScoreMatrixNavigator & dpScoreMatrixNavigator,
                      TDPTraceMatrixNavigator & dpTraceMatrixNavigator,
                      TSequenceH const & seqH,
                      TSequenceV const & seqV,
                      TScoringScheme const & scoringScheme,
                      TBand const & /*band*/,
                      DPProfile_<TAlignmentAlgo, TGapCosts, TTraceFlag, TExecPolicy> const & dpProfile,
                      NavigateColumnWise const & /*tag*/)
{
    typedef typename Iterator<TSequenceH const, Rooted>::Type TConstSeqHIterator;
    typedef typename Iterator<TSequenceV const, Rooted>::Type TConstSeqVIterator;

    // Initilaize SIMD version with multiple end points.
    _preInitScoutHorizontal(scout, 0);

    // ============================================================================
    // PREPROCESSING
    // ============================================================================

    TConstSeqVIterator seqVBegin = begin(seqV, Rooted());
    TConstSeqVIterator seqVEnd = end(seqV, Rooted());

    SEQAN_ASSERT_GT(length(seqH), 0u);
    SEQAN_ASSERT_GT(length(seqV), 0u);

    _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                  sequenceEntryForScore(scoringScheme, seqH, 0),
                  sequenceEntryForScore(scoringScheme, seqV, 0),
                  seqVBegin, seqVEnd, scoringScheme,
                  MetaColumnDescriptor<DPInitialColumn, FullColumn>(), dpProfile);

    // ============================================================================
    // MAIN DP
    // ============================================================================

    TConstSeqHIterator seqHIter = begin(seqH, Rooted());
    TConstSeqHIterator seqHIterEnd = end(seqH, Rooted()) - 1;
#ifdef __INTEL_LLVM_COMPILER
    asm ("" : : "m"(seqHIter)); // Kindly request IntelLLVM (2023.2) to not optimize seqHIter away.
#endif
    for (; seqHIter != seqHIterEnd; ++seqHIter)
    {
        _incHorizontalPos(scout);
        // We might only select it if SIMD version is available.
        if (SEQAN_UNLIKELY(_reachedHorizontalEndPoint(scout, seqHIter)))
        {
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                          sequenceEntryForScore(scoringScheme, seqV, 0),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPFinalColumn, FullColumn>(), dpProfile);
            _nextHorizontalEndPos(scout);
        }
        else
        {
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                          sequenceEntryForScore(scoringScheme, seqV, 0),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInnerColumn, FullColumn>(), dpProfile);
        }
        if (_computeAlignmentHelperCheckTerminate(scout))
        {
            return;
        }
    }

    // ============================================================================
    // POSTPROCESSING
    // ============================================================================

    _incHorizontalPos(scout);
    _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                  sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                  sequenceEntryForScore(scoringScheme, seqV, 0),
                  seqVBegin, seqVEnd, scoringScheme,
                  MetaColumnDescriptor<DPFinalColumn, FullColumn>(), dpProfile);

    // If we compute only the single option. we need to check if there are other possibilities at the end.
    // Traceback only from Diagonal, but could also come from vertical or horizontal.

//    for (unsigned i = 0; i < length(recMatrix); ++i)
//    {
//        std::cout << recMatrix[i]._score << "\t";
//    }
//    std::cout << std::endl;
}

// ----------------------------------------------------------------------------
// Function _computeAlignment() banded
// ----------------------------------------------------------------------------

// Computes the banded DP-algorithm.
template <typename TDPScout,
          typename TDPScoreMatrixNavigator,
          typename TDPTraceMatrixNavigator,
          typename TSequenceH,
          typename TSequenceV,
          typename TScoringScheme,
          typename TBand,
          typename TAlignmentAlgo, typename TGapCosts, typename TTraceFlag, typename TExecPolicy>
inline void
_computeAlignmentImpl(TDPScout & scout,
                      TDPScoreMatrixNavigator & dpScoreMatrixNavigator,
                      TDPTraceMatrixNavigator & dpTraceMatrixNavigator,
                      TSequenceH const & seqH,
                      TSequenceV const & seqV,
                      TScoringScheme const & scoringScheme,
                      TBand const & band,
                      DPProfile_<TAlignmentAlgo, TGapCosts, TTraceFlag, TExecPolicy> const & dpProfile,
                      NavigateColumnWiseBanded const & /*tag*/)
{
    typedef DPProfile_<TAlignmentAlgo, TGapCosts, TTraceFlag> TDPProfile;
    typedef typename MakeSigned<typename Size<TSequenceH>::Type>::Type TSignedSizeSeqH;
    typedef typename MakeSigned<typename Size<TSequenceV>::Type>::Type TSignedSizeSeqV;
    typedef typename Iterator<TSequenceH const, Rooted>::Type TConstSeqHIterator;
    typedef typename Iterator<TSequenceV const, Rooted>::Type TConstSeqVIterator;

    using TDPScoreValue = std::decay_t<decltype(value(dpScoreMatrixNavigator))>;
    // Caching these cells improves performance significantly.
    TDPScoreValue cacheDiag;
    TDPScoreValue cacheVert;

    if (upperDiagonal(band) == lowerDiagonal(band))
    {
        _computeHammingDistance(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator, seqH, seqV, scoringScheme, band,
                                dpProfile);
        return;
    }
    // Now we have the problem of not knowing when we are in the last cell.

