// ==========================================================================
//                 SeqAn - The Library for Sequence Analysis
// ==========================================================================
// Copyright (c) 2006-2016, Knut Reinert, FU Berlin
// All rights reserved.
//
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// 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
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//
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#ifndef SEQAN_HEADER_GRAPH_ALIGN_TCOFFEE_GUIDETREE_H
#define SEQAN_HEADER_GRAPH_ALIGN_TCOFFEE_GUIDETREE_H

namespace seqan
{

//////////////////////////////////////////////////////////////////////////////
// Guide Tree
//////////////////////////////////////////////////////////////////////////////




//////////////////////////////////////////////////////////////////////////////
// Neighbor Joining
//////////////////////////////////////////////////////////////////////////////


// Helper function for rounding to n significant digits.  Ported from
// Java code found here: http://stackoverflow.com/questions/202302
inline double
_roundToSignificantFigures(double num, int n)
{
    if (num == 0)
        return 0;

    const double d = ceil(log10(num < 0 ? -num : num));
    const int power = n - (int) d;

    const double magnitude = pow(10.0, power);
    const long shifted = static_cast<long>(round(num*magnitude));
    return shifted / magnitude;
}

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

/*!
 * @fn njTree
 * @headerfile <seqan/graph_msa.h>
 * @brief computes a guid etree from a distance matrix.
 *
 * @signature void njTree(mat, tree);
 *
 * @param[in]  mat  A @link String @endlink of pairwise distance values, representing a square matrix.
 * @param[out] tree The guide tree.
 */

template<typename TValue, typename TStringSpec, typename TCargo, typename TSpec>
inline void
njTree(String<TValue, TStringSpec> const & matIn,
       Graph<Tree<TCargo, TSpec> >& g)
{
    typedef String<TValue, TStringSpec> TMatrix;
    typedef typename Size<TMatrix>::Type TSize;
    typedef Graph<Tree<TCargo, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;

    TVertexDescriptor nilVertex = getNil<TVertexDescriptor>();
    TSize nseq = (TSize) std::sqrt((double)length(matIn));

    // Assert that the input matrix has no negative values.
// #if SEQAN_ENABLE_DEBUG
//     for (unsigned i = 0; i < length(matIn); ++i)
//         SEQAN_ASSERT_GEQ_MSG(matIn[i], 0, "i = %u", i);
// #endif  // #if SEQAN_ENABLE_DEBUG

    //for(TSize i=0;i<nseq;++i) {
    //    for(TSize j=0;j<nseq;++j) {
    //        std::cout << getValue(matIn, i*nseq+j) << ",";
    //    }
    //    std::cout << std::endl;
    //}

    // Handle base cases for one and two sequences.
    clearVertices(g);
    if (nseq == 1)
    {
        g.data_root = addVertex(g);
        return;
    }
    else if (nseq == 2)
    {
        TVertexDescriptor v1 = addVertex(g);
        TVertexDescriptor v2 = addVertex(g);
        TVertexDescriptor internalVertex = addVertex(g);
        addEdge(g, internalVertex, v1, (TCargo) _roundToSignificantFigures(matIn[1] / 2.0, 5));
        addEdge(g, internalVertex, v2, (TCargo) _roundToSignificantFigures(matIn[1] / 2.0, 5));
        g.data_root = internalVertex;
        return;
    }

    // Create a normalized copy of matIn with fixed point numbers, precision of 10 digits.
    TValue normFactor = 0;
    for (unsigned i = 0; i < length(matIn); ++i)
        normFactor = std::max(normFactor, matIn[i]);
    // In the case that normFactor is 0 (e.g. all sequences equal) then fix it to 1 so the normalization
    // does not break.
    if (!normFactor)
        normFactor = 1;
    String<int64_t> mat;
    resize(mat, length(matIn));
    for (unsigned i = 0; i < length(mat); ++i)
        mat[i] = static_cast<int64_t>(10000000.0 * ((double)(matIn[i]) / (double)(normFactor)));

    // First initialization
    String<int64_t> av;    // Average branch length to a combined node
    resize(av,nseq,0);

    String<TVertexDescriptor> connector;   // Nodes that need to be connected
    resize(connector, nseq);

    for(TSize i=0;i<nseq;++i)
    {
        addVertex(g);  // Add all the nodes that correspond to sequences
        connector[i] = i;
        mat[i*nseq+i] = 0;
    }

