kpeter@364: /* -*- mode: C++; indent-tabs-mode: nil; -*-
kpeter@364:  *
kpeter@364:  * This file is a part of LEMON, a generic C++ optimization library.
kpeter@364:  *
alpar@440:  * Copyright (C) 2003-2009
kpeter@364:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@364:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@364:  *
kpeter@364:  * Permission to use, modify and distribute this software is granted
kpeter@364:  * provided that this copyright notice appears in all copies. For
kpeter@364:  * precise terms see the accompanying LICENSE file.
kpeter@364:  *
kpeter@364:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@364:  * express or implied, and with no claim as to its suitability for any
kpeter@364:  * purpose.
kpeter@364:  *
kpeter@364:  */
kpeter@364: 
kpeter@364: #ifndef HYPERCUBE_GRAPH_H
kpeter@364: #define HYPERCUBE_GRAPH_H
kpeter@364: 
kpeter@364: #include <vector>
kpeter@364: #include <lemon/core.h>
kpeter@365: #include <lemon/assert.h>
kpeter@364: #include <lemon/bits/graph_extender.h>
kpeter@364: 
kpeter@364: ///\ingroup graphs
kpeter@364: ///\file
kpeter@365: ///\brief HypercubeGraph class.
kpeter@364: 
kpeter@364: namespace lemon {
kpeter@364: 
kpeter@365:   class HypercubeGraphBase {
kpeter@364: 
kpeter@364:   public:
kpeter@364: 
kpeter@365:     typedef HypercubeGraphBase Graph;
kpeter@364: 
kpeter@364:     class Node;
kpeter@365:     class Edge;
kpeter@364:     class Arc;
kpeter@364: 
kpeter@364:   public:
kpeter@364: 
kpeter@365:     HypercubeGraphBase() {}
kpeter@364: 
kpeter@364:   protected:
kpeter@364: 
kpeter@364:     void construct(int dim) {
kpeter@365:       LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1.");
kpeter@364:       _dim = dim;
kpeter@365:       _node_num = 1 << dim;
alpar@372:       _edge_num = dim * (1 << (dim-1));
kpeter@364:     }
kpeter@364: 
kpeter@364:   public:
kpeter@364: 
kpeter@364:     typedef True NodeNumTag;
kpeter@365:     typedef True EdgeNumTag;
kpeter@364:     typedef True ArcNumTag;
kpeter@364: 
kpeter@365:     int nodeNum() const { return _node_num; }
kpeter@365:     int edgeNum() const { return _edge_num; }
kpeter@365:     int arcNum() const { return 2 * _edge_num; }
kpeter@364: 
kpeter@365:     int maxNodeId() const { return _node_num - 1; }
kpeter@365:     int maxEdgeId() const { return _edge_num - 1; }
kpeter@365:     int maxArcId() const { return 2 * _edge_num - 1; }
kpeter@364: 
kpeter@365:     static Node nodeFromId(int id) { return Node(id); }
kpeter@365:     static Edge edgeFromId(int id) { return Edge(id); }
kpeter@365:     static Arc arcFromId(int id) { return Arc(id); }
kpeter@365: 
kpeter@365:     static int id(Node node) { return node._id; }
kpeter@365:     static int id(Edge edge) { return edge._id; }
kpeter@365:     static int id(Arc arc) { return arc._id; }
kpeter@365: 
kpeter@365:     Node u(Edge edge) const {
alpar@372:       int base = edge._id & ((1 << (_dim-1)) - 1);
alpar@372:       int k = edge._id >> (_dim-1);
alpar@372:       return ((base >> k) << (k+1)) | (base & ((1 << k) - 1));
kpeter@364:     }
kpeter@364: 
kpeter@365:     Node v(Edge edge) const {
alpar@372:       int base = edge._id & ((1 << (_dim-1)) - 1);
alpar@372:       int k = edge._id >> (_dim-1);
alpar@372:       return ((base >> k) << (k+1)) | (base & ((1 << k) - 1)) | (1 << k);
kpeter@364:     }
kpeter@364: 
kpeter@365:     Node source(Arc arc) const {
kpeter@365:       return (arc._id & 1) == 1 ? u(arc) : v(arc);
kpeter@365:     }
kpeter@364: 
kpeter@365:     Node target(Arc arc) const {