    // ============================================================================
    // PREPROCESSING
    // ============================================================================
    TSignedSizeSeqH seqHlength = static_cast<TSignedSizeSeqH>(length(seqH));
    TSignedSizeSeqH seqVlength = static_cast<TSignedSizeSeqV>(length(seqV));

    TConstSeqVIterator seqVBegin = begin(seqV, Rooted()) - _min(0, 1 + upperDiagonal(band));
    TConstSeqVIterator seqVEnd = begin(seqV, Rooted()) - _min(0, _max(-seqVlength, lowerDiagonal(band)));

    // We have to distinguish two band sizes. Some which spans the whole matrix in between and thus who not.
    // This can be distinguished, if UpperDiagonal > length(seqV) + LowerDiagonal

    // We start at least at the first position of the horizontal sequence or wherever the lower diagonal begins first.
    TConstSeqHIterator seqHIterBegin = begin(seqH, Rooted()) + _max(0, _min(seqHlength - 1, lowerDiagonal(band)));

    // The horizontal initial phase ends after the upper diagonal but at most after the horizontal sequence, or there is no horizontal initialization phase.
    TConstSeqHIterator seqHIterEndColumnTop = begin(seqH, Rooted()) + _min(seqHlength - 1, _max(0, upperDiagonal(band)));

    // The middle band phase ends after the lower diagonal crosses the bottom of the alignment matrix or after the horizontal sequence if it is smaller.
    TConstSeqHIterator seqHIterEndColumnMiddle = begin(seqH, Rooted()) + _min(seqHlength - 1, _max(0, seqVlength + lowerDiagonal(band)));
    // Swap the two iterators if we are in a band that spans over the full column.
    if (upperDiagonal(band) > seqVlength + lowerDiagonal(band))
        std::swap(seqHIterEndColumnTop, seqHIterEndColumnMiddle);

    // The bottom band phase ends after the upper diagonal of the band crosses the bottom of the matrix or after the horizontal sequence if it is smaller.
    TConstSeqHIterator seqHIterEndColumnBottom = begin(seqH, Rooted()) + _max(0, _min(seqHlength,
                                                                                      upperDiagonal(band) + seqVlength) - 1);

    // The Initial column can be PartialColumnTop which is given if the upper diagonal is >= 0,
    // otherwise it only can be PartialColumnMiddle or PartialColumnBottom depending where the lower diagonal is.

    // Check for single initialization cells in InitialColumn and FinalColumn.
    if (seqHIterBegin == end(seqH, Rooted()) - 1)
    {
        // Set the iterator to the begin of the track.
        _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), FirstCell());
        _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), FirstCell());
        _preInitScoutHorizontal(scout, coordinate(dpTraceMatrixNavigator, +DPMatrixDimension_::HORIZONTAL));
        // Only one cell
        _computeCell(scout, dpTraceMatrixNavigator, value(dpScoreMatrixNavigator),
                     cacheDiag, previousCellHorizontal(dpScoreMatrixNavigator), cacheVert,
                     sequenceEntryForScore(scoringScheme, seqH, position(seqHIterBegin)),
                     sequenceEntryForScore(scoringScheme, seqV, 0), scoringScheme,
                     MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), FirstCell(), TDPProfile());
        // we might need to additionally track this point.
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, PartialColumnTop> >, FirstCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, True(), False());
        return;
    }
    if (seqHIterEndColumnBottom == begin(seqH, Rooted()))
    {
        // Set the iterator to the begin of the track.
        _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPInitialColumn, PartialColumnBottom>(), FirstCell());
        _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPInitialColumn, PartialColumnBottom>(), FirstCell());
        _preInitScoutHorizontal(scout, coordinate(dpTraceMatrixNavigator, +DPMatrixDimension_::HORIZONTAL));
        // Only one cell
        _computeCell(scout, dpTraceMatrixNavigator, value(dpScoreMatrixNavigator),
                     cacheDiag, previousCellHorizontal(dpScoreMatrixNavigator), cacheVert,
                     sequenceEntryForScore(scoringScheme, seqH, 0),
                     sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin)), scoringScheme,
                     MetaColumnDescriptor<DPInitialColumn, PartialColumnBottom>(), FirstCell(), TDPProfile());
        // We might need to additionally track this point.
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInitialColumn, PartialColumnBottom> >, LastCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, False(), True());
        return;
    }

    if (upperDiagonal(band) < 0)
    {
        _preInitScoutHorizontal(scout, 0);
        ++seqVBegin;
        if (lowerDiagonal(band) > -seqVlength)
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, 0),
                          sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInitialColumn, PartialColumnMiddle>(), dpProfile);
        else
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, 0),
                          sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInitialColumn, PartialColumnBottom>(), dpProfile);
    }
    else if (lowerDiagonal(band) >= 0)
    {
        // Set the iterator to the begin of the track.
        _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), FirstCell());
        _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), FirstCell());
        _preInitScoutHorizontal(scout, coordinate(dpTraceMatrixNavigator, +DPMatrixDimension_::HORIZONTAL));
        //TODO(rrahn): We possibly need to set the cache values here?
        // Should we not just compute the cell?
        _computeCell(scout, dpTraceMatrixNavigator, value(dpScoreMatrixNavigator),
                     cacheDiag, previousCellHorizontal(dpScoreMatrixNavigator), cacheVert,
                     sequenceEntryForScore(scoringScheme, seqH, position(seqHIterBegin)),
                     sequenceEntryForScore(scoringScheme, seqV, 0),
                     scoringScheme,
                     MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), FirstCell(), TDPProfile());
        // we might need to additionally track this point.
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, PartialColumnTop> >, FirstCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, False(), False());
    }
    else  // Upper diagonal >= 0 and lower Diagonal < 0
    {
        _preInitScoutHorizontal(scout, 0);
        if (lowerDiagonal(band) <= -seqVlength)      // The band is bounded by the top and bottom of the matrix.
        {
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, 0),
                          sequenceEntryForScore(scoringScheme, seqV, 0),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInitialColumn, FullColumn>(), dpProfile);
        }
        else       // The band is bounded by the top but not the bottom of the matrix.
        {
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, 0),
                          sequenceEntryForScore(scoringScheme, seqV, 0),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInitialColumn, PartialColumnTop>(), dpProfile);
        }
    }
    if (_computeAlignmentHelperCheckTerminate(scout))
    {
            return;
    }

