/* Copyright (c) 1997-2021
   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.
--------------------------------------------------------------------------------
*/

#include "polymake/client.h"
#include "polymake/Array.h"
#include "polymake/PowerSet.h"

namespace polymake { namespace matroid {

using SArray = Array<Set<Int>>;

SArray bases_to_circuits(const SArray& bases, const Int n)
{
   if (bases.empty()) {
      return SArray(n, entire(all_subsets_of_k(sequence(0,n),1)));
   }
   const Int r = bases[0].size();
   if (r == 0) {
      SArray c(n);
      for (Int i = 0; i < n; ++i)
         c[i] = scalar2set(i);
      return c;
   }
   if (r == n) return SArray(0);
   Int n_circuits = 0;
   std::vector<Set<Int>> circuits;
   for (Int k = 1; k <= r; ++k) {
      for (auto j = entire(all_subsets_of_k(sequence(0, n), k)); !j.at_end(); ++j) {
         bool is_circuit = true;
         for (auto i = entire(circuits); is_circuit && !i.at_end(); ++i)
            if (incl(*i, *j) <= 0) is_circuit = false;
         for (auto i = entire(bases); is_circuit && !i.at_end(); ++i) {
            const Int l = incl(*i,*j);
            if (l == 0 || l == 1) is_circuit = false;
         }
         if (is_circuit) {
            circuits.push_back(Set<Int>(*j));
            ++n_circuits;
         }
      }
   }
   for (auto j = entire(all_subsets_of_k(sequence(0, n), r+1)); !j.at_end(); ++j) {
      bool is_circuit = true;
      for (auto i = entire(circuits); is_circuit && !i.at_end(); ++i)
         if (incl(*i, *j) <= 0) is_circuit = false;
      if (is_circuit) {
         circuits.push_back(Set<Int>(*j));
         ++n_circuits;
      }
   }
   return SArray(n_circuits, entire(circuits));
}

SArray circuits_to_bases(const SArray& circuits, const Int n)
{
   if (circuits.empty())
      return SArray(1, Set<Int>(sequence(0, n)));
   Int n_bases = 0;
   std::vector<Set<Int>> bases;
   Int r = 1;
   for (Int k = n; k >= r; --k)
      for (auto j = entire(all_subsets_of_k(sequence(0, n), k)); !j.at_end(); ++j) {
         bool is_basis = true;
         for (auto i = entire(circuits); is_basis && !i.at_end(); ++i){
            if (incl(*i, *j) <= 0) is_basis = false;
         }
         if (is_basis) {
            bases.push_back(Set<Int>(*j));
            ++n_bases;
            r=k;
         }
      }
   //If we found no basis, the empty set is the basis 
   if (bases.size() == 0) return SArray(1);
   return SArray(n_bases, entire(bases));
}


SArray circuits_to_bases_rank(const SArray& circuits, const Int n, const Int rank)
{
   if (circuits.empty()) return SArray(1, Set<Int>(sequence(0, n)));
   Int n_bases = 0;
   std::vector<Set<Int>> bases;
   for (auto j = entire(all_subsets_of_k(sequence(0, n), rank)); !j.at_end(); ++j) {
      bool is_basis=true;
      for (auto i = entire(circuits); is_basis && !i.at_end(); ++i) {
         if (incl(*i,*j) <= 0) is_basis = false;
      }
      if (is_basis) {
         bases.push_back(Set<Int>(*j));
         ++n_bases;
      }
   }
   return SArray(n_bases, entire(bases));
}

SArray circuits_to_hyperplanes(const SArray& circuits, const Int n, const Int rank)
{
   if (rank==0) {
      return SArray(0);
   }
   Set<Set<Int>> hyp;
   for (auto j = entire(all_subsets_of_k(sequence(0, n), rank-1)); !j.at_end(); ++j) {
      bool is_ind = true;
      Set<Int> h = *j;
      for (auto c = entire(circuits); is_ind && !c.at_end(); ++c) {
         if (incl(*c,*j) <=0 ) is_ind = false;
         if ((*c-*j).size() == 1) {
            h+=*c;
         }
      }
      if (is_ind) {
         hyp+=h;
      }
   }
   return SArray(hyp);
}

Function4perl(&bases_to_circuits, "bases_to_circuits");
Function4perl(&circuits_to_bases, "circuits_to_bases");
Function4perl(&circuits_to_bases_rank, "circuits_to_bases_rank");
Function4perl(&circuits_to_hyperplanes, "circuits_to_hyperplanes");

} }

// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