kpeter@365:       return (arc._id & 1) == 1 ? v(arc) : u(arc);
kpeter@365:     }
kpeter@364: 
kpeter@365:     typedef True FindEdgeTag;
kpeter@365:     typedef True FindArcTag;
kpeter@365: 
kpeter@365:     Edge findEdge(Node u, Node v, Edge prev = INVALID) const {
kpeter@365:       if (prev != INVALID) return INVALID;
kpeter@365:       int d = u._id ^ v._id;
kpeter@365:       int k = 0;
kpeter@365:       if (d == 0) return INVALID;
kpeter@365:       for ( ; (d & 1) == 0; d >>= 1) ++k;
kpeter@365:       if (d >> 1 != 0) return INVALID;
alpar@372:       return (k << (_dim-1)) | ((u._id >> (k+1)) << k) |
alpar@372:         (u._id & ((1 << k) - 1));
kpeter@365:     }
kpeter@365: 
kpeter@365:     Arc findArc(Node u, Node v, Arc prev = INVALID) const {
kpeter@365:       Edge edge = findEdge(u, v, prev);
kpeter@365:       if (edge == INVALID) return INVALID;
alpar@372:       int k = edge._id >> (_dim-1);
kpeter@365:       return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;
kpeter@365:     }
kpeter@364: 
kpeter@364:     class Node {
kpeter@365:       friend class HypercubeGraphBase;
kpeter@365: 
kpeter@364:     protected:
kpeter@365:       int _id;
kpeter@365:       Node(int id) : _id(id) {}
kpeter@364:     public:
kpeter@364:       Node() {}
kpeter@365:       Node (Invalid) : _id(-1) {}
kpeter@365:       bool operator==(const Node node) const {return _id == node._id;}
kpeter@365:       bool operator!=(const Node node) const {return _id != node._id;}
kpeter@365:       bool operator<(const Node node) const {return _id < node._id;}
kpeter@365:     };
kpeter@365: 
kpeter@365:     class Edge {
kpeter@365:       friend class HypercubeGraphBase;
kpeter@365:       friend class Arc;
kpeter@365: 
kpeter@365:     protected:
kpeter@365:       int _id;
kpeter@365: 
kpeter@365:       Edge(int id) : _id(id) {}
kpeter@365: 
kpeter@365:     public:
kpeter@365:       Edge() {}
kpeter@365:       Edge (Invalid) : _id(-1) {}
kpeter@365:       bool operator==(const Edge edge) const {return _id == edge._id;}
kpeter@365:       bool operator!=(const Edge edge) const {return _id != edge._id;}
kpeter@365:       bool operator<(const Edge edge) const {return _id < edge._id;}
kpeter@364:     };
kpeter@364: 
kpeter@364:     class Arc {
kpeter@365:       friend class HypercubeGraphBase;
kpeter@365: 
kpeter@364:     protected:
kpeter@365:       int _id;
kpeter@365: 
kpeter@365:       Arc(int id) : _id(id) {}
kpeter@365: 
kpeter@364:     public:
kpeter@365:       Arc() {}
kpeter@365:       Arc (Invalid) : _id(-1) {}
kpeter@365:       operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }
kpeter@365:       bool operator==(const Arc arc) const {return _id == arc._id;}
kpeter@365:       bool operator!=(const Arc arc) const {return _id != arc._id;}
kpeter@365:       bool operator<(const Arc arc) const {return _id < arc._id;}
kpeter@364:     };
kpeter@364: 
kpeter@364:     void first(Node& node) const {
kpeter@365:       node._id = _node_num - 1;
kpeter@364:     }
kpeter@364: 
kpeter@364:     static void next(Node& node) {
kpeter@365:       --node._id;
kpeter@365:     }
kpeter@365: 
kpeter@365:     void first(Edge& edge) const {
kpeter@365:       edge._id = _edge_num - 1;
kpeter@365:     }
kpeter@365: 
kpeter@365:     static void next(Edge& edge) {
kpeter@365:       --edge._id;
kpeter@364:     }
kpeter@364: 
kpeter@364:     void first(Arc& arc) const {
kpeter@365:       arc._id = 2 * _edge_num - 1;
kpeter@364:     }
kpeter@364: 
kpeter@364:     static void next(Arc& arc) {
kpeter@365:       --arc._id;
kpeter@365:     }
kpeter@365: 