    // ============================================================================
    // MAIN DP
    // ============================================================================

    TConstSeqHIterator seqHIter = seqHIterBegin;
    // Compute the first part of the band, where the band is bounded by the top but not by the bottom of the matrix.
    for (; seqHIter != seqHIterEndColumnTop; ++seqHIter)
    {
        _incHorizontalPos(scout);
        ++seqVEnd;
        _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                      sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                      sequenceEntryForScore(scoringScheme, seqV, 0),
                      seqVBegin, seqVEnd, scoringScheme,
                      MetaColumnDescriptor<DPInnerColumn, PartialColumnTop>(), dpProfile);
        if (_computeAlignmentHelperCheckTerminate(scout))
        {
                return;
        }
    }

    // TODO(rmaerker): Check if putting the if-statement before the actual algorithm can speedup the code.
    // Check whether the band spans over the full column or not at some point.
    if (upperDiagonal(band) > seqVlength + lowerDiagonal(band))
    {
        // Compute the second part of the band, where the band is bounded by the top and the bottom of the matrix.
        // We might want to track the current cell here, since this is the first cell that crosses the bottom but is
        // not part of the FullColumn tracks.
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, FullColumn> >, LastCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, False(), True());
        for (; seqHIter != seqHIterEndColumnMiddle; ++seqHIter)
        {
            _incHorizontalPos(scout);
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                          sequenceEntryForScore(scoringScheme, seqV, 0),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInnerColumn, FullColumn>(), dpProfile);

            if (_computeAlignmentHelperCheckTerminate(scout))
            {
                    return;
            }
        }
    }
    else  // Compute the second part of the band, where the band is not bounded by the top and bottom of the matrix
    {
        for (; seqHIter != seqHIterEndColumnMiddle; ++seqHIter)
        {
            _incHorizontalPos(scout);
            ++seqVBegin;
            ++seqVEnd;
            _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                          sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                          sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                          seqVBegin, seqVEnd, scoringScheme,
                          MetaColumnDescriptor<DPInnerColumn, PartialColumnMiddle>(), dpProfile);
            if (_computeAlignmentHelperCheckTerminate(scout))
            {
                    return;
            }
        }   // We might want to track the current cell here, since this is the first cell that crosses the bottom.
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom> >, LastCell>::VALUE)
        {
            if (lowerDiagonal(band) + seqVlength < seqHlength)
            {
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, False(), True());
            }
        }

    }
    // Compute the third part of the band, where the band, is bounded by the bottom but not by the top of the matrix.
    for (; seqHIter != seqHIterEndColumnBottom; ++seqHIter)
    {
        _incHorizontalPos(scout);
        ++seqVBegin;
        _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                      sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                      sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                      seqVBegin, seqVEnd, scoringScheme,
                      MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom>(), dpProfile);
        if (_computeAlignmentHelperCheckTerminate(scout))
        {
                return;
        }
    }

    // ============================================================================
    // POSTPROCESSING
    // ============================================================================

    _incHorizontalPos(scout);
    // Check where the last track of the column is located.
    if (seqHIter - begin(seqH, Rooted()) < seqHlength - 1)  // Case 1: The band ends before the final column is reached.
    {
        // Set the iterator to the begin of the track.
        _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom>(), FirstCell());
        _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom>(), FirstCell());

        _preInitCacheDiagonal(cacheDiag, dpScoreMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom>());

        _computeCell(scout, dpTraceMatrixNavigator, value(dpScoreMatrixNavigator),
                     cacheDiag, previousCellHorizontal(dpScoreMatrixNavigator), cacheVert,
                     sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                     sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin)),
                     scoringScheme,
                     MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom>(), FirstCell(), TDPProfile());
        // We might need to additionally track this point.
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, PartialColumnBottom> >, LastCell>::VALUE)
        {
            _setVerticalScoreOfCell(value(dpScoreMatrixNavigator), _verticalScoreOfCell(cacheVert));
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, False(), True());
        }
    }
    else if (seqHIter == end(seqH, Rooted()) - 1) // Case 2: The band ends somewhere in the final column of the matrix.
    {
        // Case2a: The band ends in the last cell of the final column.
        if (upperDiagonal(band) == seqHlength - seqVlength)
        {
            // Set the iterator to the begin of the track.
            _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom>(), FirstCell());
            _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom>(), FirstCell());

            _preInitCacheDiagonal(cacheDiag, dpScoreMatrixNavigator, MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom>());

