/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2008

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef HYPERCUBE_GRAPH_H

#define HYPERCUBE_GRAPH_H

#include <vector>

#include <lemon/core.h>

#include <lemon/assert.h>

#include <lemon/bits/graph_extender.h>

///\ingroup graphs

///\file

///\brief HypercubeGraph class.

namespace lemon {

  class HypercubeGraphBase {

  public:

    typedef HypercubeGraphBase Graph;

    class Node;

    class Edge;

    class Arc;

  public:

    HypercubeGraphBase() {}

  protected:

    void construct(int dim) {

      LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1.");

      _dim = dim;

      _node_num = 1 << dim;

      _edge_num = dim * (1 << (dim-1));

    }

  public:

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    typedef True ArcNumTag;

    int nodeNum() const { return _node_num; }

    int edgeNum() const { return _edge_num; }

    int arcNum() const { return 2 * _edge_num; }

    int maxNodeId() const { return _node_num - 1; }

    int maxEdgeId() const { return _edge_num - 1; }

    int maxArcId() const { return 2 * _edge_num - 1; }

    static Node nodeFromId(int id) { return Node(id); }

    static Edge edgeFromId(int id) { return Edge(id); }

    static Arc arcFromId(int id) { return Arc(id); }

    static int id(Node node) { return node._id; }

    static int id(Edge edge) { return edge._id; }

    static int id(Arc arc) { return arc._id; }

    Node u(Edge edge) const {

      int base = edge._id & ((1 << (_dim-1)) - 1);

      int k = edge._id >> (_dim-1);

      return ((base >> k) << (k+1)) | (base & ((1 << k) - 1));

    }

    Node v(Edge edge) const {

      int base = edge._id & ((1 << (_dim-1)) - 1);

      int k = edge._id >> (_dim-1);

      return ((base >> k) << (k+1)) | (base & ((1 << k) - 1)) | (1 << k);

    }

    Node source(Arc arc) const {

      return (arc._id & 1) == 1 ? u(arc) : v(arc);

    }

    Node target(Arc arc) const {

      return (arc._id & 1) == 1 ? v(arc) : u(arc);

    }

    typedef True FindEdgeTag;

    typedef True FindArcTag;

    Edge findEdge(Node u, Node v, Edge prev = INVALID) const {

      if (prev != INVALID) return INVALID;

      int d = u._id ^ v._id;

      int k = 0;

      if (d == 0) return INVALID;

      for ( ; (d & 1) == 0; d >>= 1) ++k;

      if (d >> 1 != 0) return INVALID;

      return (k << (_dim-1)) | ((u._id >> (k+1)) << k) |

        (u._id & ((1 << k) - 1));

    }

    Arc findArc(Node u, Node v, Arc prev = INVALID) const {

      Edge edge = findEdge(u, v, prev);

      if (edge == INVALID) return INVALID;

      int k = edge._id >> (_dim-1);

      return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;

    }

    class Node {

      friend class HypercubeGraphBase;

    protected:

      int _id;

      Node(int id) : _id(id) {}

    public:

      Node() {}

      Node (Invalid) : _id(-1) {}

      bool operator==(const Node node) const {return _id == node._id;}

      bool operator!=(const Node node) const {return _id != node._id;}

      bool operator<(const Node node) const {return _id < node._id;}

    };

    class Edge {

      friend class HypercubeGraphBase;

      friend class Arc;

    protected:

      int _id;

      Edge(int id) : _id(id) {}

    public:

      Edge() {}

      Edge (Invalid) : _id(-1) {}

      bool operator==(const Edge edge) const {return _id == edge._id;}

      bool operator!=(const Edge edge) const {return _id != edge._id;}

      bool operator<(const Edge edge) const {return _id < edge._id;}

    };

    class Arc {

      friend class HypercubeGraphBase;

    protected:

      int _id;

      Arc(int id) : _id(id) {}

    public:

      Arc() {}

      Arc (Invalid) : _id(-1) {}

      operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }

      bool operator==(const Arc arc) const {return _id == arc._id;}

      bool operator!=(const Arc arc) const {return _id != arc._id;}

      bool operator<(const Arc arc) const {return _id < arc._id;}

    };

    void first(Node& node) const {

      node._id = _node_num - 1;

    }

    static void next(Node& node) {

      --node._id;

    }

    void first(Edge& edge) const {

      edge._id = _edge_num - 1;

    }

    static void next(Edge& edge) {

      --edge._id;

    }

    void first(Arc& arc) const {

      arc._id = 2 * _edge_num - 1;

    }

    static void next(Arc& arc) {

      --arc._id;

    }

    void firstInc(Edge& edge, bool& dir, const Node& node) const {

      edge._id = node._id >> 1;

      dir = (node._id & 1) == 0;

    }

    void nextInc(Edge& edge, bool& dir) const {

      Node n = dir ? u(edge) : v(edge);

      int k = (edge._id >> (_dim-1)) + 1;

      if (k < _dim) {

        edge._id = (k << (_dim-1)) |

          ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));

        dir = ((n._id >> k) & 1) == 0;

      } else {

        edge._id = -1;

        dir = true;

      }

    }

    void firstOut(Arc& arc, const Node& node) const {

      arc._id = ((node._id >> 1) << 1) | (~node._id & 1);

    }

    void nextOut(Arc& arc) const {

      Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);

      int k = (arc._id >> _dim) + 1;

      if (k < _dim) {

        arc._id = (k << (_dim-1)) |

          ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));

        arc._id = (arc._id << 1) | (~(n._id >> k) & 1);

      } else {

        arc._id = -1;

      }

    }

    void firstIn(Arc& arc, const Node& node) const {

      arc._id = ((node._id >> 1) << 1) | (node._id & 1);

