// Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman

//

// Distributed under the Boost Software License, Version 1.0. (See

// accompanying file LICENSE_1_0.txt or copy at

// http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_GRAPH_ISOMORPHISM_HPP

#define BOOST_GRAPH_ISOMORPHISM_HPP

#include <utility>

#include <vector>

#include <iterator>

#include <algorithm>

#include <boost/config.hpp>

#include <boost/graph/depth_first_search.hpp>

#include <boost/utility.hpp>

#include <boost/detail/algorithm.hpp>

#include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap

#ifndef BOOST_GRAPH_ITERATION_MACROS_HPP

#define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file

#include <boost/graph/iteration_macros.hpp>

#endif

namespace boost {

  namespace detail {

    template <typename Graph1, typename Graph2, typename IsoMapping,

      typename Invariant1, typename Invariant2,

      typename IndexMap1, typename IndexMap2>

    class isomorphism_algo

    {

      typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;

      typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;

      typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;

      typedef typename graph_traits<Graph1>::vertices_size_type size_type;

      typedef typename Invariant1::result_type invar1_value;

      typedef typename Invariant2::result_type invar2_value;

      const Graph1& G1;

      const Graph2& G2;

      IsoMapping f;

      Invariant1 invariant1;

      Invariant2 invariant2;

      std::size_t max_invariant;

      IndexMap1 index_map1;

      IndexMap2 index_map2;

      std::vector<vertex1_t> dfs_vertices;

      typedef typename std::vector<vertex1_t>::iterator vertex_iter;

      std::vector<int> dfs_num_vec;

      typedef safe_iterator_property_map<typename std::vector<int>::iterator,

                                         IndexMap1

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

                                         , int, int&

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

                                         > DFSNumMap;

      DFSNumMap dfs_num;

      std::vector<edge1_t> ordered_edges;

      typedef typename std::vector<edge1_t>::iterator edge_iter;

      std::vector<char> in_S_vec;

      typedef safe_iterator_property_map<typename std::vector<char>::iterator,

                                         IndexMap2

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

                                         , char, char&

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

                                         > InSMap;

      InSMap in_S;

      int num_edges_on_k;

      friend struct compare_multiplicity;

      struct compare_multiplicity

      {

        compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)

          : invariant1(invariant1), multiplicity(multiplicity) { }

        bool operator()(const vertex1_t& x, const vertex1_t& y) const {

          return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];

        }

        Invariant1 invariant1;

        size_type* multiplicity;

      };

      struct record_dfs_order : default_dfs_visitor

      {

        record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e) 

          : vertices(v), edges(e) { }

        void discover_vertex(vertex1_t v, const Graph1&) const {

          vertices.push_back(v);

        }

        void examine_edge(edge1_t e, const Graph1& G1) const {

          edges.push_back(e);

        }

        std::vector<vertex1_t>& vertices;

        std::vector<edge1_t>& edges;

      };

      struct edge_cmp {

        edge_cmp(const Graph1& G1, DFSNumMap dfs_num)

          : G1(G1), dfs_num(dfs_num) { }

        bool operator()(const edge1_t& e1, const edge1_t& e2) const {

          using namespace std;

          int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];

          int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];

          int m1 = (max)(u1, v1);

          int m2 = (max)(u2, v2);

          // lexicographical comparison 

          return std::make_pair(m1, std::make_pair(u1, v1))

            < std::make_pair(m2, std::make_pair(u2, v2));

        }

        const Graph1& G1;

        DFSNumMap dfs_num;

      };

    public:

      isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,

                       Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,

                       IndexMap1 index_map1, IndexMap2 index_map2)

        : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),

          max_invariant(max_invariant),

          index_map1(index_map1), index_map2(index_map2)

      {

        in_S_vec.resize(num_vertices(G1));

        in_S = make_safe_iterator_property_map

          (in_S_vec.begin(), in_S_vec.size(), index_map2

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

           , in_S_vec.front()

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

           );

      }

      bool test_isomorphism()

      {

        {

          std::vector<invar1_value> invar1_array;

          BGL_FORALL_VERTICES_T(v, G1, Graph1)

            invar1_array.push_back(invariant1(v));

          sort(invar1_array);

          std::vector<invar2_value> invar2_array;

          BGL_FORALL_VERTICES_T(v, G2, Graph2)

            invar2_array.push_back(invariant2(v));

          sort(invar2_array);

          if (! equal(invar1_array, invar2_array))

            return false;

        }

        std::vector<vertex1_t> V_mult;

        BGL_FORALL_VERTICES_T(v, G1, Graph1)

          V_mult.push_back(v);

        {

          std::vector<size_type> multiplicity(max_invariant, 0);

          BGL_FORALL_VERTICES_T(v, G1, Graph1)

            ++multiplicity[invariant1(v)];

          sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));

