// Copyright 2016 <Christian.Panse@gmail.com>
//
// This file is part of the recmap package on CRAN.
// https://CRAN.R-project.org/package=recmap
//
// recmap 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.
//
// recmap 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 recmap. If not, see <http://www.gnu.org/licenses/>.


//  Author:  Christian Panse <Christian.Panse@gmail.com>
//  2016-04-19/20/21/22 ACCU2016 Bristol, UK
//  see also doi: 10.18637/jss.v086.c01

#ifndef SRC_RECMAP_H_
#define SRC_RECMAP_H_

#include <stdexcept>
#include <iterator>
#include <algorithm>
#include <vector>
#include <stack>
#include <list>
#include <iostream>
#include <string>
#include <sstream>
#include <cmath>
#include <set>

namespace crecmap {

  // keeps map and pseudo dual graph
  typedef struct {
    double x, y, dx, dy, z;
    int id;
    double area_desired;
    int placed;
    std::string name;
    std::vector<int> connected;
    double topology_error;
    double relative_position_error;
    double relative_position_neighborhood_error;
    int dfs_num;
  } map_region;

struct mbb_node {
  double key;
  int id;

  mbb_node(const double& strKey = 0, const int& intId = 0)
    : key(strKey),
      id(intId) {}

  bool operator<(const mbb_node& rhs) const {
    return key < rhs.key;
  }
};
  // keeps all (x, y) centers
  // use it as sorted list
  // insert/upper_bound: O(ln(n))
  typedef struct {
    double max_dx;
    double max_dy;
    std::multiset<mbb_node> x;
    std::multiset<mbb_node> y;
  } mbb_set;

  typedef std::vector<map_region> recmapvector;

  // computes the bearing of two points in R^2
  // source: http://en.cppreference.com/w/cpp/numeric/math/atan2
  // http://www.cplusplus.com/reference/cmath/atan2/
  double get_angle(const map_region &a, const map_region &b) {
    double alpha = std::atan2(b.x - a.x, b.y - a.y);
    return (alpha);
  }

  // detects whether two minimal bounding boxes (MBB) overlap
  // source: http://gamemath.com/2011/09/detecting-whether-two-boxes-overlap/
  inline bool mbb_check(const map_region &a, const map_region &b) {
    if (a.x + a.dx < b.x - b.dx) return false;  // a is left of b
    else if (a.x - a.dx > b.x + b.dx) return false;  // a is right of b
    else if (a.y + a.dy < b.y - b.dy) return false;  // a is above b
    else if (a.y - a.dy > b.y + b.dy) return false;  // a is below b

    // rectangles can touch each other but do not overlap
    return true;
  }

  // computes the new center (x, y) values on the cartogram map region c
  // map_region a has a fix position
  // uses c.dx and c.dy for the computation
  // TODO(cp): consider giving eps as argument
  //           to have space between the map regions
  void place_rectangle(const map_region &a, double alpha, map_region &c) {
    double tanx, tany;
    double eps = 0.01;

    double dy = a.dy + c.dy + eps;
    double dx = a.dx + c.dx + eps;

    if (std::sin(alpha) >= 0 && std::cos(alpha) >= 0) {
      // Quad I
      tanx = a.x + (dx * std::tan(alpha));
      tany = a.y + (dy * std::tan(M_PI/2 - alpha));

      c.x = a.x + dx;
      c.y = a.y + dy;

      // there are always two intersection; choose the right one
      if (tany >= c.y) c.x = tanx;
      else
        c.y = tany;

    } else if (std::sin(alpha) >= 0 && std::cos(alpha) < 0) {
      // Quad II
      tanx = a.x + (dx * std::tan(M_PI - alpha));
      tany = a.y - (dy * std::tan(alpha - M_PI/2));

      c.x = a.x + dx;
      c.y = a.y - dy;

      if (tanx <= c.x) c.x = tanx;
      else
        c.y = tany;

    } else if (std::sin(alpha) < 0 && std::cos(alpha) < 0) {
      // Quad III
      tanx = a.x - (dx * std::tan(alpha - M_PI));
      tany = a.y - (dy * std::tan(3 * M_PI / 2 - alpha));

      c.x = a.x - dx;
      c.y = a.y - dy;

      if (tany > c.y) c.y = tany;
      else
        c.x = tanx;