            _computeCell(scout, dpTraceMatrixNavigator, value(dpScoreMatrixNavigator),
                         cacheDiag, previousCellHorizontal(dpScoreMatrixNavigator), cacheVert,
                         sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                         sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin)),
                         scoringScheme,
                         MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom>(), FirstCell(), TDPProfile());
            // we might need to additionally track this point.
            if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom> >, LastCell>::VALUE)
            {
                _setVerticalScoreOfCell(value(dpScoreMatrixNavigator), _verticalScoreOfCell(cacheVert));
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, True(), True());
            }
        }
        else  // Case2b: At least two cells intersect between the band and the matrix in the final column of the matrix.
        {
            if (upperDiagonal(band) >= seqHlength)  // The band is bounded by the top of the matrix only or by the top and the bottom.
            {
                if (lowerDiagonal(band) + seqVlength > seqHlength) // The band is bounded by the top of the matrix
                {
                    ++seqVEnd;
                    _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                                  sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                                  sequenceEntryForScore(scoringScheme, seqV, 0),
                                  seqVBegin, seqVEnd, scoringScheme,
                                  MetaColumnDescriptor<DPFinalColumn, PartialColumnTop>(), dpProfile);
                }
                else  // The band is bounded by the top and the bottom of the matrix.
                {
                    if (lowerDiagonal(band) + seqVlength + 1 > seqHlength)  // We have to go into the last cell.
                    {
                        ++seqVEnd;
                        _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                                      sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                                      sequenceEntryForScore(scoringScheme, seqV, 0),
                                      seqVBegin, seqVEnd, scoringScheme, cacheDiag, cacheVert,
                                      MetaColumnDescriptor<DPFinalColumn, PartialColumnTop>(), dpProfile);
                        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, FullColumn> >, LastCell>::VALUE)
                        {
                            _setVerticalScoreOfCell(value(dpScoreMatrixNavigator), _verticalScoreOfCell(cacheVert));
                            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, True(), True());
                        }
                    }
                    else
                        _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                                      sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                                      sequenceEntryForScore(scoringScheme, seqV, 0),
                                      seqVBegin, seqVEnd, scoringScheme,
                                      MetaColumnDescriptor<DPFinalColumn, FullColumn>(), dpProfile);
                }

            }
            else  // The band is bounded by bottom of matrix or completely unbounded.
            {
                ++seqVBegin;
                if (lowerDiagonal(band) + seqVlength <= seqHlength)  // The band is bounded by the bottom of the matrix.
                {
                    if (lowerDiagonal(band) + seqVlength == seqHlength)  // We have to go into the last cell.
                    {
                        ++seqVEnd;
                        _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                                      sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                                      sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                                      seqVBegin, seqVEnd, scoringScheme, cacheDiag, cacheVert,
                                      MetaColumnDescriptor<DPFinalColumn, PartialColumnMiddle>(), dpProfile);
                        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom> >, LastCell>::VALUE)
                        {
                            _setVerticalScoreOfCell(value(dpScoreMatrixNavigator), _verticalScoreOfCell(cacheVert));
                            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator, True(), True());
                        }
                    }
                    else
                    {
                        _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                                      sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                                      sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                                      seqVBegin, seqVEnd, scoringScheme,
                                      MetaColumnDescriptor<DPFinalColumn, PartialColumnBottom>(), dpProfile);
                    }
                }
                else  // The band is unbounded by the matrix.
                {
                    ++seqVEnd;
                    _computeTrack(scout, dpScoreMatrixNavigator, dpTraceMatrixNavigator,
                                  sequenceEntryForScore(scoringScheme, seqH, position(seqHIter)),
                                  sequenceEntryForScore(scoringScheme, seqV, position(seqVBegin) - 1),
                                  seqVBegin, seqVEnd, scoringScheme,
                                  MetaColumnDescriptor<DPFinalColumn, PartialColumnMiddle>(), dpProfile);
                }
            }
        }
    }
}

// ----------------------------------------------------------------------------
// Function _computeHammingDistance()
// ----------------------------------------------------------------------------

// Computes the Hamming-Distance if the band-size is 1.
template <typename TDPScout,
          typename TDPScoreMatrixNavigator,
          typename TDPTraceMatrixNavigator,
          typename TSequenceH,
          typename TSequenceV,
          typename TScoringScheme,
          typename TBand,
          typename TAlignmentAlgo, typename TGapCosts, typename TTraceFlag, typename TExecPolicy>
inline void
_computeHammingDistance(TDPScout & scout,
                        TDPScoreMatrixNavigator & dpScoreMatrixNavigator,
                        TDPTraceMatrixNavigator & dpTraceMatrixNavigator,
                        TSequenceH const & seqH,
                        TSequenceV const & seqV,
                        TScoringScheme const & scoringScheme,
                        TBand const & band,
                        DPProfile_<TAlignmentAlgo, TGapCosts, TTraceFlag, TExecPolicy> const &)
{
    typedef typename MakeSigned<typename Size<TSequenceH const>::Type>::Type TSignedSizeSeqH;
    typedef typename MakeSigned<typename Size<TSequenceV const>::Type>::Type TSignedSizeSeqV;
    typedef typename Iterator<TSequenceH const, Rooted>::Type TConstSeqHIterator;
    typedef typename Iterator<TSequenceV const, Rooted>::Type TConstSeqVIterator;
    typedef typename Value<TDPScoreMatrixNavigator>::Type TDPCell;
    typedef DPProfile_<TAlignmentAlgo, TGapCosts, TTraceFlag> TDPProfile;

    // ============================================================================
    // PREPROCESSING
    // ============================================================================

    TSignedSizeSeqH seqHlength = static_cast<TSignedSizeSeqH>(length(seqH));
    TSignedSizeSeqH seqVlength = static_cast<TSignedSizeSeqV>(length(seqV));

    TConstSeqHIterator itH = begin(seqH, Rooted()) + _max(0, _min(seqHlength - 1, upperDiagonal(band)));
    TConstSeqHIterator itHEnd = begin(seqH, Rooted()) + _min(seqHlength - 1, upperDiagonal(band) + seqVlength);

    TConstSeqVIterator itV = begin(seqV, Rooted()) + _max(0, _min(seqVlength - 1, -lowerDiagonal(band)));
    TConstSeqVIterator itVEnd = begin(seqV, Rooted()) + _min(seqVlength - 1, lowerDiagonal(band) + seqHlength);

    _preInitScoutHorizontal(scout, coordinate(dpTraceMatrixNavigator, +DPMatrixDimension_::HORIZONTAL));
    _preInitScoutVertical(scout, coordinate(dpTraceMatrixNavigator, +DPMatrixDimension_::VERTICAL));