        }

        std::vector<default_color_type> color_vec(num_vertices(G1));

        safe_iterator_property_map<std::vector<default_color_type>::iterator,

                                   IndexMap1

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

                                   , default_color_type, default_color_type&

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

                                   >

          color_map(color_vec.begin(), color_vec.size(), index_map1);

        record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);

        typedef color_traits<default_color_type> Color;

        for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {

          if (color_map[*u] == Color::white()) {

            dfs_visitor.start_vertex(*u, G1);

            depth_first_visit(G1, *u, dfs_visitor, color_map);

          }

        }

        // Create the dfs_num array and dfs_num_map

        dfs_num_vec.resize(num_vertices(G1));

        dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),

                                                  dfs_num_vec.size(), 

                                                  index_map1

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

                                                  , dfs_num_vec.front()

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

                                                  );

        size_type n = 0;

        for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)

          dfs_num[*v] = n++;

        sort(ordered_edges, edge_cmp(G1, dfs_num));

        int dfs_num_k = -1;

        return this->match(ordered_edges.begin(), dfs_num_k);

      }

    private:

      bool match(edge_iter iter, int dfs_num_k)

      {

        if (iter != ordered_edges.end()) {

          vertex1_t i = source(*iter, G1), j = target(*iter, G2);

          if (dfs_num[i] > dfs_num_k) {

            vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];

            BGL_FORALL_VERTICES_T(u, G2, Graph2) {

              if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {

                f[kp1] = u;

                in_S[u] = true;

                num_edges_on_k = 0;

                if (match(iter, dfs_num_k + 1))

#if 0

                    // dwa 2003/7/11 -- this *HAS* to be a bug!

                    ;

#endif 

                    return true;

                in_S[u] = false;

              }

            }

          }

          else if (dfs_num[j] > dfs_num_k) {

            vertex1_t k = dfs_vertices[dfs_num_k];

            num_edges_on_k -= 

              count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S));

            for (int jj = 0; jj < dfs_num_k; ++jj) {

              vertex1_t j = dfs_vertices[jj];

              num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]);

            }

            if (num_edges_on_k != 0)

              return false;

            BGL_FORALL_ADJ_T(f[i], v, G2, Graph2)

              if (invariant2(v) == invariant1(j) && in_S[v] == false) {

                f[j] = v;

                in_S[v] = true;

                num_edges_on_k = 1;

                BOOST_USING_STD_MAX();

                int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));

                if (match(next(iter), next_k))

                  return true;

                in_S[v] = false;

              }

          }

          else {

            if (contains(adjacent_vertices(f[i], G2), f[j])) {

              ++num_edges_on_k;

              if (match(next(iter), dfs_num_k))

                return true;

            }

          }

        } else 

          return true;

        return false;

      }

    };

    template <typename Graph, typename InDegreeMap>

    void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)

    {

      BGL_FORALL_VERTICES_T(v, g, Graph)

        put(in_degree_map, v, 0);

      BGL_FORALL_VERTICES_T(u, g, Graph)

        BGL_FORALL_ADJ_T(u, v, g, Graph)

        put(in_degree_map, v, get(in_degree_map, v) + 1);

    }

  } // namespace detail

  template <typename InDegreeMap, typename Graph>

  class degree_vertex_invariant

  {

    typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;

    typedef typename graph_traits<Graph>::degree_size_type size_type;

  public:

    typedef vertex_t argument_type;

    typedef size_type result_type;

    degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)

      : m_in_degree_map(in_degree_map), m_g(g) { }

    size_type operator()(vertex_t v) const {

      return (num_vertices(m_g) + 1) * out_degree(v, m_g)

        + get(m_in_degree_map, v);

    }

    // The largest possible vertex invariant number

    size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { 

      return num_vertices(m_g) * num_vertices(m_g) + num_vertices(m_g);

    }

  private:

    InDegreeMap m_in_degree_map;

    const Graph& m_g;

  };

  template <typename Graph1, typename Graph2, typename IsoMapping, 

    typename Invariant1, typename Invariant2,

    typename IndexMap1, typename IndexMap2>

  bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f, 

                   Invariant1 invariant1, Invariant2 invariant2, 

                   std::size_t max_invariant,

                   IndexMap1 index_map1, IndexMap2 index_map2)

  {

    // Graph requirements

    function_requires< VertexListGraphConcept<Graph1> >();

    function_requires< EdgeListGraphConcept<Graph1> >();

    function_requires< VertexListGraphConcept<Graph2> >();

    function_requires< BidirectionalGraphConcept<Graph2> >();

    typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;

    typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;

    typedef typename graph_traits<Graph1>::vertices_size_type size_type;