    } else if (std::sin(alpha) < 0 && std::cos(alpha) >  0) {
      // Quad IV
      tanx = a.x - (dy * std::tan(2 * M_PI - alpha));
      tany = a.y + (dx * std::tan(alpha - 3 * M_PI /2));

      c.x = a.x - dx;
      c.y = a.y + dy;

      if (tanx < c.x) c.y = tany;
      else
        c.x = tanx;

    } else {
      // error
      }
  }

  // iterating over distinct pairs
  // source: http://stackoverflow.com/questions/17787410/nested-range-based-for-loops
  template<typename C, typename Op1>
  void each_unique_pair(C& container, Op1 fun1) {
    for (auto it = container.begin(); it != container.end() - 1; ++it)
      for (auto it2 = std::next(it); it2 != container.end(); ++it2)
        fun1(*it, *it2, container);
  }

  template<typename C0, typename C1, typename Op>
  void each_unique_pair(C0& container0, C1& container1, Op fun) {
    for (auto it = container0.begin(); it != container0.end() - 1; ++it)
      for (auto it2 = std::next(it); it2 != container0.end(); ++it2)
        fun(*it, *it2, container0, container1);
  }
  
// keeps map and cartogram data
// input is feeded by using the push function
// the run method invokes the generation of the cartogram
// output is returned by get_map_region
class RecMap{
  recmapvector Map;
  recmapvector Cartogram;
  mbb_set MBB;
  int intersect_count;
  bool map_region_intersect_multiset = true;

  int num_regions;

  std::list<std::string> msg;
  std::list<std::string> warnings;

 public:
  RecMap() {
      num_regions = 0;
      MBB.max_dx = 0;
      MBB.max_dy = 0;
      intersect_count = 0;
      }

  // TODO(cp): Think about a destructor?
  void push_region(double x, double y, double dx, double dy, double z,
            std::string name) {
    map_region R, R1;

    R.x = x; R.y = y; R.dx = dx; R.dy = dy; R.z = z;
    R.id = num_regions;
    R.area_desired = -1;
    R.connected = {};
    R.placed = 1;
    R.name = name;
    R.dfs_num = -1;

    R1.x = -1; R1.y = -1; R1.dx = dx; R1.dy = dy; R1.z = z;
    R1.id = num_regions;
    R1.area_desired = -1;
    R1.connected = {};
    R1.placed = 0;
    R1.name = name;
    R1.dfs_num = -1;
    R1.topology_error = -1;
    R1.relative_position_error = 0.0;
    R1.relative_position_neighborhood_error = 0.0;

    Map.push_back(R);
    Cartogram.push_back(R1);
    num_regions++;


    //if (num_regions != Map.size()) {
      // TODO(cp): call an exception?
    //}
  }

  void push_pd_edge(int u, int v){
	  Map[u].connected.push_back(v);
	  Map[v].connected.push_back(u);
  }

  std::string warnings_pop() {
    std::string s = warnings.front(); warnings.pop_front();
    return s;
  }

  bool warnings_empty() {return warnings.empty();}

  int get_size() {return num_regions;}

  int get_intersect_count() { return intersect_count; }
  void set_map_region_intersect_multiset(bool b) { map_region_intersect_multiset = b; }

  map_region& get_map_region(int i) { return(Cartogram[i]); }


  void ComputePseudoDual(recmapvector &M) {
    each_unique_pair(M, [](map_region &a, map_region &b,
                               recmapvector &M) {
                       // add edges tp pseudo dual graph
                       // iff boxes are connected
                       if (mbb_check(a, b)) {
                         M[a.id].connected.push_back(b.id);
                         M[b.id].connected.push_back(a.id);
                       }
                     });
  }

  // taken from the CartoDraw scanline approach date back to yr2000
  void ComputeDesiredArea(recmapvector &M, recmapvector &C) {
    double sum_z = 0.0;
    double sum_area = 0.0;

    std::for_each(M.begin(), M.end(), [&] (map_region &r) {sum_z += r.z;});
    std::for_each(M.begin(), M.end(),
                  [&] (map_region &r) {sum_area += (4 * r.dx * r.dy);});

    std::for_each(C.begin(), C.end(), [&] (map_region &r) {
      double area_desired = r.z * sum_area / sum_z;
      double ratio = r.dy / r.dx;
      r.dx = sqrt(area_desired / (4 * ratio));
      r.dy = r.dx * ratio;
      });
  }


  // TODO(cp): Is the original core polygon implementation really usefull?
  //           the 8x8 checker board suffers but for the x77 map it seems
  //           to work great
  //           if yes; implement it here.
  int ComputeCoreRegion(recmapvector &M, recmapvector &C) {
    int core_region_id = num_regions / 2;