    TDPCell dummy;
    assignValue(dpTraceMatrixNavigator,
                _computeScore(value(dpScoreMatrixNavigator), dummy, dummy, dummy,
                              sequenceEntryForScore(scoringScheme, seqH, position(itH)),
                              sequenceEntryForScore(scoringScheme, seqV, position(itV)),
                              scoringScheme, RecursionDirectionZero(), TDPProfile()));

    if (upperDiagonal(band) < 0)
    {
        if (upperDiagonal(band) == -seqVlength)
        {
            if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInitialColumn, FullColumn> >, LastCell>::VALUE)
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
            return;
        }
        else
        {
            if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInitialColumn, FullColumn> >, InnerCell>::VALUE)
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
        }
    }
    else if (lowerDiagonal(band) > 0)
    {
        if (lowerDiagonal(band) == seqHlength)
        {
            if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, FullColumn> >, FirstCell>::VALUE)
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
            return;
        }
        else
        {
            if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, FullColumn> >, FirstCell>::VALUE)
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
        }
    }
    else
    {
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInitialColumn, FullColumn> >, FirstCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
    }

    TDPCell prevDiagonal = value(dpScoreMatrixNavigator);

    // ============================================================================
    // MAIN DP
    // ============================================================================

    while (itH != itHEnd && itV != itVEnd)
    {
        _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, FullColumn>(), FirstCell());
        _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, FullColumn>(), FirstCell());
        _incHorizontalPos(scout);
        _incVerticalPos(scout);
        assignValue(dpTraceMatrixNavigator,
                    _computeScore(value(dpScoreMatrixNavigator), prevDiagonal, dummy, dummy,
                                  sequenceEntryForScore(scoringScheme, seqH, position(itH)),
                                  sequenceEntryForScore(scoringScheme, seqV, position(itV)),
                                  scoringScheme, RecursionDirectionDiagonal(), TDPProfile()));
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, FullColumn> >, InnerCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
        prevDiagonal = value(dpScoreMatrixNavigator);
        ++itH;
        ++itV;
    }

    // ============================================================================
    // POSTPROCESSING
    // ============================================================================

    _goNextCell(dpScoreMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, FullColumn>(), FirstCell());
    _goNextCell(dpTraceMatrixNavigator, MetaColumnDescriptor<DPInnerColumn, FullColumn>(), FirstCell());
    _incHorizontalPos(scout);
    _incVerticalPos(scout);
    assignValue(dpTraceMatrixNavigator,
                _computeScore(value(dpScoreMatrixNavigator), prevDiagonal, dummy, dummy,
                              sequenceEntryForScore(scoringScheme, seqH, position(itH)),
                              sequenceEntryForScore(scoringScheme, seqV, position(itV)),
                              scoringScheme, RecursionDirectionDiagonal(), TDPProfile()));

    if (itH == itHEnd)
    {
        if (itV == itVEnd)   // Is in the last cell of final column
        {
            if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, FullColumn> >, LastCell>::VALUE)
                _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
        }
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPInnerColumn, FullColumn> >, LastCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
    }
    else
    {
        if (TrackingEnabled_<DPMetaColumn_<TDPProfile, MetaColumnDescriptor<DPFinalColumn, FullColumn> >, InnerCell>::VALUE)
            _scoutBestScore(scout, value(dpScoreMatrixNavigator), dpTraceMatrixNavigator);
    }
}

// ----------------------------------------------------------------------------
// Function _printScoreMatrix()
// ----------------------------------------------------------------------------

template <typename TTraceMatrix>
void _printScoreMatrix(TTraceMatrix & scoreMatrix)
{
    typedef typename Size<TTraceMatrix>::Type TSize;
    TSize dimH = length(scoreMatrix, +DPMatrixDimension_::HORIZONTAL);
    TSize dimV = length(scoreMatrix, +DPMatrixDimension_::VERTICAL);

    for (unsigned row = 0; row < dimV; ++row)
    {
        for (unsigned column = 0; column < dimH; ++column)
            if (_scoreOfCell(value(scoreMatrix, row + column * dimV)) <= DPCellDefaultInfinity<DPCell_<int, LinearGaps>>::VALUE)
                std::cout << "-∞\t";
            else
                std::cout << _scoreOfCell(value(scoreMatrix, row + column * dimV)) << "\t";
        std::cout << std::endl;
    }
    std::cout << std::endl;
}

// ----------------------------------------------------------------------------
// Function _printTracebackMatrix()
// ----------------------------------------------------------------------------

template <typename TTraceMatrix>
void _printTracebackMatrix(TTraceMatrix & dpTraceMatrix)
{
    typedef typename Size<TTraceMatrix>::Type TSize;
    TSize dimH = length(dpTraceMatrix, +DPMatrixDimension_::HORIZONTAL);
    TSize dimV = length(dpTraceMatrix, +DPMatrixDimension_::VERTICAL);

    for (unsigned row = 0; row < dimV; ++row)
    {
        for (unsigned column = 0; column < dimH; ++column)
            std::cout << _translateTraceValue(value(dpTraceMatrix, row + column * dimV)) << "\t";
        std::cout << std::endl;
    }
    std::cout << std::endl;
}

template <typename TTraceMatrix, typename TPosition>
void _printTracebackMatrix(TTraceMatrix & dpTraceMatrix, TPosition const simdLane)
{
    typedef typename Size<TTraceMatrix>::Type TSize;
    TSize dimH = length(dpTraceMatrix, +DPMatrixDimension_::HORIZONTAL);
    TSize dimV = length(dpTraceMatrix, +DPMatrixDimension_::VERTICAL);

    for (unsigned row = 0; row < dimV; ++row)
    {
        for (unsigned column = 0; column < dimH; ++column)
            std::cout << _translateTraceValue(value(dpTraceMatrix, row + column * dimV)[simdLane]) << "\t";
        std::cout << std::endl;
    }
    std::cout << std::endl;
}