    // Main cycle
    int64_t fnseqs = static_cast<int64_t>(nseq);
    for(TSize nc=0; nc<(nseq-3); ++nc) {
        int64_t sumOfBranches = 0;

        // Determine the sum of all branches and
        // copy upper triangle matrix to lower triangle
        for(TSize col=1; col<nseq; ++col)
            for(TSize row=0; row<col; ++row)
                sumOfBranches += mat[col*nseq+row] = mat[row*nseq+col];

        // Compute the sum of branch lengths for all possible pairs
        bool notFound = true;
        int64_t tmin = 0;
        TSize mini = 0;  // Next pair of seq i and j to join
        TSize minj = 0;
        int64_t diToAllOthers = 0;
        int64_t djToAllOthers = 0;
        int64_t total = 0;
        for(TSize col=1; col<nseq; ++col)  {
            if (connector[col] != nilVertex) {
                for(TSize row=0; row<col; ++row) {
                    if (connector[row] != nilVertex) {
                        diToAllOthers = 0;
                        djToAllOthers = 0;

                        for(TSize i=0; i<nseq; ++i) {
                            diToAllOthers += mat[i*nseq+row];
                            djToAllOthers += mat[i*nseq+col];
                        }

                        total = diToAllOthers + djToAllOthers + (fnseqs - 2) * mat[row*nseq+col] + 2 * (sumOfBranches - diToAllOthers - djToAllOthers);
                        total /= (2*(fnseqs - 2));

                        if ((notFound) || (total < tmin)) {
                            notFound = false;
                            tmin = total;
                            mini = row;
                            minj = col;
                        }
                    }
                }
            }
        }

        // Print nodes that are about to be joined
        //std::cout << mini << std::endl;
        //std::cout << minj << std::endl;
        //std::cout << tmin << std::endl;
        //std::cout << std::endl;

        // Compute branch lengths
        int64_t dMinIToOthers = 0;
        int64_t dMinJToOthers = 0;
        for(TSize i=0; i<nseq; ++i) {
            dMinIToOthers += mat[i*nseq + mini];
            dMinJToOthers += mat[i*nseq + minj];
        }
        int64_t dmin = mat[mini*nseq + minj];
        dMinIToOthers = dMinIToOthers / (fnseqs - 2);
        dMinJToOthers = dMinJToOthers / (fnseqs - 2);
        int64_t iBranch = (dmin + dMinIToOthers - dMinJToOthers) / 2;
        int64_t jBranch = dmin - iBranch;
        iBranch -= av[mini];
        jBranch -= av[minj];

        // Set negative branch length to zero
        if( iBranch < 0) iBranch = 0;
        if( jBranch < 0) jBranch = 0;

        // Print branch lengths
        //std::cout << iBranch << std::endl;
        //std::cout << jBranch << std::endl;
        //std::cout << std::endl;

        // Build tree
        TVertexDescriptor internalVertex = addVertex(g);
        addEdge(g, internalVertex, connector[mini], (TCargo) _roundToSignificantFigures((iBranch / 10000000.0) * normFactor, 5));
        addEdge(g, internalVertex, connector[minj], (TCargo) _roundToSignificantFigures((jBranch / 10000000.0) * normFactor, 5));

        // Remember the average branch length for the new combined node
        // Must be subtracted from all branches that include this node
        if(dmin < 0) dmin = 0;
        av[mini] = dmin / 2;


        // Re-initialisation
        // mini becomes the new combined node, minj is killed
        --fnseqs;
        connector[minj] = nilVertex;
        connector[mini] = internalVertex;

        for(TSize j=0; j<nseq; ++j) {
            if( connector[j] != nilVertex ) {
                // Use upper triangle
                if((TSize) mini < j) mat[mini*nseq+j] = (mat[mini*nseq+j] + mat[minj*nseq+j]) / 2;
                if((TSize) mini > j) mat[j*nseq+mini] = (mat[mini*nseq+j] + mat[minj*nseq+j]) / 2;
            }
        }
        for(TSize j=0; j<nseq; ++j)
            mat[j*nseq+minj] = mat[minj*nseq+j] = 0;
    }

    // Only three nodes left

    // Find the remaining nodes
    String<TSize> l;
    resize(l,3);
    TSize count = 0;
    for(TSize i=0; i<nseq; ++i) {
        if(connector[i] != nilVertex) {
            l[count] = i;
            ++count;
        }
    }