    // Vertex invariant requirement

    function_requires< AdaptableUnaryFunctionConcept<Invariant1,

      size_type, vertex1_t> >();

    function_requires< AdaptableUnaryFunctionConcept<Invariant2,

      size_type, vertex2_t> >();

    // Property map requirements

    function_requires< ReadWritePropertyMapConcept<IsoMapping, vertex1_t> >();

    typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;

    BOOST_STATIC_ASSERT((is_same<IsoMappingValue, vertex2_t>::value));

    function_requires< ReadablePropertyMapConcept<IndexMap1, vertex1_t> >();

    typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;

    BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));

    function_requires< ReadablePropertyMapConcept<IndexMap2, vertex2_t> >();

    typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;

    BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));

    if (num_vertices(G1) != num_vertices(G2))

      return false;

    if (num_vertices(G1) == 0 && num_vertices(G2) == 0)

      return true;

    detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,

      Invariant2, IndexMap1, IndexMap2> 

      algo(G1, G2, f, invariant1, invariant2, max_invariant, 

           index_map1, index_map2);

    return algo.test_isomorphism();

  }

  namespace detail {

    template <typename Graph1, typename Graph2, 

      typename IsoMapping, 

      typename IndexMap1, typename IndexMap2,

      typename P, typename T, typename R>

    bool isomorphism_impl(const Graph1& G1, const Graph2& G2, 

                          IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,

                          const bgl_named_params<P,T,R>& params)

    {

      std::vector<std::size_t> in_degree1_vec(num_vertices(G1));

      typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,

                                         IndexMap1

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

                                         , std::size_t, std::size_t&

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

                                         > InDeg1;

      InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);

      compute_in_degree(G1, in_degree1);

      std::vector<std::size_t> in_degree2_vec(num_vertices(G2));

      typedef safe_iterator_property_map<std::vector<std::size_t>::iterator, 

                                         IndexMap2

#ifdef BOOST_NO_STD_ITERATOR_TRAITS

                                         , std::size_t, std::size_t&

#endif /* BOOST_NO_STD_ITERATOR_TRAITS */

                                         > InDeg2;

      InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);

      compute_in_degree(G2, in_degree2);

      degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);

      degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);

      return isomorphism(G1, G2, f,

                         choose_param(get_param(params, vertex_invariant1_t()), invariant1),

                         choose_param(get_param(params, vertex_invariant2_t()), invariant2),

                         choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),

                         index_map1, index_map2

                         );  

    }  

  } // namespace detail

  // Named parameter interface

  template <typename Graph1, typename Graph2, class P, class T, class R>

  bool isomorphism(const Graph1& g1,

                   const Graph2& g2,

                   const bgl_named_params<P,T,R>& params)

  {

    typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;

    typename std::vector<vertex2_t>::size_type n = num_vertices(g1);

    std::vector<vertex2_t> f(n);

    return detail::isomorphism_impl

      (g1, g2, 

       choose_param(get_param(params, vertex_isomorphism_t()),

                    make_safe_iterator_property_map(f.begin(), f.size(),

                                                    choose_const_pmap(get_param(params, vertex_index1),

                                                                      g1, vertex_index), vertex2_t())),

       choose_const_pmap(get_param(params, vertex_index1), g1, vertex_index),

       choose_const_pmap(get_param(params, vertex_index2), g2, vertex_index),

       params

       );

  }

  // All defaults interface

  template <typename Graph1, typename Graph2>

  bool isomorphism(const Graph1& g1, const Graph2& g2)

  {

    return isomorphism(g1, g2,

                       bgl_named_params<int, buffer_param_t>(0));// bogus named param

  }

  // Verify that the given mapping iso_map from the vertices of g1 to the

  // vertices of g2 describes an isomorphism.

  // Note: this could be made much faster by specializing based on the graph

  // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,

  // O(n^4) won't hurt us.

  template<typename Graph1, typename Graph2, typename IsoMap>

  inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)

  {

#if 0

    // problematic for filtered_graph!

    if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))

      return false;

#endif

    for (typename graph_traits<Graph1>::edge_iterator e1 = edges(g1).first;

         e1 != edges(g1).second; ++e1) {

      bool found_edge = false;

      for (typename graph_traits<Graph2>::edge_iterator e2 = edges(g2).first;

           e2 != edges(g2).second && !found_edge; ++e2) {

        if (source(*e2, g2) == get(iso_map, source(*e1, g1)) &&

            target(*e2, g2) == get(iso_map, target(*e1, g1))) {

          found_edge = true;

        }

      }

      if (!found_edge)

        return false;

    }

    return true;

  }

} // namespace boost

#ifdef BOOST_ISO_INCLUDED_ITER_MACROS

#undef BOOST_ISO_INCLUDED_ITER_MACROS

#include <boost/graph/iteration_macros_undef.hpp>

#endif

#endif // BOOST_GRAPH_ISOMORPHISM_HPP