    C[core_region_id].x = M[core_region_id].x;
    C[core_region_id].y = M[core_region_id].y;
    C[core_region_id].placed++;
    C[core_region_id].topology_error = 0;

    mbb_node mn;
    mn.key = C[core_region_id].x; mn.id = C[core_region_id].id;
    MBB.x.insert(mn);

    mn.key = C[core_region_id].y; mn.id = C[core_region_id].id;
    MBB.y.insert(mn);

    MBB.max_dx = C[core_region_id].dx;
    MBB.max_dy = C[core_region_id].dy;

    return core_region_id;
  }

  // obsolet version of the linear intersection test; keep it for testing
  bool map_region_intersect(const recmapvector &C, const map_region &a) {
    for (map_region b : C) {
      if (a.id != b.id && b.placed > 0) {
      intersect_count++;
      if (mbb_check(a, b)) {
        return true;
      }}
    }
  return false;
  }

  // MBB intersection test; doing binary search
  bool map_region_intersect_set(recmapvector &C, const mbb_set &S,
                                const map_region &a) {
    double eps = 0.0;

    // 1st: range query on the x-axis
    auto lower_x = std::lower_bound(S.x.begin(), S.x.end(),
                                    a.x - a.dx - S.max_dx - eps,
                                    [](const mbb_node& f1, const mbb_node& f2)
                                      { return f1.key < f2.key; });

    auto upper_x = std::upper_bound(S.x.begin(), S.x.end(),
                                    a.x + a.dx + S.max_dx + eps,
                                    [](const mbb_node& f1, const mbb_node& f2)
                                      { return f1.key < f2.key; });


    for (auto it_x = lower_x; it_x != upper_x; ++it_x) {

      intersect_count++;
      if ((*it_x).id != a.id &&  mbb_check(a, C[(*it_x).id])) {
        return true;
      }
    }

    // no intersetions until now;
    // 2nd: check the y-axis
    auto lower_y = std::lower_bound(S.y.begin(), S.y.end(),
                               a.y - a.dy - S.max_dy - eps,
                               [](const mbb_node& f1, const mbb_node& f2)
                                 { return f1.key < f2.key; });

    auto upper_y = std::upper_bound(S.y.begin(), S.y.end(),
                                    a.y + a.dy + S.max_dy + eps,
                                    [](const mbb_node& f1, const mbb_node& f2)
                                      { return f1.key < f2.key; });

    for (auto it_y = lower_y; it_y != upper_y; ++it_y) {
      intersect_count++;
      if ((*it_y).id != a.id && mbb_check(a, C[(*it_y).id])) {
        return true;
      }
    }

    return false;
  }

  // place rectangle around predecessor_region_id
  bool PlaceRectangle(recmapvector &M, recmapvector &C, int region_id) {
    double alpha0, alpha;
    mbb_node mn;

    double beta_sign = 1.0;
    bool intersect = true;

    // strategy one: try to place it in the neighborhood;
    // and only one => allow non feasible solution to be filtered out
    // by the metaheuristic
    for (double beta = 0.0; beta <=  M_PI && C[region_id].placed == 0;
      beta += M_PI/180) {
      // iterate over all already placed adjacent rectangles
      for (const int &adj_region_id : M[region_id].connected) {
        if (C[adj_region_id].placed > 0) {
	  // orginal bearing of two map regions in the input map
          alpha0 = get_angle(M[adj_region_id], M[region_id]);
          alpha = alpha0 + (beta_sign * beta);
          beta_sign *= -1;

          place_rectangle(C[adj_region_id], alpha, C[region_id]);

	  if (map_region_intersect_multiset)
		  intersect = map_region_intersect_set(C, MBB, C[region_id]);
	  else
		  intersect = map_region_intersect(C, C[region_id]);

          if (!intersect) {
            C[region_id].placed++;
            C[region_id].topology_error = 0;  // for the moment

            mn.key = C[region_id].x; mn.id = C[region_id].id;
            MBB.x.insert(mn);

            mn.key = C[region_id].y; mn.id = C[region_id].id;
            MBB.y.insert(mn);

            if (C[region_id].dx > MBB.max_dx) {MBB.max_dx = C[region_id].dx;}
            if (C[region_id].dy > MBB.max_dy) {MBB.max_dy = C[region_id].dy;}