    // Remaining nodes
    //std::cout << l[0] << std::endl;
    //std::cout << l[1] << std::endl;
    //std::cout << l[2] << std::endl;
    //std::cout << std::endl;

    String<int64_t> branch;
    resize(branch, 3);
    branch[0] = (mat[l[0]*nseq+l[1]] + mat[l[0]*nseq+l[2]] - mat[l[1]*nseq+l[2]]) / 2;
    branch[1] = (mat[l[1]*nseq+l[2]] + mat[l[0]*nseq+l[1]] - mat[l[0]*nseq+l[2]]) / 2;
    branch[2] = (mat[l[1]*nseq+l[2]] + mat[l[0]*nseq+l[2]] - mat[l[0]*nseq+l[1]]) / 2;

    branch[0] -= av[l[0]];
    branch[1] -= av[l[1]];
    branch[2] -= av[l[2]];

    // Print branch lengths
    //std::cout << branch[0] << std::endl;
    //std::cout << branch[1] << std::endl;
    //std::cout << branch[2] << std::endl;
    //std::cout << std::endl;

    // Reset negative branch lengths to zero
    if( branch[0] < 0) branch[0] = 0;
    if( branch[1] < 0) branch[1] = 0;
    if( branch[2] < 0) branch[2] = 0;

    // Build tree
    TVertexDescriptor internalVertex = addVertex(g);
    addEdge(g, internalVertex, getValue(connector, l[0]), (TCargo) _roundToSignificantFigures((branch[0] / 10000000.0)* normFactor, 5));
    addEdge(g, internalVertex, getValue(connector, l[1]), (TCargo) _roundToSignificantFigures((branch[1] / 10000000.0) * normFactor, 5));
    TVertexDescriptor the_root = addVertex(g);
    addEdge(g, the_root, getValue(connector, l[2]), (TCargo) _roundToSignificantFigures((branch[2] / 20000000.0) * normFactor, 5));
    addEdge(g, the_root, internalVertex, (TCargo) _roundToSignificantFigures((branch[2] / 20000000.0) * normFactor, 5));
    g.data_root = the_root;
}






//////////////////////////////////////////////////////////////////////////////
// Unweighted Pair Group Mean Average (UPGMA)
//////////////////////////////////////////////////////////////////////////////

/*!
 * @defgroup UpgmaConfiguratorTags
 * @brief Tags for configuring the guide tree construction.
 *
 * @tag UpgmaConfiguratorTags#UpgmaMin
 * @headerfile <seqan/graph_msa.h>
 * @brief Uses the min operation in the UPGMA algorithm.
 *
 * @signature typedef Tag<UpgmaMin_> const UpgmaMin;
 *
 * @tag UpgmaConfiguratorTags#UpgmaMax
 * @headerfile <seqan/graph_msa.h>
 * @brief Uses the max operation in the UPGMA algorithm.
 *
 * @signature typedef Tag<UpgmaMax_> const UpgmaMax;
 *
 * @tag UpgmaConfiguratorTags#UpgmaAvg
 * @headerfile <seqan/graph_msa.h>
 * @brief Uses the avg operation in the UPGMA algorithm.
 *
 * @signature typedef Tag<UpgmaAvg_> const UpgmaAvg;
 *
 * @tag UpgmaConfiguratorTags#UpgmaWeightAvg
 * @headerfile <seqan/graph_msa.h>
 * @brief Uses the weighted avg operation in the UPGMA algorithm.
 *
 * @signature typedef Tag<UpgmaAvg_> const UpgmaWeightAvg;
 */

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

struct UpgmaMin_;
typedef Tag<UpgmaMin_> const UpgmaMin;

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

struct UpgmaMax_;
typedef Tag<UpgmaMax_> const UpgmaMax;

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

struct UpgmaAvg_;
typedef Tag<UpgmaAvg_> const UpgmaAvg;

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

struct UpgmaWeightAvg_;
typedef Tag<UpgmaWeightAvg_> const UpgmaWeightAvg;



