# dlib C++ Library - bottom_up_cluster.h

    // Copyright (C) 2015  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_BOTTOM_uP_CLUSTER_Hh_
    #define DLIB_BOTTOM_uP_CLUSTER_Hh_

    #include <queue>
    #include <map>

    #include "bottom_up_cluster_abstract.h"
    #include "../algs.h"
    #include "../matrix.h"
    #include "../disjoint_subsets.h"
    #include "../graph_utils.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        namespace buc_impl
        {
            inline void merge_sets (
                matrix<double>& dists,
                unsigned long dest,
                unsigned long src
            )
            {
                for (long r = 0; r < dists.nr(); ++r)
                    dists(dest,r) = dists(r,dest) = std::max(dists(r,dest), dists(r,src));
            }

            struct compare_dist
            {
                bool operator() (
                    const sample_pair& a,
                    const sample_pair& b
                ) const
                {
                    return a.distance() > b.distance();
                }
            };
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename EXP
            >
        unsigned long bottom_up_cluster (
            const matrix_exp<EXP>& dists_,
            std::vector<unsigned long>& labels,
            unsigned long min_num_clusters,
            double max_dist = std::numeric_limits<double>::infinity()
        )
        {
            matrix<double> dists = matrix_cast<double>(dists_);
            // make sure requires clause is not broken
            DLIB_CASSERT(dists.nr() == dists.nc() && min_num_clusters > 0,
                "\t unsigned long bottom_up_cluster()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t dists.nr(): " << dists.nr()
                << "\n\t dists.nc(): " << dists.nc()
                << "\n\t min_num_clusters: " << min_num_clusters
                );

            using namespace buc_impl;

            labels.resize(dists.nr());
            disjoint_subsets sets;
            sets.set_size(dists.nr());
            if (labels.size() == 0)
                return 0;

            // push all the edges in the graph into a priority queue so the best edges to merge
            // come first.
            std::priority_queue<sample_pair, std::vector<sample_pair>, compare_dist> que;
            for (long r = 0; r < dists.nr(); ++r)
                for (long c = r+1; c < dists.nc(); ++c)
                    que.push(sample_pair(r,c,dists(r,c)));

            // Now start merging nodes.
            for (unsigned long iter = min_num_clusters; iter < sets.size(); ++iter)
            {
                // find the next best thing to merge.
                double best_dist = que.top().distance();
                unsigned long a = sets.find_set(que.top().index1());
                unsigned long b = sets.find_set(que.top().index2());
                que.pop();
                // we have been merging and modifying the distances, so make sure this distance
                // is still valid and these guys haven't been merged already.
                while(a == b || best_dist < dists(a,b))
                {
                    // Haven't merged it yet, so put it back in with updated distance for
                    // reconsideration later.
                    if (a != b)
                        que.push(sample_pair(a, b, dists(a, b)));

                    best_dist = que.top().distance();
                    a = sets.find_set(que.top().index1());
                    b = sets.find_set(que.top().index2());
                    que.pop();
                }

                // now merge these sets if the best distance is small enough
                if (best_dist > max_dist)
                    break;
                unsigned long news = sets.merge_sets(a,b);
                unsigned long olds = (news==a)?b:a;
                merge_sets(dists, news, olds);
            }

            // figure out which cluster each element is in.  Also make sure the labels are
            // contiguous.
            std::map<unsigned long, unsigned long> relabel;
            for (unsigned long r = 0; r < labels.size(); ++r)
            {
                unsigned long l = sets.find_set(r);
                // relabel to make contiguous
                if (relabel.count(l) == 0)
                {
                    unsigned long next = relabel.size();
                    relabel[l] = next;
                }
                labels[r] = relabel[l];
            }

            return relabel.size();
        }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        struct snl_range
        {
            snl_range() = default;
            snl_range(double val) : lower(val), upper(val) {}
            snl_range(double l, double u) : lower(l), upper(u) { DLIB_ASSERT(lower <= upper)}

            double lower = 0;
            double upper = 0;

            double width() const { return upper-lower; }
            bool operator<(const snl_range& item) const { return lower < item.lower; }
        };

        inline snl_range merge(const snl_range& a, const snl_range& b)
        {
            return snl_range(std::min(a.lower, b.lower), std::max(a.upper, b.upper));
        }

        inline double distance (const snl_range& a, const snl_range& b)
        {
            return std::max(a.lower,b.lower) - std::min(a.upper,b.upper);
        }

        inline std::ostream& operator<< (std::ostream& out, const snl_range& item )
        {
            out << "["<<item.lower<<","<<item.upper<<"]";
            return out;
        }

    // ----------------------------------------------------------------------------------------

        inline std::vector<snl_range> segment_number_line (
            const std::vector<double>& x,
            const double max_range_width
        )
        {
            DLIB_CASSERT(max_range_width >= 0);

            // create initial ranges, one for each value in x.  So initially, all the ranges have
            // width of 0.
            std::vector<snl_range> ranges;
            for (auto v : x)
                ranges.push_back(v);
            std::sort(ranges.begin(), ranges.end());

            std::vector<snl_range> greedy_final_ranges;
            if (ranges.size() == 0)
                return greedy_final_ranges;
            // We will try two different clustering strategies.  One that does a simple greedy left
            // to right sweep and another that does a bottom up agglomerative clustering.  This
            // first loop runs the greedy left to right sweep.  Then at the end of this routine we
            // will return the results that produced the tightest clustering.
            greedy_final_ranges.push_back(ranges[0]);
            for (size_t i = 1; i < ranges.size(); ++i)
            {
                auto m = merge(greedy_final_ranges.back(), ranges[i]);
                if (m.width() <= max_range_width)
                    greedy_final_ranges.back() = m;
                else
                    greedy_final_ranges.push_back(ranges[i]);
            }

            // Here we do the bottom up clustering.  So compute the edges connecting our ranges.
            // We will simply say there are edges between ranges if and only if they are
            // immediately adjacent on the number line.
            std::vector<sample_pair> edges;
            for (size_t i = 1; i < ranges.size(); ++i)
                edges.push_back(sample_pair(i-1,i, distance(ranges[i-1],ranges[i])));
            std::sort(edges.begin(), edges.end(), order_by_distance<sample_pair>);

            disjoint_subsets sets;
            sets.set_size(ranges.size());

            // Now start merging nodes.
            for (auto edge : edges)
            {
                // find the next best thing to merge.
                unsigned long a = sets.find_set(edge.index1());
                unsigned long b = sets.find_set(edge.index2());

                // merge it if it doesn't result in an interval that's too big.
                auto m = merge(ranges[a], ranges[b]);
                if (m.width() <= max_range_width)
                {
                    unsigned long news = sets.merge_sets(a,b);
                    ranges[news] = m;
                }
            }

            // Now create a list of the final ranges.  We will do this by keeping track of which
            // range we already added to final_ranges.
            std::vector<snl_range> final_ranges;
            std::vector<bool> already_output(ranges.size(), false);
            for (unsigned long i = 0; i < sets.size(); ++i)
            {
                auto s = sets.find_set(i);
                if (!already_output[s])
                {
                    final_ranges.push_back(ranges[s]);
                    already_output[s] = true;
                }
            }

            // only use the greedy clusters if they found a clustering with fewer clusters.
            // Otherwise, the bottom up clustering probably produced a more sensible clustering.
            if (final_ranges.size() <= greedy_final_ranges.size())
                return final_ranges;
            else
                return greedy_final_ranges;
        }

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_BOTTOM_uP_CLUSTER_Hh_