/* Copyright (c) 1997-2015
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
   http://www.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/Set.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/graph/Lattice.h"
#include "polymake/Graph.h"
#include "polymake/graph/maximal_chains.h"

namespace polymake { namespace graph {

   template <typename Decoration, typename SeqType>
      IncidenceMatrix<> maximal_chains_of_lattice(perl::Object face_lattice_obj, perl::OptionSet options) {
         Lattice<Decoration, SeqType> lattice(face_lattice_obj);
         bool ignore_bottom_node = options["ignore_bottom_node"];
         bool ignore_top_node = options["ignore_top_node"];
         const Array<Set<int> > max_chains = maximal_chains( lattice, ignore_bottom_node, ignore_top_node);
         return IncidenceMatrix<>(max_chains);
      }

   template <typename Decoration, typename SeqType>
      perl::Object lattice_of_chains(perl::Object lattice_obj) {
         Lattice<Decoration, SeqType> lattice(lattice_obj);
         Array<Set<int> > max_chains = maximal_chains(lattice,false, false);
         perl::Object chains_complex("topaz::SimplicialComplex");
         chains_complex.take("FACETS") << max_chains;
         perl::Object chain_hasse = chains_complex.give("HASSE_DIAGRAM");
         return chain_hasse;
      }

   UserFunctionTemplate4perl("# @category Combinatorics"
                     "# For a given lattice, this computes the lattice of chains from bottom to top node."
                     "# The result always includes an artificial top node."
                     "# @param Lattice<Decoration> lattice"
                     "# @return Lattice<BasicDecoration> Faces are sets of nodes of elements in the original"
                     "# lattice forming a chain, ranks are lenghts of chains"
                     "# @example [application polytope] The following prints all faces with their ranks of the lattice of"
                     "# chains of the face lattice of the 0-simplex (a single point):"
                     "# > print lattice_of_chains(simplex(0)->HASSE_DIAGRAM)->DECORATION;"
                     "# | ({-1} 3)"
                     "# | ({0 1} 2)"
                     "# | ({0} 1)"
                     "# | ({1} 1)"
                     "# | ({} 0)",
                     "lattice_of_chains<Decoration, SeqType>(Lattice<Decoration, SeqType>)");

   UserFunctionTemplate4perl("# @category Combinatorics"
                     "# Computes the set of maximal chains of a Lattice object."
                     "# @param Lattice F"
                     "# @option Bool ignore_bottom_node If true, the bottom node is not included in the chains. False by default"
                     "# @option Bool ignore_top_node If true, the top node is not included in the chains. False by default"
                     "# @return IncidenceMatrix Each row is a maximal chain, "
                     "# indices refer to nodes of the Lattice"
                     "# @example [application polytope] [prefer cdd] The following prints all maximal chains of the face lattice of the"
                     "# 1-simplex (an edge):"
                     "# > print maximal_chains_of_lattice(simplex(1)->HASSE_DIAGRAM);"
                     "# | {0 1 3}"
                     "# | {0 2 3}",
                     "maximal_chains_of_lattice<Decoration, SeqType>(Lattice<Decoration, SeqType>, {ignore_bottom_node=>0, ignore_top_node=>0})");

}}