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

template<typename TMatrix, typename TActive, typename TSize>
inline void
_upgmaTreeMerge(TMatrix& mat,
                TActive& active,
                TSize index_i,
                TSize index_j,
                TSize nseq,
                UpgmaWeightAvg)
{
    typedef typename Value<TMatrix>::Type TValue;
    // Average
    for(TSize i=0;i<nseq;++i) {
        if ((i != index_i) && (i != index_j) && (active[i] != 0)) {
            if (index_i < i) {
                mat[index_i*nseq + i] = ((TValue) active[index_i] / (TValue) (active[index_i] + active[index_j])) * mat[index_i * nseq + i];
                if (index_j < i) mat[index_i*nseq + i] += ((TValue) active[index_j] / (TValue) (active[index_i] + active[index_j])) * mat[index_j * nseq + i];
                else mat[index_i*nseq + i] += ((TValue) active[index_j] / (TValue) (active[index_i] + active[index_j])) * mat[i * nseq + index_j];
            } else {
                mat[i*nseq + index_i] = ((TValue) active[index_i] / (TValue) (active[index_i] + active[index_j])) * mat[i * nseq + index_i];
                if (index_j < i) value(mat, i*nseq + index_i) += ((TValue) active[index_j] / (TValue) (active[index_i] + active[index_j])) * mat[index_j * nseq + i];
                else mat[i*nseq + index_i] += ((TValue) active[index_j] / (TValue) (active[index_i] + active[index_j])) * mat[i * nseq + index_j];
            }
        }
    }
}

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


template<typename TMatrix, typename TActive, typename TSize>
inline void
_upgmaTreeMerge(TMatrix& mat,
                TActive& active,
                TSize index_i,
                TSize index_j,
                TSize nseq,
                UpgmaAvg)
{
    typedef typename Value<TMatrix>::Type TValue;

    // Minimum
    for(TSize i=0;i<nseq;++i) {
        if ((i != index_i) && (i != index_j) && (active[i] != 0)) {
            TValue val1 = (index_i < i) ? mat[index_i * nseq + i] : mat[i * nseq + index_i];
            TValue val2 = (index_j < i) ? mat[index_j * nseq + i] : mat[i * nseq + index_j];
            if (index_i < i) mat[index_i * nseq + i] = (val1 + val2) / 2;
            else mat[i * nseq + index_i] = (val1 + val2) / 2;
        }
    }
}

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


template<typename TMatrix, typename TActive, typename TSize>
inline void
_upgmaTreeMerge(TMatrix& mat,
                TActive& active,
                TSize index_i,
                TSize index_j,
                TSize nseq,
                UpgmaMin)
{
    typedef typename Value<TMatrix>::Type TValue;

    // Minimum
    for(TSize i=0;i<nseq;++i) {
        if ((i != index_i) && (i != index_j) && (active[i] != 0)) {
            TValue newDist = (index_i < i) ? mat[index_i * nseq + i] : mat[i * nseq + index_i];
            TValue newDist2 = (index_j < i) ? mat[index_j * nseq + i] : mat[i * nseq + index_j];
            if (index_i < i) mat[index_i * nseq + i] = _min(newDist, newDist2);
            else mat[i * nseq + index_i] = _min(newDist, newDist2);
        }
    }
}

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

template<typename TMatrix, typename TActive, typename TSize>
inline void
_upgmaTreeMerge(TMatrix& mat,
                TActive& active,
                TSize index_i,
                TSize index_j,
                TSize nseq,
                UpgmaMax)
{
    typedef typename Value<TMatrix>::Type TValue;

    // Maximum
    for(TSize i=0;i<nseq;++i) {
        if ((i != index_i) && (i != index_j) && (active[i] != 0)) {
            TValue newDist = (index_i < i) ? mat[index_i * nseq + i] : mat[i * nseq + index_i];
            TValue newDist2 = (index_j < i) ? mat[index_j * nseq + i] : mat[i * nseq + index_j];
            if (index_i < i) mat[index_i * nseq + i] = _max(newDist, newDist2);
            else mat[i * nseq + index_i] = _max(newDist, newDist2);
        }
    }
}

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

template<typename TCargo, typename TSpec, typename TActive, typename TEdgeDescriptor>
inline void
_upgmaTreeMerge(Graph<Undirected<TCargo, TSpec> >& pairGraph,
                TActive const&,
                TEdgeDescriptor best,
                UpgmaMax)
{
    typedef Graph<Undirected<TCargo, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    //typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;

