/* This file is part of the Gudhi Library. The Gudhi library 
 *    (Geometric Understanding in Higher Dimensions) is a generic C++ 
 *    library for computational topology.
 *
 *    Author(s):       David Salinas
 *
 *    Copyright (C) 2014  INRIA Sophia Antipolis-Mediterranee (France)
 *
 *    This program is free software: you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation, either version 3 of the License, or
 *    (at your option) any later version.
 *
 *    This program is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
 * 
 */

#ifndef UTILS_FURTHEST_POINT_EPSILON_NET_H_
#define UTILS_FURTHEST_POINT_EPSILON_NET_H_

#include <vector>
#include <algorithm>  // for sort

#include "utils/UI_utils.h"

/**
 * Computes an epsilon net with furthest point strategy.
 */
template<typename SkBlComplex> class Furthest_point_epsilon_net {
 private:
  SkBlComplex& complex_;
  typedef typename SkBlComplex::Vertex_handle Vertex_handle;
  typedef typename SkBlComplex::Edge_handle Edge_handle;

  /**
   * Let V be the set of vertices.
   * Initially v0 is one arbitrarly vertex and the set V0 is {v0}.
   * Then Vk is computed as follows.
   * First we compute the vertex pk that is the furthest from Vk
   * then Vk = Vk \cup pk.
   * The radius of pk is its distance to Vk and its meeting vertex
   * is the vertex of Vk for which this distance is achieved.
   */
  struct Net_filtration_vertex {
    Vertex_handle vertex_handle;
    Vertex_handle meeting_vertex;
    double radius;

    Net_filtration_vertex(Vertex_handle vertex_handle_,
                          Vertex_handle meeting_vertex_,
                          double radius_) :
        vertex_handle(vertex_handle_), meeting_vertex(meeting_vertex_), radius(radius_) { }

    bool operator<(const Net_filtration_vertex& other) const {
      return radius < other.radius;
    }
  };

 public:
  std::vector<Net_filtration_vertex> net_filtration_;

  /**
   * @brief Modify complex to be the expansion of the k-nearest neighbor
   * symetric graph.
   */
  Furthest_point_epsilon_net(SkBlComplex& complex) :
      complex_(complex) {
    if (!complex.empty()) {
      init_filtration();
      for (std::size_t k = 2; k < net_filtration_.size(); ++k) {
        update_radius_value(k);
      }
    }
  }

  // xxx does not work if complex not full

  double radius(Vertex_handle v) {
    return net_filtration_[v.vertex].radius;
  }

 private:
  void init_filtration() {
    Vertex_handle v0 = *(complex_.vertex_range().begin());
    net_filtration_.reserve(complex_.num_vertices());
    for (auto v : complex_.vertex_range()) {
      if (v != v0)
        net_filtration_.push_back(Net_filtration_vertex(v,
                                                        Vertex_handle(-1),
                                                        squared_eucl_distance(v, v0)));
    }
    net_filtration_.push_back(Net_filtration_vertex(v0, Vertex_handle(-1), 1e10));
    auto n = net_filtration_.size();
    sort_filtration(n - 1);
  }

  void update_radius_value(int k) {
    int n = net_filtration_.size();
    int index_to_update = n - k;
    for (int i = 0; i < index_to_update; ++i) {
      net_filtration_[i].radius = (std::min)(net_filtration_[i].radius,
                                             squared_eucl_distance(net_filtration_[i].vertex_handle,
                                                                   net_filtration_[index_to_update].vertex_handle));
    }
    sort_filtration(n - k);
  }

  /**
   * sort all i first elements.
   */
  void sort_filtration(int i) {
    std::sort(net_filtration_.begin(), net_filtration_.begin() + i);
  }

  double squared_eucl_distance(Vertex_handle v1, Vertex_handle v2) const {
    return std::sqrt(Geometry_trait::Squared_distance_d()(complex_.point(v1), complex_.point(v2)));
  }

  void print_filtration() const {
    for (auto v : net_filtration_) {
      std::cerr << "v=" << v.vertex_handle << "-> d=" << v.radius << std::endl;
    }
  }
};

#endif  // UTILS_FURTHEST_POINT_EPSILON_NET_H_