// ----------------------------------------------------------------------------
// Function _correctTraceValue()
// ----------------------------------------------------------------------------

template <typename TTraceNavigator, typename TScoreValue, typename TDPScoutSpec>
inline SEQAN_FUNC_ENABLE_IF(Not<Is<SimdVectorConcept<TScoreValue> > >, void)
_correctTraceValue(TTraceNavigator &,
                   DPScout_<DPCell_<TScoreValue, LinearGaps>, TDPScoutSpec> const &)
{
    // Nothing to do.
}

template <typename TTraceNavigator, typename TScoreValue, typename TDPScoutSpec>
inline SEQAN_FUNC_ENABLE_IF(Is<SimdVectorConcept<TScoreValue> >, void)
_correctTraceValue(TTraceNavigator &,
                   DPScout_<DPCell_<TScoreValue, LinearGaps>, TDPScoutSpec> const &)
{
    // Nothing to do.
}

template <typename TTraceNavigator, typename TScoreValue, typename TDPScoutSpec>
inline SEQAN_FUNC_ENABLE_IF(Not<Is<SimdVectorConcept<TScoreValue> > >, void)
_correctTraceValue(TTraceNavigator & traceNavigator,
                   DPScout_<DPCell_<TScoreValue, AffineGaps>, TDPScoutSpec>  const & dpScout)
{
    _setToPosition(traceNavigator, maxHostPosition(dpScout));

    if (_verticalScoreOfCell(dpScout._maxScore) == _scoreOfCell(dpScout._maxScore))
    {
        value(traceNavigator) &= ~TraceBitMap_<TScoreValue>::DIAGONAL;
        value(traceNavigator) |= TraceBitMap_<TScoreValue>::MAX_FROM_VERTICAL_MATRIX;
    }
    else if (_horizontalScoreOfCell(dpScout._maxScore) == _scoreOfCell(dpScout._maxScore))
    {
        value(traceNavigator) &= ~TraceBitMap_<TScoreValue>::DIAGONAL;
        value(traceNavigator) |= TraceBitMap_<TScoreValue>::MAX_FROM_HORIZONTAL_MATRIX;
    }
}

template <typename TTraceNavigator, typename TScoreValue, typename TDPScoutSpec>
inline SEQAN_FUNC_ENABLE_IF(Is<SimdVectorConcept<TScoreValue> >, void)
_correctTraceValue(TTraceNavigator & traceNavigator,
                   DPScout_<DPCell_<TScoreValue, AffineGaps>, TDPScoutSpec>  const & dpScout)
{
    using TMaskType = typename SimdMaskVector<TScoreValue>::Type;
    _setToPosition(traceNavigator, toGlobalPosition(traceNavigator,
                                                    maxHostCoordinate(dpScout, +DPMatrixDimension_::HORIZONTAL),
                                                    maxHostCoordinate(dpScout, +DPMatrixDimension_::VERTICAL)));
    TMaskType flag = createVector<TMaskType>(0);
    assignValue(flag, dpScout._simdLane, -1);
    auto cmpV = cmpEq(_verticalScoreOfCell(dpScout._maxScore), _scoreOfCell(dpScout._maxScore)) & flag;
    auto cmpH = cmpEq(_horizontalScoreOfCell(dpScout._maxScore), _scoreOfCell(dpScout._maxScore)) & flag;

    value(traceNavigator) = blend(value(traceNavigator),
                                  value(traceNavigator) & ~TraceBitMap_<TScoreValue>::DIAGONAL,
                                  cmpV | cmpH);
    value(traceNavigator) = blend(value(traceNavigator),
                                  value(traceNavigator) | TraceBitMap_<TScoreValue>::MAX_FROM_VERTICAL_MATRIX,
                                  cmpV);
    value(traceNavigator) = blend(value(traceNavigator),
                                  value(traceNavigator) | TraceBitMap_<TScoreValue>::MAX_FROM_HORIZONTAL_MATRIX,
                                  cmpH);
}

template <typename TTraceNavigator, typename TScoreValue, typename TDPScoutSpec>
inline SEQAN_FUNC_ENABLE_IF(Not<Is<SimdVectorConcept<TScoreValue> > >, void)
_correctTraceValue(TTraceNavigator & traceNavigator,
                   DPScout_<DPCell_<TScoreValue, DynamicGaps>, TDPScoutSpec>  const & dpScout)
{
    _setToPosition(traceNavigator, maxHostPosition(dpScout));
    if (isGapExtension(dpScout._maxScore, DynamicGapExtensionVertical()))
    {
        value(traceNavigator) &= ~TraceBitMap_<TScoreValue>::DIAGONAL;
        value(traceNavigator) |= TraceBitMap_<TScoreValue>::MAX_FROM_VERTICAL_MATRIX;
    }
    else if (isGapExtension(dpScout._maxScore, DynamicGapExtensionHorizontal()))
    {
        value(traceNavigator) &= ~TraceBitMap_<TScoreValue>::DIAGONAL;
        value(traceNavigator) |= TraceBitMap_<TScoreValue>::MAX_FROM_HORIZONTAL_MATRIX;
    }
}

template <typename TTraceNavigator, typename TScoreValue, typename TDPScoutSpec>
inline SEQAN_FUNC_ENABLE_IF(Is<SimdVectorConcept<TScoreValue> >, void)
_correctTraceValue(TTraceNavigator & traceNavigator,
                   DPScout_<DPCell_<TScoreValue, DynamicGaps>, TDPScoutSpec>  const & dpScout)
{
    using TMaskType = typename SimdMaskVector<TScoreValue>::Type;

