// Copyright (c) 2013-2015  The University of Western Sydney, Australia.
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// 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.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Authors: Weisheng Si, Quincy Tse

/*! \file Construct_yao_graph_2.h
 *
 * This header implements the functor for constructing Yao graphs.
 */

#ifndef CGAL_CONSTRUCT_YAO_GRAPH_2_H
#define CGAL_CONSTRUCT_YAO_GRAPH_2_H

#include <iostream>
#include <cstdlib>
#include <utility>
#include <CGAL/Polynomial.h>
#include <CGAL/number_utils.h>
#include <CGAL/enum.h>
#include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>
#include <CGAL/Compute_cone_boundaries_2.h>
#include <CGAL/Cone_spanners_2/Less_by_direction_2.h>

#include <boost/config.hpp>
#include <boost/graph/adjacency_list.hpp>

namespace CGAL {

/*! \ingroup PkgConeBasedSpanners

  \brief A functor for constructing yao graphs with a given set of 2D points.

  \tparam Kernel_ The CGAL kernel used by this functor. If this parameter is
      `CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt`,
      the graph will be constructed exactly; otherwise, inexactly using an approximate PI=3.1415...

  \tparam Graph_  The graph type to store the constructed Yao graph. It should be a model of
      both concepts MutableGraph and VertexAndEdgeListGraph in BGL. Of the two graph classes provided
      in BGL: `adjacency_list` and `adjacency_matrix`, only `adjacency_list` is such a model.
      So pls use `adjacency_list` to be your graph type. Note that there are seven template parameters for
      `boost::adjacency_list`: `OutEdgeList`, `VertexList`, `Directed`, `VertexProperties`, `EdgeProperties`,
	  `GraphProperties`, `EdgeList`, of which we require `VertexProperties` be `Point_2` from \cgal,
      and other parameters can be chosen freely. Here `Point_2` is passed directly as bundled properties
	  to `adjacency_list` because this makes our implementation much more straightforward than using property maps.
	  For detailed information about bundled properties, pls refer to
      http://www.boost.org/doc/libs/1_58_0/libs/graph/doc/bundles.html.
 */
template <typename Kernel_, typename Graph_>
class Construct_yao_graph_2 {

public:
	/*! Indicate the \cgal kernel type. */
    typedef Kernel_                          kernel_type;
	/*! Indicate the specific type of `boost::adjacency_list`. */
    typedef Graph_                           graph_type;

private:
    typedef typename Kernel_::Direction_2             Direction_2;
    typedef typename Kernel_::Point_2                 Point_2;
    typedef typename Kernel_::Line_2                  Line_2;
    typedef Less_by_direction_2<Kernel_, Graph_>      Less_by_direction;
    // a type for the set to store vertices sorted by a direction
    typedef std::set<typename Graph_::vertex_descriptor, Less_by_direction> Point_set;

    /* Store the number of cones.  */
    unsigned int  cone_number;

    /* Store the directions of the rays dividing the plane. The initial direction will be
       stored in rays[0].  */
    std::vector<Direction_2>   rays;

public:
    /*! \brief Constructor.
     *
     *  Constructs a `Construct_yao_graph_2` object.
     *
     * \param k     Number of cones to divide space into
     * \param initial_direction  A direction denoting one of the rays dividing the
     *              cones. This allows arbitary rotations of the rays that divide
     *              the plane.  (default: positive x-axis)
     */
    Construct_yao_graph_2 (unsigned int k,
                           Direction_2 initial_direction = Direction_2(1,0) )

    {
        if (k<2) {
            std::cout << "The number of cones should be larger than 1!" << std::endl;
            std::exit(1);
        }

        cone_number = k;
        /* Initialize a functor, specialization will happen here depending on the kernel type to
         compute the cone boundaries either exactly or inexactly */
        Compute_cone_boundaries_2<Kernel_> compute_cones;
        // compute the rays using the functor
        compute_cones(k, initial_direction, rays);
    }

    /*! \brief Copy constructor.
     *  \param x  another Construct_yao_graph_2 object to copy from.
     */
    Construct_yao_graph_2 (const Construct_yao_graph_2& x) : cone_number(x.cone_number), rays(x.rays) {}