kpeter@365:     void firstInc(Edge& edge, bool& dir, const Node& node) const {
kpeter@365:       edge._id = node._id >> 1;
kpeter@365:       dir = (node._id & 1) == 0;
kpeter@365:     }
kpeter@365: 
kpeter@365:     void nextInc(Edge& edge, bool& dir) const {
kpeter@365:       Node n = dir ? u(edge) : v(edge);
alpar@372:       int k = (edge._id >> (_dim-1)) + 1;
kpeter@365:       if (k < _dim) {
alpar@372:         edge._id = (k << (_dim-1)) |
alpar@372:           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
kpeter@365:         dir = ((n._id >> k) & 1) == 0;
kpeter@365:       } else {
kpeter@365:         edge._id = -1;
kpeter@365:         dir = true;
kpeter@365:       }
kpeter@364:     }
kpeter@364: 
kpeter@364:     void firstOut(Arc& arc, const Node& node) const {
kpeter@365:       arc._id = ((node._id >> 1) << 1) | (~node._id & 1);
kpeter@364:     }
kpeter@364: 
kpeter@364:     void nextOut(Arc& arc) const {
kpeter@365:       Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);
kpeter@365:       int k = (arc._id >> _dim) + 1;
kpeter@365:       if (k < _dim) {
alpar@372:         arc._id = (k << (_dim-1)) |
alpar@372:           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
kpeter@365:         arc._id = (arc._id << 1) | (~(n._id >> k) & 1);
kpeter@365:       } else {
kpeter@365:         arc._id = -1;
kpeter@365:       }
kpeter@364:     }
kpeter@364: 
kpeter@364:     void firstIn(Arc& arc, const Node& node) const {
kpeter@365:       arc._id = ((node._id >> 1) << 1) | (node._id & 1);
kpeter@364:     }
kpeter@364: 
kpeter@364:     void nextIn(Arc& arc) const {
kpeter@365:       Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);
kpeter@365:       int k = (arc._id >> _dim) + 1;
kpeter@365:       if (k < _dim) {
alpar@372:         arc._id = (k << (_dim-1)) |
alpar@372:           ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1));
kpeter@365:         arc._id = (arc._id << 1) | ((n._id >> k) & 1);
kpeter@364:       } else {
kpeter@365:         arc._id = -1;
kpeter@364:       }
kpeter@364:     }
kpeter@364: 
kpeter@365:     static bool direction(Arc arc) {
kpeter@365:       return (arc._id & 1) == 1;
kpeter@365:     }
kpeter@365: 
kpeter@365:     static Arc direct(Edge edge, bool dir) {
kpeter@365:       return Arc((edge._id << 1) | (dir ? 1 : 0));
kpeter@365:     }
kpeter@365: 
kpeter@364:     int dimension() const {
kpeter@364:       return _dim;
kpeter@364:     }
kpeter@364: 
kpeter@364:     bool projection(Node node, int n) const {
kpeter@365:       return static_cast<bool>(node._id & (1 << n));
kpeter@365:     }
kpeter@365: 
kpeter@365:     int dimension(Edge edge) const {
alpar@372:       return edge._id >> (_dim-1);
kpeter@364:     }
kpeter@364: 
kpeter@364:     int dimension(Arc arc) const {
kpeter@365:       return arc._id >> _dim;
kpeter@364:     }
kpeter@364: 
kpeter@778:     static int index(Node node) {
kpeter@365:       return node._id;
kpeter@364:     }
kpeter@364: 
kpeter@364:     Node operator()(int ix) const {
kpeter@364:       return Node(ix);
kpeter@364:     }
kpeter@364: 
kpeter@364:   private:
kpeter@365:     int _dim;
kpeter@365:     int _node_num, _edge_num;
kpeter@364:   };
kpeter@364: 
kpeter@364: 
kpeter@365:   typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;
kpeter@364: 
kpeter@365:   /// \ingroup graphs
kpeter@364:   ///
kpeter@365:   /// \brief Hypercube graph class
kpeter@364:   ///
kpeter@735:   /// HypercubeGraph implements a special graph type. The nodes of the
kpeter@735:   /// graph are indexed with integers having at most \c dim binary digits.