    TVertexDescriptor s = sourceVertex(pairGraph,best);
    TVertexDescriptor t = targetVertex(pairGraph,best);
    typedef String<TEdgeDescriptor> TEdgeString;
    typedef typename Iterator<TEdgeString>::Type TEdgeIter;
    TEdgeString removeEdges;
    for(TOutEdgeIterator outIt(pairGraph, s);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == t) continue;
        TEdgeDescriptor e = findEdge(pairGraph, targetVertex(outIt), t);
        if (e == 0) appendValue(removeEdges, value(outIt));
        else {
            if (cargo(e) > cargo(value(outIt))) cargo(value(outIt)) = cargo(e);
        }
    }
    TEdgeIter eIt = begin(removeEdges);
    TEdgeIter eItEnd = end(removeEdges);
    for(;eIt != eItEnd; goNext(eIt)) removeEdge(pairGraph, value(eIt));
    removeVertex(pairGraph, t);
}

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

template<typename TCargo, typename TSpec, typename TActive, typename TEdgeDescriptor>
inline void
_upgmaTreeMerge(Graph<Undirected<TCargo, TSpec> >& pairGraph,
                TActive const&,
                TEdgeDescriptor best,
                UpgmaMin)
{
    typedef Graph<Undirected<TCargo, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    //typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;

    TVertexDescriptor s = sourceVertex(pairGraph,best);
    TVertexDescriptor t = targetVertex(pairGraph,best);
    for(TOutEdgeIterator outIt(pairGraph, s);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == t) continue;
        TEdgeDescriptor e = findEdge(pairGraph, targetVertex(outIt), t);
        if (e != 0) {
            if (cargo(e) < cargo(value(outIt))) cargo(value(outIt)) = cargo(e);
        }
    }
    for(TOutEdgeIterator outIt(pairGraph, t);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == s) continue;
        TEdgeDescriptor e = findEdge(pairGraph, targetVertex(outIt), s);
        if (e == 0) addEdge(pairGraph, s, targetVertex(outIt), cargo(value(outIt)));
    }
    removeVertex(pairGraph, t);
}


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

template<typename TCargo, typename TSpec, typename TActive, typename TEdgeDescriptor>
inline void
_upgmaTreeMerge(Graph<Undirected<TCargo, TSpec> >& pairGraph,
                TActive const& active,
                TEdgeDescriptor best,
                UpgmaWeightAvg)
{
    typedef Graph<Undirected<TCargo, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    //typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;

    TCargo infCargo = _getInfinity<TCargo>();
    TVertexDescriptor s = sourceVertex(pairGraph,best);
    TVertexDescriptor t = targetVertex(pairGraph,best);

    for(TOutEdgeIterator outIt(pairGraph, s);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == t) continue;
        TEdgeDescriptor e1 = value(outIt);
        TEdgeDescriptor e2 = findEdge(pairGraph, targetVertex(outIt), t);
        if (e2 != 0) cargo(e1) = ((TCargo) value(active,s) / (TCargo) (value(active,s) + value(active,t))) * cargo(e1) + ((TCargo) value(active,t) / (TCargo) (value(active,s) + value(active,t))) * cargo(e2);
        else cargo(e1) = ((TCargo) value(active,s) / (TCargo) (value(active,s) + value(active,t))) * cargo(e1) + ((TCargo) value(active,t) / (TCargo) (value(active,s) + value(active,t))) * infCargo;
    }
    for(TOutEdgeIterator outIt(pairGraph, t);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == s) continue;
        TEdgeDescriptor e = findEdge(pairGraph, targetVertex(outIt), s);
        TCargo c = ((TCargo) value(active,s) / (TCargo) (value(active,s) + value(active,t))) * infCargo + ((TCargo) value(active,t) / (TCargo) (value(active,s) + value(active,t))) * cargo(value(outIt));
        if (e == 0)  addEdge(pairGraph, s, targetVertex(outIt), c);
    }
    removeVertex(pairGraph, t);
}


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

template<typename TCargo, typename TSpec, typename TActive, typename TEdgeDescriptor>
inline void
_upgmaTreeMerge(Graph<Undirected<TCargo, TSpec> >& pairGraph,
                TActive const&,
                TEdgeDescriptor best,
                UpgmaAvg)
{
    typedef Graph<Undirected<TCargo, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    //typedef typename Iterator<TGraph, VertexIterator>::Type TVertexIterator;
    typedef typename Iterator<TGraph, OutEdgeIterator>::Type TOutEdgeIterator;