    _setToPosition(traceNavigator, maxHostPosition(dpScout));
    TMaskType flag = createVector<TMaskType>(0);
    assignValue(flag, dpScout._simdLane, -1);
    auto cmpV = isGapExtension(dpScout._maxScore, DynamicGapExtensionVertical()) & flag;
    auto cmpH = isGapExtension(dpScout._maxScore, DynamicGapExtensionHorizontal()) & flag;
    value(traceNavigator) = blend(value(traceNavigator),
                                  value(traceNavigator) & ~TraceBitMap_<TScoreValue>::DIAGONAL,
                                  cmpV | cmpH);
    value(traceNavigator) = blend(value(traceNavigator),
                                  value(traceNavigator) | TraceBitMap_<TScoreValue>::MAX_FROM_VERTICAL_MATRIX,
                                  cmpV);
    value(traceNavigator) = blend(value(traceNavigator),
                                  value(traceNavigator) | TraceBitMap_<TScoreValue>::MAX_FROM_HORIZONTAL_MATRIX,
                                  cmpH);
}

// ----------------------------------------------------------------------------
// Function _finishAlignment()
// ----------------------------------------------------------------------------

template <typename TTraceTarget,
          typename TTraceMatNavigator,
          typename TScoreValue, typename TGapsModel, typename TDPScoutSpec,
          typename TSeqH,
          typename TSeqV,
          typename TBandSwitch,
          typename TAlignmentAlgorithm, typename TGapScheme, typename TTraceFlag, typename TExecPolicy>
inline SEQAN_FUNC_ENABLE_IF(Not<IsTracebackEnabled_<TTraceFlag> >, TScoreValue)
_finishAlignment(TTraceTarget & /*traceSegments*/,
                 TTraceMatNavigator & /*dpTraceMatrixNavigator*/,
                 DPScout_<DPCell_<TScoreValue, TGapsModel>, TDPScoutSpec> & dpScout,
                 TSeqH const & /*seqH*/,
                 TSeqV const & /*seqV*/,
                 DPBandConfig<TBandSwitch> const & /*band*/,
                 DPProfile_<TAlignmentAlgorithm, TGapScheme, TTraceFlag, TExecPolicy> const & /*dpProfile*/)
{
    return maxScore(dpScout);
}

template <typename TTraceTarget,
          typename TTraceMatNavigator,
          typename TScoreValue, typename TGapsModel, typename TDPScoutSpec,
          typename TSeqH,
          typename TSeqV,
          typename TBandSwitch,
          typename TAlignmentAlgorithm, typename TGapScheme, typename TTraceFlag, typename TExecPolicy>
inline SEQAN_FUNC_ENABLE_IF(And<Is<SimdVectorConcept<TScoreValue> >, IsTracebackEnabled_<TTraceFlag> >, TScoreValue)
_finishAlignment(TTraceTarget & traceSegments,
                 TTraceMatNavigator & dpTraceMatrixNavigator,
                 DPScout_<DPCell_<TScoreValue, TGapsModel>, TDPScoutSpec> & scout,
                 TSeqH const & seqH,
                 TSeqV const & seqV,
                 DPBandConfig<TBandSwitch> const & band,
                 DPProfile_<TAlignmentAlgorithm, TGapScheme, TTraceFlag, TExecPolicy> const & dpProfile)
{
    typedef typename Size<TTraceTarget>::Type TSize;

    for(TSize i = 0; i < length(traceSegments); ++i)
    {
        _setSimdLane(dpTraceMatrixNavigator, i);
        _setSimdLane(scout, i);

        if (IsSingleTrace_<TTraceFlag>::VALUE)
        {
            _correctTraceValue(dpTraceMatrixNavigator, scout);
        }
        _computeTraceback(traceSegments[i], dpTraceMatrixNavigator,
                          toGlobalPosition(dpTraceMatrixNavigator,
                                           maxHostCoordinate(scout, +DPMatrixDimension_::HORIZONTAL),
                                           maxHostCoordinate(scout, +DPMatrixDimension_::VERTICAL)),
                          _hostLengthH(scout, seqH),
                          _hostLengthV(scout, seqV), band, dpProfile);
    }
    return maxScore(scout);
}

template <typename TTraceTarget,
          typename TTraceMatNavigator,
          typename TScoreValue, typename TGapsModel, typename TDPScoutSpec,
          typename TSeqH,
          typename TSeqV,
          typename TBandSwitch,
          typename TAlignmentAlgorithm, typename TGapScheme, typename TTraceFlag, typename TExecPolicy>
inline SEQAN_FUNC_ENABLE_IF(And<Not<Is<SimdVectorConcept<TScoreValue> > >, IsTracebackEnabled_<TTraceFlag> >, TScoreValue)
_finishAlignment(TTraceTarget & traceSegments,
                 TTraceMatNavigator & dpTraceMatrixNavigator,
                 DPScout_<DPCell_<TScoreValue, TGapsModel>, TDPScoutSpec> & dpScout,
                 TSeqH const & seqH,
                 TSeqV const & seqV,
                 DPBandConfig<TBandSwitch> const & band,
                 DPProfile_<TAlignmentAlgorithm, TGapScheme, TTraceFlag, TExecPolicy> const & dpProfile)
{
    if (IsSingleTrace_<TTraceFlag>::VALUE)
        _correctTraceValue(dpTraceMatrixNavigator, dpScout);