kpeter@365:   /// Two nodes are connected in the graph if and only if their indices
kpeter@365:   /// differ only on one position in the binary form.
kpeter@735:   /// This class is completely static and it needs constant memory space.
kpeter@737:   /// Thus you can neither add nor delete nodes or edges, however 
kpeter@737:   /// the structure can be resized using resize().
kpeter@735:   ///
kpeter@735:   /// This type fully conforms to the \ref concepts::Graph "Graph concept".
kpeter@735:   /// Most of its member functions and nested classes are documented
kpeter@735:   /// only in the concept class.
kpeter@364:   ///
kpeter@787:   /// This class provides constant time counting for nodes, edges and arcs.
kpeter@787:   ///
kpeter@365:   /// \note The type of the indices is chosen to \c int for efficiency
kpeter@365:   /// reasons. Thus the maximum dimension of this implementation is 26
kpeter@365:   /// (assuming that the size of \c int is 32 bit).
kpeter@365:   class HypercubeGraph : public ExtendedHypercubeGraphBase {
kpeter@617:     typedef ExtendedHypercubeGraphBase Parent;
kpeter@617: 
kpeter@364:   public:
kpeter@364: 
kpeter@365:     /// \brief Constructs a hypercube graph with \c dim dimensions.
kpeter@364:     ///
kpeter@365:     /// Constructs a hypercube graph with \c dim dimensions.
kpeter@365:     HypercubeGraph(int dim) { construct(dim); }
kpeter@364: 
kpeter@737:     /// \brief Resizes the graph
kpeter@737:     ///
kpeter@737:     /// This function resizes the graph. It fully destroys and
kpeter@737:     /// rebuilds the structure, therefore the maps of the graph will be
kpeter@737:     /// reallocated automatically and the previous values will be lost.
kpeter@737:     void resize(int dim) {
kpeter@737:       Parent::notifier(Arc()).clear();
kpeter@737:       Parent::notifier(Edge()).clear();
kpeter@737:       Parent::notifier(Node()).clear();
kpeter@737:       construct(dim);
kpeter@737:       Parent::notifier(Node()).build();
kpeter@737:       Parent::notifier(Edge()).build();
kpeter@737:       Parent::notifier(Arc()).build();
kpeter@737:     }
kpeter@737: 
kpeter@365:     /// \brief The number of dimensions.
kpeter@364:     ///
kpeter@365:     /// Gives back the number of dimensions.
kpeter@364:     int dimension() const {
kpeter@364:       return Parent::dimension();
kpeter@364:     }
kpeter@364: 
kpeter@365:     /// \brief Returns \c true if the n'th bit of the node is one.
kpeter@364:     ///
kpeter@365:     /// Returns \c true if the n'th bit of the node is one.
kpeter@364:     bool projection(Node node, int n) const {
kpeter@364:       return Parent::projection(node, n);
kpeter@364:     }
kpeter@364: 
kpeter@365:     /// \brief The dimension id of an edge.
kpeter@364:     ///
kpeter@365:     /// Gives back the dimension id of the given edge.
kpeter@735:     /// It is in the range <tt>[0..dim-1]</tt>.
kpeter@365:     int dimension(Edge edge) const {
kpeter@365:       return Parent::dimension(edge);
kpeter@365:     }
kpeter@365: 
kpeter@365:     /// \brief The dimension id of an arc.
kpeter@365:     ///
kpeter@365:     /// Gives back the dimension id of the given arc.
kpeter@735:     /// It is in the range <tt>[0..dim-1]</tt>.
kpeter@364:     int dimension(Arc arc) const {
kpeter@364:       return Parent::dimension(arc);
kpeter@364:     }
kpeter@364: 
kpeter@365:     /// \brief The index of a node.
kpeter@364:     ///
kpeter@365:     /// Gives back the index of the given node.
kpeter@365:     /// The lower bits of the integer describes the node.
kpeter@778:     static int index(Node node) {
kpeter@364:       return Parent::index(node);
kpeter@364:     }
kpeter@364: 
kpeter@365:     /// \brief Gives back a node by its index.
kpeter@364:     ///
kpeter@365:     /// Gives back a node by its index.