    TCargo infCargo = _getInfinity<TCargo>();
    TVertexDescriptor s = sourceVertex(pairGraph,best);
    TVertexDescriptor t = targetVertex(pairGraph,best);

    for(TOutEdgeIterator outIt(pairGraph, s);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == t) continue;
        TEdgeDescriptor e1 = value(outIt);
        TEdgeDescriptor e2 = findEdge(pairGraph, targetVertex(outIt), t);
        cargo(e1) = (e2 != 0) ? (cargo(e1) + cargo(e2)) / 2 : (cargo(e1) + infCargo) / 2;
    }
    for(TOutEdgeIterator outIt(pairGraph, t);!atEnd(outIt);goNext(outIt)) {
        if (targetVertex(outIt) == s) continue;
        TEdgeDescriptor e = findEdge(pairGraph, targetVertex(outIt), s);
        if (e == 0) {
            TCargo c = (infCargo + cargo(value(outIt))) / 2;
            addEdge(pairGraph, s, targetVertex(outIt), c);
        }
    }
    removeVertex(pairGraph, t);
}

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

template<typename TStringValue, typename TStringSpec, typename TCargo, typename TSpec, typename TTag>
inline void
upgmaTree(String<TStringValue, TStringSpec>& mat,
          Graph<Tree<TCargo, TSpec> >& g,
          TTag)
{
    typedef Graph<Tree<TCargo, TSpec> > TGraph;
    typedef typename VertexDescriptor<TGraph>::Type TVertexDescriptor;
    typedef typename Size<TGraph>::Type TSize;
    typedef String<TStringValue, TStringSpec> TMatrix;
    typedef typename Value<TMatrix>::Type TValue;
    //typedef typename Iterator<TMatrix>::Type TMatrixIter;

    // First initialization
    TSize nseq = (TSize) std::sqrt((double)length(mat));
    clearVertices(g);

    // Is it possible to make a guide tree?
    if (nseq == 1) {
        g.data_root = addVertex(g);
        return;
    } else if (nseq == 2) {
        TVertexDescriptor v1 = addVertex(g);
        TVertexDescriptor v2 = addVertex(g);
        TVertexDescriptor internalVertex = addVertex(g);
        addEdge(g, internalVertex, v1, (TCargo) 1);
        addEdge(g, internalVertex, v2, (TCargo) 1);
        g.data_root = internalVertex;
        return;
    }

    // Which entries in the matrix are still active and how many members belong to this group
    String<TSize> active;
    resize(active, nseq, 1);
    // Vertex descriptor that represents that entry
    String<TVertexDescriptor> nodes;
    reserve(nodes, nseq);


    // Find the minimal value
    bool notFound = true;
    TValue minVal = 0;
    TSize index_i = 0;
    TSize index_j = 1;
    for(TSize row=0;row<nseq;++row) {
        for(TSize col=row+1;col<nseq;++col) {
            if ((notFound) || (minVal > mat[row*nseq + col])) {
                notFound = false;
                minVal = mat[row*nseq + col];
                index_i = row;
                index_j = col;
            }
        }
        appendValue(nodes, addVertex(g));    // For each sequence one vertex
    }

    // Property map for sum of weights for each node
    String<TCargo> weights;
    resize(weights, nseq, (TCargo) 0);
    reserve(weights, 2*nseq - 1);

    // Merge groups
    TSize m = nseq;
    while (m>1) {
        // Merge nodes
        TVertexDescriptor internalNode = addVertex(g);

        //// Debug code
        //for(TSize i=0;i<nseq;++i) {
        //    if (value(active,i)==0) continue;
        //    for(TSize j=i+1;j<nseq;++j) {
        //        if (value(active,j)==0) continue;
        //        std::cout << value(mat, i*nseq+j) << ",";
        //    }
        //    std::cout << std::endl;
        //}
        //std::cout << minVal << ',' << index_i << ',' << index_j << ',' << std::endl;
        //std::cout << nodes[index_i] << ',' << nodes[index_j] << std::endl;
        //std::cout << std::endl;

        TCargo w = (TCargo) (minVal / 2);
        addEdge(g, internalNode, nodes[index_i], w - property(weights, nodes[index_i]));
        addEdge(g, internalNode, nodes[index_j], w - property(weights, nodes[index_j]));
        appendValue(weights, w);

        // Get the new distance values
        _upgmaTreeMerge(mat, active, index_i, index_j, nseq, TTag());

