/* Copyright (c) 1997-2020
   Ewgenij Gawrilow, Michael Joswig, and the polymake team
   Technische Universität Berlin, Germany
   https://polymake.org

   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 2, or (at your option) any
   later version: http://www.gnu.org/licenses/gpl.txt.

   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.
--------------------------------------------------------------------------------
*/

#ifndef POLYMAKE_TOPAZ_MULTI_ASSOCIAHEDRON_SPHERE_H
#define POLYMAKE_TOPAZ_MULTI_ASSOCIAHEDRON_SPHERE_H

#include "polymake/hash_map"
#include "polymake/hash_set"
#include "polymake/Set.h"
#include "polymake/PowerSet.h"
#include "polymake/group/orbit.h"
#include "polymake/group/named_groups.h"
#include <algorithm>

namespace polymake { namespace topaz {

namespace multi_associahedron_sphere_utils {

using Diagonal = std::pair<Int, Int>;
using DiagonalIndex = hash_map<Diagonal, Int> ;
using DiagonalList = std::vector<Diagonal>;
using DiagonalLabels = std::vector<std::string>;

bool inside(Int x, const Diagonal& d)
{
   return x > d.first && x < d.second;
}

bool cross(const Diagonal& d1, const Diagonal& d2)
{
   assert(d1.first < d1.second && d2.first < d2.second);

   if (d1.first==d2.first || d1.second==d2.second)
      return false;

   const Int v0 = std::min(d1.first, d2.first);

   const Diagonal d1t{ d1.first - v0, d1.second - v0 },
                  d2t{ d2.first - v0, d2.second - v0 };
      
   return 
      inside(d2t.first, d1t) && !inside(d2t.second, d1t) ||
      inside(d2t.second, d1t) && !inside(d2t.first, d1t);
}

bool cross_mutually(const Set<Int>& c,
                    const DiagonalList& diagonals)
{
   assert(c.size() >= 2);
   for (auto pit = entire(all_subsets_of_k(c,2)); !pit.at_end(); ++pit)
      if (!cross(diagonals[(*pit).front()], diagonals[(*pit).back()]))
         return false;
   return true;
}

bool crosses_all(Int new_d,
                 const Set<Int>& family,
                 const DiagonalList& diagonals)
{
   for (const auto& i: family)
      if (!cross(diagonals[new_d], diagonals[i]))
         return false;
   return true;
}

bool contains_new_k_plus_1_crossing(Int new_d,
                                    Int k,
                                    const Set<Int>& family,
                                    const DiagonalList& diagonals)
{
   if (k > 1) {
      for (auto kc_it = entire(all_subsets_of_k(family, k)); !kc_it.at_end(); ++kc_it) {
         if (!crosses_all(new_d, *kc_it, diagonals)) // first, a linear test
            continue;
         if (cross_mutually(*kc_it, diagonals)) // then a quadratic one
            return true;
      }
      return false;
   } else { // k==1
      for (auto f_it = entire(family); !f_it.at_end(); ++f_it)
         if (cross(diagonals[new_d], diagonals[*f_it]))
            return true;
      return false;
   }
}

Array<Int> induced_gen(const Array<Int>& g,
                       const DiagonalList& diagonals,
                       const DiagonalIndex& index_of)
{
   Array<Int> induced_gen(diagonals.size());
   auto igit = entire(induced_gen);
   for (const auto& d: diagonals) {
      const Diagonal unordered_img{ g[d.first], g[d.second] };
      const Diagonal img = unordered_img.first < unordered_img.second
                           ? unordered_img
                           : Diagonal{ unordered_img.second, unordered_img.first };
      *igit = index_of.at(img);
      ++igit;
   }
   return induced_gen;
}

Array<Array<Int>>
induced_action_gens_impl(const Array<Array<Int>>& gens,
                         const DiagonalList& diagonals,
                         const DiagonalIndex& index_of)
{
   Array<Array<Int>> igens(gens.size());
   std::transform(gens.begin(), gens.end(), igens.begin(),
                  [&diagonals, &index_of](auto gen) { return induced_gen(gen, diagonals, index_of); });
   return igens;
}

void prepare_diagonal_data(Int n,
                           Int k,
                           DiagonalIndex& index_of,
                           DiagonalList& diagonals,
                           DiagonalLabels& labels)
{
   Int index = -1;
   std::ostringstream oss;
   for (Int steps = k+1; steps <= n/2; ++steps) {
      for (Int u = 0; u<n; ++u) {
         if (n%2==0 && steps==n/2 && u==n/2)
            break; // for even n-gons, the big diagonals must be counted only once
         const Int v = (u+steps) % n;
         const Diagonal d{ std::min(u, v), std::max(u, v) };
         index_of[d] = ++index;
         diagonals.push_back(d);
         oss.str("");
         wrap(oss) << "(" << d << ")";
         labels.push_back(oss.str());
      }
   }
}

} } }

#endif // POLYMAKE_TOPAZ_MULTI_ASSOCIAHEDRON_SPHERE_H

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