    _computeTraceback(traceSegments, dpTraceMatrixNavigator, dpScout, seqH, seqV, band, dpProfile);
    return maxScore(dpScout);
}

// ----------------------------------------------------------------------------
// Function _computeAligmnment()
// ----------------------------------------------------------------------------

template <typename TDPScoreValue, typename TTraceValue, typename TScoreMatHost, typename TTraceMatHost,
          typename TTraceTarget,
          typename TScoutState,
          typename TSequenceH,
          typename TSequenceV,
          typename TScoreScheme,
          typename TBandSwitch,
          typename TAlignmentAlgorithm, typename TGapScheme, typename TTraceFlag, typename TExecPolicy>
inline typename Value<TScoreScheme>::Type
_computeAlignment(DPContext<TDPScoreValue, TTraceValue, TScoreMatHost, TTraceMatHost> & dpContext,
                  TTraceTarget & traceSegments,
                  TScoutState & scoutState,
                  TSequenceH const & seqH,
                  TSequenceV const & seqV,
                  TScoreScheme const & scoreScheme,
                  DPBandConfig<TBandSwitch> const & band,
                  DPProfile_<TAlignmentAlgorithm, TGapScheme, TTraceFlag, TExecPolicy> const & dpProfile)
{

    typedef typename DefaultScoreMatrixSpec_<TAlignmentAlgorithm>::Type TScoreMatrixSpec;

    typedef DPMatrix_<TDPScoreValue, TScoreMatrixSpec, TScoreMatHost>   TDPScoreMatrix;
    typedef DPMatrix_<TTraceValue, FullDPMatrix, TTraceMatHost>         TDPTraceMatrix;

    using TNavigationSpec = std::conditional_t<std::is_same<TBandSwitch, BandOff>::value,
                                               NavigateColumnWise,
                                               NavigateColumnWiseBanded>;

    typedef DPMatrixNavigator_<TDPScoreMatrix, DPScoreMatrix, TNavigationSpec> TDPScoreMatrixNavigator;
    typedef DPMatrixNavigator_<TDPTraceMatrix, DPTraceMatrix<TTraceFlag>, TNavigationSpec> TDPTraceMatrixNavigator;

    typedef typename ScoutSpecForAlignmentAlgorithm_<TAlignmentAlgorithm, TScoutState>::Type TDPScoutSpec;
    typedef DPScout_<TDPScoreValue, TDPScoutSpec> TDPScout;

    typedef typename Value<TScoreScheme>::Type TScoreValue;

    // Check if current dp settings are valid. If not return infinity value for dp score value.
    if (!_isValidDPSettings(seqH, seqV, band, dpProfile))
        return createVector<TScoreValue>(std::numeric_limits<typename Value<TScoreValue>::Type>::min());  // NOTE(rrahn): In case of non-simd version, createVector returns just a scalar.

    TDPScoreMatrix dpScoreMatrix;
    TDPTraceMatrix dpTraceMatrix;

    // TODO(rmaerker): Check whether the matrix allocation can be reduced if upperDiagonal < 0?
    setLength(dpScoreMatrix, +DPMatrixDimension_::HORIZONTAL, length(seqH) + 1 - std::max(0, lowerDiagonal(band)));
    setLength(dpTraceMatrix, +DPMatrixDimension_::HORIZONTAL, length(seqH) + 1 - std::max(0, lowerDiagonal(band)));

    SEQAN_IF_CONSTEXPR (IsSameType<TBandSwitch, BandOff>::VALUE)
    {
        setLength(dpScoreMatrix, +DPMatrixDimension_::VERTICAL, length(seqV) + 1);
        setLength(dpTraceMatrix, +DPMatrixDimension_::VERTICAL, length(seqV) + 1);
    }
    else
    {
        int bandSize = _min(static_cast<int>(length(seqH)), upperDiagonal(band)) - _max(lowerDiagonal(band), -static_cast<int>(length(seqV))) + 1;
        setLength(dpScoreMatrix, +DPMatrixDimension_::VERTICAL, _min(static_cast<int>(length(seqV)) + 1, bandSize));
        setLength(dpTraceMatrix, +DPMatrixDimension_::VERTICAL, _min(static_cast<int>(length(seqV)) + 1, bandSize));
    }

    // We set the host to the score matrix and the dp matrix.
    setHost(dpScoreMatrix, getDpScoreMatrix(dpContext));
    setHost(dpTraceMatrix, getDpTraceMatrix(dpContext));

    resize(dpScoreMatrix);
    // We do not need to allocate the memory for the trace matrix if the traceback is disabled.
    if (IsTracebackEnabled_<TTraceFlag>::VALUE)
        resize(dpTraceMatrix);

    TDPScoreMatrixNavigator dpScoreMatrixNavigator{dpScoreMatrix, band};
    TDPTraceMatrixNavigator dpTraceMatrixNavigator{dpTraceMatrix, band};

    TDPScout dpScout(scoutState);
#if SEQAN_ALIGN_SIMD_PROFILE
    profile.preprTimer += sysTime() - timer;
    timer = sysTime();
#endif
    // Execute the alignment.
    _computeAlignmentImpl(dpScout, dpScoreMatrixNavigator, dpTraceMatrixNavigator, seqH, seqV, scoreScheme, band,
                          dpProfile, TNavigationSpec{});

#if SEQAN_ALIGN_SIMD_PROFILE
    profile.alignTimer += sysTime() - timer;
    timer = sysTime();
#endif
    return _finishAlignment(traceSegments, dpTraceMatrixNavigator, dpScout, seqH, seqV, band, dpProfile);
}

}  // namespace seqan2

#endif  // #ifndef SEQAN_INCLUDE_SEQAN_ALIGN_DP_ALGORITHM_IMPL_H_