kpeter@364:     Node operator()(int ix) const {
kpeter@364:       return Parent::operator()(ix);
kpeter@364:     }
kpeter@364: 
kpeter@364:     /// \brief Number of nodes.
kpeter@364:     int nodeNum() const { return Parent::nodeNum(); }
kpeter@365:     /// \brief Number of edges.
kpeter@365:     int edgeNum() const { return Parent::edgeNum(); }
kpeter@364:     /// \brief Number of arcs.
kpeter@364:     int arcNum() const { return Parent::arcNum(); }
kpeter@364: 
kpeter@364:     /// \brief Linear combination map.
kpeter@364:     ///
kpeter@365:     /// This map makes possible to give back a linear combination
kpeter@365:     /// for each node. It works like the \c std::accumulate function,
kpeter@365:     /// so it accumulates the \c bf binary function with the \c fv first
kpeter@365:     /// value. The map accumulates only on that positions (dimensions)
kpeter@365:     /// where the index of the node is one. The values that have to be
kpeter@365:     /// accumulated should be given by the \c begin and \c end iterators
kpeter@365:     /// and the length of this range should be equal to the dimension
kpeter@365:     /// number of the graph.
kpeter@364:     ///
kpeter@364:     ///\code
kpeter@364:     /// const int DIM = 3;
kpeter@365:     /// HypercubeGraph graph(DIM);
kpeter@364:     /// dim2::Point<double> base[DIM];
kpeter@364:     /// for (int k = 0; k < DIM; ++k) {
kpeter@364:     ///   base[k].x = rnd();
kpeter@364:     ///   base[k].y = rnd();
kpeter@364:     /// }
kpeter@365:     /// HypercubeGraph::HyperMap<dim2::Point<double> >
kpeter@365:     ///   pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
kpeter@364:     ///\endcode
kpeter@364:     ///
kpeter@365:     /// \see HypercubeGraph
kpeter@364:     template <typename T, typename BF = std::plus<T> >
kpeter@364:     class HyperMap {
kpeter@364:     public:
kpeter@364: 
kpeter@365:       /// \brief The key type of the map
kpeter@364:       typedef Node Key;
kpeter@365:       /// \brief The value type of the map
kpeter@364:       typedef T Value;
kpeter@364: 
kpeter@364:       /// \brief Constructor for HyperMap.
kpeter@364:       ///
kpeter@365:       /// Construct a HyperMap for the given graph. The values that have
kpeter@365:       /// to be accumulated should be given by the \c begin and \c end
kpeter@365:       /// iterators and the length of this range should be equal to the
kpeter@365:       /// dimension number of the graph.
kpeter@364:       ///
kpeter@365:       /// This map accumulates the \c bf binary function with the \c fv
kpeter@365:       /// first value on that positions (dimensions) where the index of
kpeter@365:       /// the node is one.
kpeter@364:       template <typename It>
kpeter@365:       HyperMap(const Graph& graph, It begin, It end,
kpeter@365:                T fv = 0, const BF& bf = BF())
kpeter@365:         : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)
kpeter@364:       {
kpeter@365:         LEMON_ASSERT(_values.size() == graph.dimension(),
kpeter@365:                      "Wrong size of range");
kpeter@364:       }
kpeter@364: 
kpeter@365:       /// \brief The partial accumulated value.
kpeter@364:       ///
kpeter@364:       /// Gives back the partial accumulated value.
kpeter@365:       Value operator[](const Key& k) const {
kpeter@364:         Value val = _first_value;
kpeter@364:         int id = _graph.index(k);
kpeter@364:         int n = 0;
kpeter@364:         while (id != 0) {
kpeter@364:           if (id & 1) {
kpeter@364:             val = _bin_func(val, _values[n]);
kpeter@364:           }
kpeter@364:           id >>= 1;
kpeter@364:           ++n;
kpeter@364:         }
kpeter@364:         return val;
kpeter@364:       }
kpeter@364: 
kpeter@364:     private:
kpeter@365:       const Graph& _graph;
kpeter@364:       std::vector<T> _values;
kpeter@364:       T _first_value;
kpeter@364:       BF _bin_func;
kpeter@364:     };
kpeter@364: 
kpeter@364:   };
kpeter@364: 
kpeter@364: }
kpeter@364: 
kpeter@364: #endif