    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_EDGE_LIST_GrAPHS_H__
    #define DLIB_EDGE_LIST_GrAPHS_H__

    #include "edge_list_graphs_abstract.h"
    #include <limits>
    #include <vector>
    #include "../string.h"
    #include "../rand.h"
    #include <algorithm>
    #include "sample_pair.h"
    #include "ordered_sample_pair.h"

    namespace dlib
    {

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

        template <
            typename vector_type
            >
        void remove_duplicate_edges (
            vector_type& pairs
        )
        {
            typedef typename vector_type::value_type T;
            if (pairs.size() > 0)
            {
                // sort pairs so that we can avoid duplicates in the loop below
                std::sort(pairs.begin(), pairs.end(), &order_by_index<T>);

                // now put edges into temp while avoiding duplicates
                vector_type temp;
                temp.reserve(pairs.size());
                temp.push_back(pairs[0]);
                for (unsigned long i = 1; i < pairs.size(); ++i)
                {
                    if (pairs[i] != pairs[i-1])
                    {
                        temp.push_back(pairs[i]);
                    }
                }

                temp.swap(pairs);
            }
        }

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

        namespace impl
        {
            template <typename iterator>
            iterator iterator_of_worst (
                iterator begin,
                const iterator& end
            )
            /*!
                ensures
                    - returns an iterator that points to the element in the given range
                      that has the biggest distance
            !*/
            {
                double dist = begin->distance();
                iterator worst = begin;
                for (; begin != end; ++begin)
                {
                    if (begin->distance() > dist)
                    {
                        dist = begin->distance();
                        worst = begin;
                    }
                }

                return worst;
            }

        }

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

        template <
            typename vector_type,
            typename distance_function_type,
            typename alloc,
            typename T
            >
        void find_percent_shortest_edges_randomly (
            const vector_type& samples,
            const distance_function_type& dist_funct,
            const double percent,
            const unsigned long num,
            const T& random_seed,
            std::vector<sample_pair, alloc>& out
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( 0 < percent && percent <= 1 &&
                        num > 0,
                "\t void find_percent_shortest_edges_randomly()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t samples.size(): " << samples.size()
                << "\n\t percent:        " << percent
                << "\n\t num:            " << num
                );

            out.clear();

            if (samples.size() <= 1)
            {
                return;
            }

            std::vector<sample_pair, alloc> edges;
            edges.reserve(num);

            dlib::rand rnd;
            rnd.set_seed(cast_to_string(random_seed));

            // randomly sample a bunch of edges
            for (unsigned long i = 0; i < num; ++i)
            {
                const unsigned long idx1 = rnd.get_random_32bit_number()%samples.size();
                const unsigned long idx2 = rnd.get_random_32bit_number()%samples.size();
                if (idx1 != idx2)
                {
                    const double dist = dist_funct(samples[idx1], samples[idx2]);
                    if (dist < std::numeric_limits<double>::infinity())
                    {
                        edges.push_back(sample_pair(idx1, idx2, dist));
                    }
                }
            }

            // now put edges into out while avoiding duplicates
            if (edges.size() > 0)
            {
                remove_duplicate_edges(edges);

                // now sort all the edges by distance and take the percent with the smallest distance
                std::sort(edges.begin(), edges.end(), &order_by_distance<sample_pair>);

                const unsigned long out_size = std::min<unsigned long>((unsigned long)(num*percent), edges.size());
                out.assign(edges.begin(), edges.begin() + out_size);
            }
        }

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

        template <
            typename vector_type,
            typename distance_function_type,
            typename alloc,
            typename T
            >
        void find_approximate_k_nearest_neighbors (
            const vector_type& samples,
            const distance_function_type& dist_funct,
            const unsigned long k,
            unsigned long num,
            const T& random_seed,
            std::vector<sample_pair, alloc>& out
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( num > 0 && k > 0,
                "\t void find_approximate_k_nearest_neighbors()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t samples.size(): " << samples.size()
                << "\n\t k:              " << k
                << "\n\t num:            " << num
                );

            out.clear();

            if (samples.size() <= 1)
            {
                return;
            }

            // we add each edge twice in the following loop.  So multiply num by 2 to account for that.
            num *= 2;

            std::vector<ordered_sample_pair> edges;
            edges.reserve(num);
            std::vector<sample_pair, alloc> temp;
            temp.reserve(num);

            dlib::rand rnd;
            rnd.set_seed(cast_to_string(random_seed));

            // randomly sample a bunch of edges
            for (unsigned long i = 0; i < num; ++i)
            {
                const unsigned long idx1 = rnd.get_random_32bit_number()%samples.size();
                const unsigned long idx2 = rnd.get_random_32bit_number()%samples.size();
                if (idx1 != idx2)
                {
                    const double dist = dist_funct(samples[idx1], samples[idx2]);
                    if (dist < std::numeric_limits<double>::infinity())
                    {
                        edges.push_back(ordered_sample_pair(idx1, idx2, dist));
                        edges.push_back(ordered_sample_pair(idx2, idx1, dist));
                    }
                }
            }

            std::sort(edges.begin(), edges.end(), &order_by_index<ordered_sample_pair>);

            std::vector<ordered_sample_pair>::iterator beg, itr;
            // now copy edges into temp when they aren't duplicates and also only move in the k shortest for
            // each index.
            itr = edges.begin();
            while (itr != edges.end())
            {
                // first find the bounding range for all the edges connected to node itr->index1()
                beg = itr;
                while (itr != edges.end() && itr->index1() == beg->index1())
                    ++itr;