        // Inactivate one group, adjust the member count for the other one
        active[index_i] += active[index_j];
        active[index_j] = 0;
        nodes[index_i] = internalNode;

        // Find new minimum
        notFound = true;
        for(TSize i=0;i<nseq;++i) {
            if (active[i] == 0) continue;
            for(TSize j=i+1;j<nseq;++j) {
                if (active[j] == 0) continue;
                if ((notFound) || (minVal > mat[i*nseq + j])) {
                    notFound = false;
                    minVal = mat[i*nseq + j];
                    index_i = i;
                    index_j = j;
                }
            }
        }
        --m;
    }
    g.data_root = numVertices(g) - 1;
}

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

template<typename TValue, typename TSpec1, typename TCargo, typename TSpec2, typename TTag>
inline void
upgmaTree(Graph<Undirected<TValue, TSpec1> >& pairGraph,
          Graph<Tree<TCargo, TSpec2> >& g,
          TTag)
{
    typedef Graph<Undirected<TValue, TSpec1> > TPairGraph;
    typedef Graph<Tree<TCargo, TSpec2> > TGuideTree;
    typedef typename VertexDescriptor<TGuideTree>::Type TVertexDescriptor;
    typedef typename VertexDescriptor<TPairGraph>::Type TVD;
    typedef typename EdgeDescriptor<TPairGraph>::Type TED;
    typedef typename Iterator<TPairGraph, EdgeIterator>::Type TEdgeI;
    typedef typename Iterator<TPairGraph, OutEdgeIterator>::Type TEdgeOutI;
    typedef typename Iterator<TPairGraph, VertexIterator>::Type TVertexI;
    typedef typename Size<TPairGraph>::Type TSize;

    // First initialization
    TCargo const maxVal = maxValue<TCargo>();
    TSize nseq = numVertices(pairGraph);
    TCargo infCargo = _getInfinity<TCargo>();
    clearVertices(g);

    // Is it possible to make a guide tree?
    if (nseq == 1) {
        g.data_root = addVertex(g);
        return;
    } else if (nseq == 2) {
        TVertexDescriptor v1 = addVertex(g);
        TVertexDescriptor v2 = addVertex(g);
        TVertexDescriptor internalVertex = addVertex(g);
        addEdge(g, internalVertex, v1, (TCargo) 1);
        addEdge(g, internalVertex, v2, (TCargo) 1);
        g.data_root = internalVertex;
        return;
    }

    // Which entries in the matrix are still active and how many members belong to this group
    String<TSize> active;
    resize(active, nseq, 1);
    // Vertex descriptor that represents that entry
    typedef String<TVertexDescriptor> TNodeString;
    typedef typename Iterator<TNodeString, Standard>::Type TNodeIter;
    TNodeString nodes;
    resize(nodes, nseq);
    TNodeIter nodeIt = begin(nodes, Standard() );
    TNodeIter nodeItEnd = end(nodes, Standard() );
    for(;nodeIt<nodeItEnd;goNext(nodeIt))
        *nodeIt = addVertex(g);    // For each sequence one vertex

    // Find the minimal value for all vertices (with respect to all greater vertices)
    typedef Pair<TValue, TVD> TWeightEdgePair;
    typedef String<TWeightEdgePair> TMinValues;
    TMinValues minValues;
    resize(minValues, nseq, TWeightEdgePair(maxVal, 0));
    TEdgeI itE(pairGraph);
    for(;!atEnd(itE);goNext(itE)) {
        TVD s = sourceVertex(itE);
        TVD t = targetVertex(itE);
        if (cargo(*itE) < (minValues[s].i1))
            minValues[s] = TWeightEdgePair(cargo(*itE), t);
    }
    // Find the overall minimum
    typedef typename Iterator<TMinValues, Standard>::Type TMinIter;
    TMinIter itMin = begin(minValues, Standard() );
    TMinIter itMinEnd = end(minValues, Standard() );
    TValue minVal = maxVal;
    TVD sourceBest = 0;
    TVD targetBest = 0;
    for(TVD index=0;itMin != itMinEnd; goNext(itMin), ++index) {
        if ((*itMin).i1 < minVal) {
            minVal = (*itMin).i1;
            sourceBest = index;
            targetBest = (*itMin).i2;
        }
    }
    TED best = 0;
    if (sourceBest == targetBest) { // If none is found we have to insert a new edge
        TVertexI itV(pairGraph);
        sourceBest = value(itV); goNext(itV);
        targetBest = value(itV);
        best = addEdge(pairGraph, sourceBest, targetBest, infCargo);
    } else best = findEdge(pairGraph, sourceBest, targetBest);