    /*! \brief Operator to construct a Yao graph.
     *
     * This operator implements the algorithm for adding edges to build the Yao graph.
     * The algorithm implemented is described in:
     * Giri Narasimhan and Michiel Smid, Chapter 4: Spanners based on the Yao graph, Geometric Spanner Networks,
     * Cambridge University Press, 2007.
     * This algorithm has the complexity of O(n*log(n)), which is optimal.
     *
     * \param start[in] An iterator pointing to the first point (vertex).
     * \param end[in]   An iterator pointing to the place that passes the last point.
     * \param g[out]    The constructed graph object.
     */
    template <typename PointInputIterator>
    Graph_& operator()(const PointInputIterator& start,
                       const PointInputIterator& end,
                       Graph_& g) {

        // add vertices into the graph
        for (PointInputIterator curr = start; curr != end; ++curr) {
            g[boost::add_vertex(g)] = *curr;
        }

        unsigned int i;   // ray index of the cw ray
        unsigned int j;   // index of the ccw ray

        // add edges into the graph for every cone
        for (i = 0; i < cone_number; i++) {
            j = (i+1) % cone_number;
            add_edges_in_cone(rays[i], rays[j], g);
        }

        return g;
    }

    /*! \brief returns the number of cones.
     */
    const unsigned int number_of_cones() const {
        return cone_number;
    }

    /*! \brief returns the vector of the directions of the rays dividing the plane.
     *
     *  \return a vector of Direction_2
     */
    const std::vector<Direction_2>& directions() const {
        return rays;
    }

protected:

    /* \brief Construct edges in one cone bounded by two directions.

     \param cwBound      The direction of the clockwise boundary of the cone.
     \param ccwBound     The direction of the counter-clockwise boundary.
     \param g            The Yao graph to be built.
    */
    void add_edges_in_cone(const Direction_2& cwBound, const Direction_2& ccwBound, Graph_& g) {
        if (ccwBound == cwBound) {
            // Degenerate case,  not allowed.
            throw std::out_of_range("The cw boundary and the ccw boundary shouldn't be same!");
        }

        // Ordering
        // here D1 is the reverse of D1 in the book, we find this is easier to implement
        const Less_by_direction  orderD1 (g, ccwBound);
        const Less_by_direction  orderD2 (g, cwBound);

        typename Graph_::vertex_iterator vit, ve;
        boost::tie(vit, ve) = boost::vertices(g);

        // Step 1: Sort S according to order induced by D1
        std::vector<typename Graph_::vertex_descriptor> S(vit, ve);
        std::sort(S.begin (), S.end (), orderD1);

        // Step 2: Initialise an empty set to store vertices sorted by orderD2
        Point_set pst(orderD2);

        // Step 3: visit S in orderD1
        //         insert 'it' into pst
        //         search the min in pst
        for (typename std::vector<typename Graph_::vertex_descriptor>::const_iterator
                it = S.begin(); it != S.end(); ++it) {
            Less_euclidean_distance comp(g[*it], g);

            pst.insert(*it);
            // Find the last added node - O(logn)
            typename Point_set::iterator it2 = pst.find(*it);
            // Find minimum in pst from last ended node - O(n)
            typename Point_set::iterator min = std::min_element(++it2, pst.end(), comp);
			// add an edge
            if (min != pst.end()) {
                typename Graph_::edge_descriptor existing_e;
			    bool                    existing;
				// check whether the edge already exists
				boost::tie(existing_e, existing)=boost::edge(*it, *min, g);
				if (!existing)
                    boost::add_edge(*it, *min, g);
                //else
				 //   std::cout << "Edge " << *it << ", " << *min << " already exists!" << std::endl;
			}

        } // end of for

    };     // end of add edges in cone


    /* Functor for comparing Euclidean distances of two vertices in a graph g to a given vertex.
      It is implemented by encapsulating the CGAL::has_smaller_distance_to_point() function.
     */
    struct Less_euclidean_distance {
        const Point_2& p;
        const Graph_& g;

		// constructor
        Less_euclidean_distance(const Point_2&p, const Graph_& g) : p(p), g(g) {}

		// operator
        bool operator() (const typename Point_set::iterator::value_type& i, const typename Point_set::iterator::value_type& j) {
            const Point_2& p1 = g[i];
            const Point_2& p2 = g[j];
            return has_smaller_distance_to_point(p, p1, p2);
        }
    };

};      // class Construct_yao_graph_2


}  // namespace CGAL


#endif