                // If the node has more than k edges then sort them by distance so that
                // we will end up with the k best.
                if (static_cast<unsigned long>(itr - beg) > k)
                {
                    std::sort(beg, itr, &order_by_distance_and_index<ordered_sample_pair>);
                }

                // take the k best unique edges from the range [beg,itr)
                temp.push_back(sample_pair(beg->index1(), beg->index2(), beg->distance()));
                unsigned long prev_index2 = beg->index2();
                ++beg;
                unsigned long count = 1;
                for (; beg != itr && count < k; ++beg)
                {
                    if (beg->index2() != prev_index2)
                    {
                        temp.push_back(sample_pair(beg->index1(), beg->index2(), beg->distance()));
                        ++count;
                    }
                    prev_index2 = beg->index2();
                }
            }

            remove_duplicate_edges(temp);
            temp.swap(out);
        }

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

        template <
            typename vector_type,
            typename distance_function_type,
            typename alloc
            >
        void find_k_nearest_neighbors (
            const vector_type& samples,
            const distance_function_type& dist_funct,
            const unsigned long k,
            std::vector<sample_pair, alloc>& out
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(k > 0,
                "\t void find_k_nearest_neighbors()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t samples.size(): " << samples.size()
                << "\n\t k:              " << k
                );

            out.clear();

            if (samples.size() <= 1)
            {
                return;
            }

            using namespace impl;
            std::vector<sample_pair> edges;

            // Initialize all the edges to an edge with an invalid index
            edges.resize(samples.size()*k,
                         sample_pair(samples.size(),samples.size(),std::numeric_limits<double>::infinity()));

            // Hold the length for the longest edge for each node.  Initially they are all infinity.
            std::vector<double> worst_dists(samples.size(), std::numeric_limits<double>::infinity());

            std::vector<sample_pair>::iterator begin_i, end_i, begin_j, end_j, itr;
            begin_i = edges.begin();
            end_i = begin_i + k;

            // Loop over all combinations of samples.   We will maintain the iterator ranges so that
            // within the inner for loop we have:
            //   [begin_i, end_i) == the range in edges that contains neighbors of samples[i]
            //   [begin_j, end_j) == the range in edges that contains neighbors of samples[j]
            for (unsigned long i = 0; i+1 < samples.size(); ++i)
            {
                begin_j = begin_i;
                end_j = end_i;

                for (unsigned long j = i+1; j < samples.size(); ++j)
                {
                    begin_j += k;
                    end_j += k;

                    const double dist = dist_funct(samples[i], samples[j]);

                    if (dist < worst_dists[i])
                    {
                        *iterator_of_worst(begin_i, end_i) = sample_pair(i, j, dist);
                        worst_dists[i] = iterator_of_worst(begin_i, end_i)->distance();
                    }

                    if (dist < worst_dists[j])
                    {
                        *iterator_of_worst(begin_j, end_j) = sample_pair(i, j, dist);
                        worst_dists[j] = iterator_of_worst(begin_j, end_j)->distance();
                    }
                }

                begin_i += k;
                end_i += k;
            }

            // sort the edges so that duplicate edges will be adjacent
            std::sort(edges.begin(), edges.end(), &order_by_index<sample_pair>);

            // if the first edge is valid
            if (edges[0].index1() < samples.size())
            {
                // now put edges into out while avoiding duplicates and any remaining invalid edges.
                out.reserve(edges.size());
                out.push_back(edges[0]);
                for (unsigned long i = 1; i < edges.size(); ++i)
                {
                    // if we hit an invalid edge then we can stop
                    if (edges[i].index1() >= samples.size())
                        break;

                    // if this isn't a duplicate edge
                    if (edges[i] != edges[i-1])
                    {
                        out.push_back(edges[i]);
                    }
                }
            }