    }

    void nextIn(Arc& arc) const {

      Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);

      int k = (arc._id >> _dim) + 1;

      if (k < _dim) {

        arc._id = (k << (_dim-1)) |

          ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));

        arc._id = (arc._id << 1) | ((n._id >> k) & 1);

      } else {

        arc._id = -1;

      }

    }

    static bool direction(Arc arc) {

      return (arc._id & 1) == 1;

    }

    static Arc direct(Edge edge, bool dir) {

      return Arc((edge._id << 1) | (dir ? 1 : 0));

    }

    int dimension() const {

      return _dim;

    }

    bool projection(Node node, int n) const {

      return static_cast<bool>(node._id & (1 << n));

    }

    int dimension(Edge edge) const {

      return edge._id >> (_dim-1);

    }

    int dimension(Arc arc) const {

      return arc._id >> _dim;

    }

    int index(Node node) const {

      return node._id;

    }

    Node operator()(int ix) const {

      return Node(ix);

    }

  private:

    int _dim;

    int _node_num, _edge_num;

  };

  typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;

  /// \ingroup graphs

  ///

  /// \brief Hypercube graph class

  ///

  /// This class implements a special graph type. The nodes of the graph

  /// are indiced with integers with at most \c dim binary digits.

  /// Two nodes are connected in the graph if and only if their indices

  /// differ only on one position in the binary form.

  ///

  /// \note The type of the indices is chosen to \c int for efficiency

  /// reasons. Thus the maximum dimension of this implementation is 26

  /// (assuming that the size of \c int is 32 bit).

  ///

  /// This graph type is fully conform to the \ref concepts::Graph

  /// "Graph" concept, and it also has an important extra feature

  /// that its maps are real \ref concepts::ReferenceMap

  /// "reference map"s.

  class HypercubeGraph : public ExtendedHypercubeGraphBase {

  public:

    typedef ExtendedHypercubeGraphBase Parent;

    /// \brief Constructs a hypercube graph with \c dim dimensions.

    ///

    /// Constructs a hypercube graph with \c dim dimensions.

    HypercubeGraph(int dim) { construct(dim); }

    /// \brief The number of dimensions.

    ///

    /// Gives back the number of dimensions.

    int dimension() const {

      return Parent::dimension();

    }

    /// \brief Returns \c true if the n'th bit of the node is one.

    ///

    /// Returns \c true if the n'th bit of the node is one.

    bool projection(Node node, int n) const {

      return Parent::projection(node, n);

    }

    /// \brief The dimension id of an edge.

    ///

    /// Gives back the dimension id of the given edge.

    /// It is in the [0..dim-1] range.

    int dimension(Edge edge) const {

      return Parent::dimension(edge);

    }

    /// \brief The dimension id of an arc.

    ///

    /// Gives back the dimension id of the given arc.

    /// It is in the [0..dim-1] range.

    int dimension(Arc arc) const {

      return Parent::dimension(arc);

    }

    /// \brief The index of a node.

    ///

    /// Gives back the index of the given node.

    /// The lower bits of the integer describes the node.

    int index(Node node) const {

      return Parent::index(node);

    }

    /// \brief Gives back a node by its index.

    ///

    /// Gives back a node by its index.

    Node operator()(int ix) const {

      return Parent::operator()(ix);

    }

    /// \brief Number of nodes.

    int nodeNum() const { return Parent::nodeNum(); }

    /// \brief Number of edges.

    int edgeNum() const { return Parent::edgeNum(); }

    /// \brief Number of arcs.

    int arcNum() const { return Parent::arcNum(); }

    /// \brief Linear combination map.

    ///

    /// This map makes possible to give back a linear combination

    /// for each node. It works like the \c std::accumulate function,

    /// so it accumulates the \c bf binary function with the \c fv first

    /// value. The map accumulates only on that positions (dimensions)

    /// where the index of the node is one. The values that have to be

    /// accumulated should be given by the \c begin and \c end iterators

    /// and the length of this range should be equal to the dimension

    /// number of the graph.

    ///

    ///\code

    /// const int DIM = 3;

    /// HypercubeGraph graph(DIM);

    /// dim2::Point<double> base[DIM];

    /// for (int k = 0; k < DIM; ++k) {

    ///   base[k].x = rnd();

    ///   base[k].y = rnd();

    /// }

    /// HypercubeGraph::HyperMap<dim2::Point<double> >

    ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));

    ///\endcode

    ///

    /// \see HypercubeGraph

    template <typename T, typename BF = std::plus<T> >

    class HyperMap {

    public:

      /// \brief The key type of the map

      typedef Node Key;

      /// \brief The value type of the map

      typedef T Value;

      /// \brief Constructor for HyperMap.

      ///

      /// Construct a HyperMap for the given graph. The values that have

      /// to be accumulated should be given by the \c begin and \c end

      /// iterators and the length of this range should be equal to the

      /// dimension number of the graph.

      ///

      /// This map accumulates the \c bf binary function with the \c fv

      /// first value on that positions (dimensions) where the index of

      /// the node is one.

      template <typename It>

      HyperMap(const Graph& graph, It begin, It end,

               T fv = 0, const BF& bf = BF())

        : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)

      {

        LEMON_ASSERT(_values.size() == graph.dimension(),

                     "Wrong size of range");

      }

      /// \brief The partial accumulated value.

      ///

      /// Gives back the partial accumulated value.

      Value operator[](const Key& k) const {

        Value val = _first_value;

        int id = _graph.index(k);

        int n = 0;

        while (id != 0) {

          if (id & 1) {

            val = _bin_func(val, _values[n]);

          }

          id >>= 1;

          ++n;

        }

        return val;

      }

    private:

      const Graph& _graph;

      std::vector<T> _values;

      T _first_value;

      BF _bin_func;

    };

  };

}

#endif