    // Property map for sum of weights for each node
    String<TCargo> weights;
    resize(weights, nseq, (TCargo) 0);
    reserve(weights, 2*nseq - 1);

    // Merge groups
    TSize m = nseq;
    while (m>1) {
        // Merge nodes
        TVertexDescriptor internalNode = addVertex(g);

        // Set the weights
        TCargo w = (TCargo) (minVal / 2);
        addEdge(g, internalNode, nodes[sourceBest], w - property(weights, nodes[sourceBest]));
        addEdge(g, internalNode, nodes[targetBest], w - property(weights, nodes[targetBest]));
        appendValue(weights, w);

        // Get the new distance values
        _upgmaTreeMerge(pairGraph, active, best, TTag());

        // Inactivate one group, adjust the member count for the other one
        active[sourceBest] += active[targetBest];
        active[targetBest] = 0;
        nodes[sourceBest] = internalNode;

        // Update the minimum values
        minValues[sourceBest] = TWeightEdgePair(maxVal, 0);
        for(TEdgeOutI itOutE(pairGraph, sourceBest);!atEnd(itOutE);goNext(itOutE)) {
            TVD localTVD = targetVertex(itOutE);
            if (sourceBest < localTVD) {
                if (cargo(value(itOutE)) < (minValues[sourceBest].i1)) minValues[sourceBest] = TWeightEdgePair(cargo(value(itOutE)), localTVD);
            }
        }
        // Find the new minimum value
        itMin = begin(minValues, Standard() );
        itMinEnd = end(minValues, Standard() );
        minVal = maxVal;
        TVD oldSourceBest = sourceBest;
        sourceBest = 0;
        targetBest = 0;
        for(TVD index= 0;itMin != itMinEnd; goNext(itMin), ++index) {
            if (active[index] == 0) continue;
            if (((*itMin).i2 == oldSourceBest) || (active[(*itMin).i2] == 0)) {
                // Update the values
                (*itMin).i1 = maxVal;
                TEdgeOutI itOutLocal(pairGraph, index);
                for(;!atEnd(itOutLocal);goNext(itOutLocal)) {
                    TVD targ = targetVertex(itOutLocal);
                    if (targ < index) continue;
                    if (cargo(value(itOutLocal)) < (*itMin).i1) *itMin = TWeightEdgePair(cargo(value(itOutLocal)), targ);
                }
            }
            if ((*itMin).i1 < minVal) {
                minVal = (*itMin).i1;
                sourceBest = index;
                targetBest = (*itMin).i2;
            }
        }
        // If none is found we have to insert a new edge
        if ((sourceBest == targetBest) && (m>2)) {
            TVertexI itV(pairGraph);
            sourceBest = value(itV); goNext(itV);
            targetBest = value(itV);
            best = addEdge(pairGraph, sourceBest, targetBest, infCargo);
        } else best = findEdge(pairGraph, sourceBest, targetBest);
        --m;
    }
    g.data_root = numVertices(g) - 1;
}

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

/*!
 * @fn upgmaTree
 * @headerfile <seqan/graph_msa.h>
 * @brief Computes a guide tree from a distance matrix.
 *
 * @signature void upgmaTree(mat, tree[, tag]);
 *
 * @param[in]  mat  A matrix with pairwise distance values.  Can be a @link String @endlink representing a (dense)
 *                  square matrix or a @link UndirectedGraph @endlink where each edge weight corresponds to the
 *                  distance between sequence i and j (if the edge is present).
 * @param[out] tree An undirected guide tre.
 * @param[in]  tag  Tag indicating how to calcualte the cluster distances.  See: @link UpgmaConfiguratorTags @endlink.
 *                  Default: <tt>UpgmaWeightAvg</tt>.
 */

template<typename TDistance, typename TCargo, typename TSpec>
inline void
upgmaTree(TDistance& dist,
          Graph<Tree<TCargo, TSpec> >& g)
{
    upgmaTree(dist, g, UpgmaWeightAvg());
}


}// namespace seqan

#endif //#ifndef SEQAN_HEADER_...