        }

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

        template <
            typename vector_type
            >
        bool contains_duplicate_pairs (
            const vector_type& pairs
        )
        {
            typedef typename vector_type::value_type T;
            vector_type temp(pairs);
            std::sort(temp.begin(), temp.end(), &order_by_index<T>);

            for (unsigned long i = 1; i < temp.size(); ++i)
            {
                // if we found a duplicate
                if (temp[i-1] == temp[i])
                    return true;
            }

            return false;
        }

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

        template <
            typename vector_type
            >
        typename enable_if_c<(is_same_type<sample_pair, typename vector_type::value_type>::value ||
                              is_same_type<ordered_sample_pair, typename vector_type::value_type>::value),
                              unsigned long>::type
        max_index_plus_one (
            const vector_type& pairs
        )
        {
            if (pairs.size() == 0)
            {
                return 0;
            }
            else
            {
                unsigned long max_idx = 0;
                for (unsigned long i = 0; i < pairs.size(); ++i)
                {
                    if (pairs[i].index1() > max_idx)
                        max_idx = pairs[i].index1();
                    if (pairs[i].index2() > max_idx)
                        max_idx = pairs[i].index2();
                }

                return max_idx + 1;
            }
        }

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

        template <
            typename vector_type
            >
        void remove_long_edges (
            vector_type& pairs,
            double distance_threshold
        )
        {
            vector_type temp;
            temp.reserve(pairs.size());

            // add all the pairs shorter than the given threshold into temp
            for (unsigned long i = 0; i < pairs.size(); ++i)
            {
                if (pairs[i].distance() <= distance_threshold)
                    temp.push_back(pairs[i]);
            }

            // move temp into the output vector
            temp.swap(pairs);
        }

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

        template <
            typename vector_type
            >
        void remove_short_edges (
            vector_type& pairs,
            double distance_threshold
        )
        {
            vector_type temp;
            temp.reserve(pairs.size());

            // add all the pairs longer than the given threshold into temp
            for (unsigned long i = 0; i < pairs.size(); ++i)
            {
                if (pairs[i].distance() >= distance_threshold)
                    temp.push_back(pairs[i]);
            }

            // move temp into the output vector
            temp.swap(pairs);
        }

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

        template <
            typename vector_type
            >
        void remove_percent_longest_edges (
            vector_type& pairs,
            double percent
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( 0 <= percent && percent < 1,
                "\t void remove_percent_longest_edges()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t percent:        " << percent
                );

            typedef typename vector_type::value_type T;
            std::sort(pairs.begin(), pairs.end(), &order_by_distance<T>);

            const unsigned long num = static_cast<unsigned long>((1.0-percent)*pairs.size());

            // pick out the num shortest pairs
            vector_type temp(pairs.begin(), pairs.begin() + num);

            // move temp into the output vector
            temp.swap(pairs);
        }

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

        template <
            typename vector_type
            >
        void remove_percent_shortest_edges (
            vector_type& pairs,
            double percent
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( 0 <= percent && percent < 1,
                "\t void remove_percent_shortest_edges()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t percent:        " << percent
                );

            typedef typename vector_type::value_type T;
            std::sort(pairs.rbegin(), pairs.rend(), &order_by_distance<T>);

            const unsigned long num = static_cast<unsigned long>((1.0-percent)*pairs.size());

            // pick out the num shortest pairs
            vector_type temp(pairs.begin(), pairs.begin() + num);

            // move temp into the output vector
            temp.swap(pairs);
        }

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

        template <
            typename vector_type
            >
        bool is_ordered_by_index (
            const vector_type& edges
        )
        {
            for (unsigned long i = 1; i < edges.size(); ++i)
            {
                if (order_by_index(edges[i], edges[i-1]))
                    return false;
            }
            return true;
        }

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

        template <
            typename alloc1,
            typename alloc2
            >
        void find_neighbor_ranges (
            const std::vector<ordered_sample_pair,alloc1>& edges,
            std::vector<std::pair<unsigned long, unsigned long>,alloc2>& neighbors
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_ordered_by_index(edges),
                        "\t void find_neighbor_ranges()"
                        << "\n\t Invalid inputs were given to this function"
            );

            // setup neighbors so that [neighbors[i].first, neighbors[i].second) is the range
            // within edges that contains all node i's edges.
            const unsigned long num_nodes = max_index_plus_one(edges);
            neighbors.assign(num_nodes, std::make_pair(0,0));
            unsigned long cur_node = 0;
            unsigned long start_idx = 0;
            for (unsigned long i = 0; i < edges.size(); ++i)
            {
                if (edges[i].index1() != cur_node)
                {
                    neighbors[cur_node] = std::make_pair(start_idx, i);
                    start_idx = i;
                    cur_node = edges[i].index1();
                }
            }
            if (neighbors.size() != 0)
                neighbors[cur_node] = std::make_pair(start_idx, (unsigned long)edges.size());
        }

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

        template <
            typename alloc1,
            typename alloc2
            >
        void convert_unordered_to_ordered (
            const std::vector<sample_pair,alloc1>& edges,
            std::vector<ordered_sample_pair,alloc2>& out_edges
        )
        {
            out_edges.clear();
            out_edges.reserve(edges.size()*2);
            for (unsigned long i = 0; i < edges.size(); ++i)
            {
                out_edges.push_back(ordered_sample_pair(edges[i].index1(), edges[i].index2(), edges[i].distance()));
                if (edges[i].index1() != edges[i].index2())
                    out_edges.push_back(ordered_sample_pair(edges[i].index2(), edges[i].index1(), edges[i].distance()));
            }
        }

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

    }

    #endif // DLIB_EDGE_LIST_GrAPHS_H__