            // update dual graph
            C[adj_region_id].connected.push_back(region_id);
            C[region_id].connected.push_back(adj_region_id);
            return true;
          }
        }
      }  // END for (int adj_region_id : M[region_id].connected)
    }

    // placement failed => make map region as not placed
    C[region_id].x = -1;
    C[region_id].y = -1;
    C[region_id].topology_error = -1;
    // communicate this to the user later
    warnings.push_back(M[region_id].name
                         + " could not be placed on the first attempt;");
    return false;
  }

  // dfs explore of existing input map M; output cartogram C
  void DrawCartogram(recmapvector &M, recmapvector &C, int core_region_id) {
    std::list<int> stack;
    std::vector<int> visited(num_regions, 0);
    std::vector<int> dfs_num(num_regions, 0);

    int dfs_num_counter = 0;
    int current_region_id = core_region_id;
    stack.push_back(current_region_id);
    visited[current_region_id]++;

    while (stack.size()  > 0) {
      current_region_id = stack.back() ; stack.pop_back();
      dfs_num[current_region_id] = dfs_num_counter++;
      C[current_region_id].dfs_num = dfs_num[current_region_id];

      if (current_region_id != core_region_id) {
        if (!PlaceRectangle(M, C, current_region_id)) {
          // bad luck - lets place first the other map regions
        }
      }

      for (const int & adj_region_id : M[current_region_id].connected) {
        if (visited[adj_region_id] == 0) {
          visited[adj_region_id]++;
          stack.push_back(adj_region_id);
        }
      }
    }  // while

    std::for_each(C.begin(), C.end(), [&] (map_region &r) {
      if (r.placed == 0) {
		PlaceRectangle(M, C, r.id);
		if (r.placed == 0) {
		  // yes -
		  // accept a non feasible solution to save computational resources
		  // the metaheuristic has to fix that with the fitness function
		  warnings.push_back(r.name + " was not placed!!");
		}
		//
	      }});
	  }


	  void ComputeError(recmapvector &M, recmapvector &C) {
	    double gammaM, gammaC, delta;
	    // relative position error
	    // TODO(cp): make the  each_unique_pair construct working to
	    //           save 50% of the hand shakes
	    for (const auto & a : M) {
	      for (const auto & b : M) {
		gammaM = get_angle(M[a.id], M[b.id]);
		gammaC = get_angle(C[a.id], C[b.id]);

		if ((gammaM < 0 && gammaC > 0) || ( gammaM > 0 && gammaC < 0))
		  delta = fabs(gammaC + gammaM) / C.size();
	else
          delta = fabs(gammaC - gammaM) / C.size();

        C[a.id].relative_position_error += delta;
      }

      // alternative to the relative position error; play with it
      for (const auto & idx : a.connected) {
        gammaM = get_angle(M[a.id], M[idx]);
        gammaC = get_angle(C[a.id], C[idx]);
	if ((gammaM < 0 && gammaC > 0) || ( gammaM > 0 && gammaC < 0))
          delta = fabs(gammaC + gammaM) / a.connected.size();
	else
          delta = fabs(gammaC - gammaM) / a.connected.size();

        C[a.id].relative_position_neighborhood_error += delta;
      }

      // topology error,
      // http://www.cplusplus.com/reference/algorithm/set_symmetric_difference/
      std::vector<int> v(M[a.id].connected.size() + C[a.id].connected.size());
      std::vector<int>::iterator it;
      std::sort(M[a.id].connected.begin(), M[a.id].connected.end());
      std::sort(C[a.id].connected.begin(), C[a.id].connected.end());


      it = std::set_symmetric_difference(M[a.id].connected.begin(),
                                          M[a.id].connected.end(),
                                          C[a.id].connected.begin(),
                                          C[a.id].connected.end(),
                                          v.begin());
      v.resize(it-v.begin());
      
      if (C[a.id].topology_error != -1)
        C[a.id].topology_error = (v.size());
      // for debug print all three vectors once
    }
  }

  void run(bool computePseudoDual = true) {
    if (computePseudoDual) ComputePseudoDual(Map);
    ComputeDesiredArea(Map, Cartogram);
    int core_region_id = ComputeCoreRegion(Map, Cartogram);
    msg.push_back("CORE REGION: " + Map[core_region_id].name);
    DrawCartogram(Map, Cartogram, core_region_id);
    ComputeError(Map, Cartogram);
  }  // run


};
}  // namespace crecmap
#endif  // SRC_RECMAP_H_
