1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/hypercube_graph.h Thu Nov 06 14:40:32 2008 +0000
1.3 @@ -0,0 +1,439 @@
1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library.
1.7 + *
1.8 + * Copyright (C) 2003-2008
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef HYPERCUBE_GRAPH_H
1.23 +#define HYPERCUBE_GRAPH_H
1.24 +
1.25 +#include <vector>
1.26 +#include <lemon/core.h>
1.27 +#include <lemon/assert.h>
1.28 +#include <lemon/bits/graph_extender.h>
1.29 +
1.30 +///\ingroup graphs
1.31 +///\file
1.32 +///\brief HypercubeGraph class.
1.33 +
1.34 +namespace lemon {
1.35 +
1.36 + class HypercubeGraphBase {
1.37 +
1.38 + public:
1.39 +
1.40 + typedef HypercubeGraphBase Graph;
1.41 +
1.42 + class Node;
1.43 + class Edge;
1.44 + class Arc;
1.45 +
1.46 + public:
1.47 +
1.48 + HypercubeGraphBase() {}
1.49 +
1.50 + protected:
1.51 +
1.52 + void construct(int dim) {
1.53 + LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1.");
1.54 + _dim = dim;
1.55 + _node_num = 1 << dim;
1.56 + _edge_num = dim * (1 << dim-1);
1.57 + }
1.58 +
1.59 + public:
1.60 +
1.61 + typedef True NodeNumTag;
1.62 + typedef True EdgeNumTag;
1.63 + typedef True ArcNumTag;
1.64 +
1.65 + int nodeNum() const { return _node_num; }
1.66 + int edgeNum() const { return _edge_num; }
1.67 + int arcNum() const { return 2 * _edge_num; }
1.68 +
1.69 + int maxNodeId() const { return _node_num - 1; }
1.70 + int maxEdgeId() const { return _edge_num - 1; }
1.71 + int maxArcId() const { return 2 * _edge_num - 1; }
1.72 +
1.73 + static Node nodeFromId(int id) { return Node(id); }
1.74 + static Edge edgeFromId(int id) { return Edge(id); }
1.75 + static Arc arcFromId(int id) { return Arc(id); }
1.76 +
1.77 + static int id(Node node) { return node._id; }
1.78 + static int id(Edge edge) { return edge._id; }
1.79 + static int id(Arc arc) { return arc._id; }
1.80 +
1.81 + Node u(Edge edge) const {
1.82 + int base = edge._id & ((1 << _dim-1) - 1);
1.83 + int k = edge._id >> _dim-1;
1.84 + return ((base >> k) << k+1) | (base & ((1 << k) - 1));
1.85 + }
1.86 +
1.87 + Node v(Edge edge) const {
1.88 + int base = edge._id & ((1 << _dim-1) - 1);
1.89 + int k = edge._id >> _dim-1;
1.90 + return ((base >> k) << k+1) | (base & ((1 << k) - 1)) | (1 << k);
1.91 + }
1.92 +
1.93 + Node source(Arc arc) const {
1.94 + return (arc._id & 1) == 1 ? u(arc) : v(arc);
1.95 + }
1.96 +
1.97 + Node target(Arc arc) const {
1.98 + return (arc._id & 1) == 1 ? v(arc) : u(arc);
1.99 + }
1.100 +
1.101 + typedef True FindEdgeTag;
1.102 + typedef True FindArcTag;
1.103 +
1.104 + Edge findEdge(Node u, Node v, Edge prev = INVALID) const {
1.105 + if (prev != INVALID) return INVALID;
1.106 + int d = u._id ^ v._id;
1.107 + int k = 0;
1.108 + if (d == 0) return INVALID;
1.109 + for ( ; (d & 1) == 0; d >>= 1) ++k;
1.110 + if (d >> 1 != 0) return INVALID;
1.111 + return (k << _dim-1) | ((u._id >> k+1) << k) | (u._id & ((1 << k) - 1));
1.112 + }
1.113 +
1.114 + Arc findArc(Node u, Node v, Arc prev = INVALID) const {
1.115 + Edge edge = findEdge(u, v, prev);
1.116 + if (edge == INVALID) return INVALID;
1.117 + int k = edge._id >> _dim-1;
1.118 + return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1;
1.119 + }
1.120 +
1.121 + class Node {
1.122 + friend class HypercubeGraphBase;
1.123 +
1.124 + protected:
1.125 + int _id;
1.126 + Node(int id) : _id(id) {}
1.127 + public:
1.128 + Node() {}
1.129 + Node (Invalid) : _id(-1) {}
1.130 + bool operator==(const Node node) const {return _id == node._id;}
1.131 + bool operator!=(const Node node) const {return _id != node._id;}
1.132 + bool operator<(const Node node) const {return _id < node._id;}
1.133 + };
1.134 +
1.135 + class Edge {
1.136 + friend class HypercubeGraphBase;
1.137 + friend class Arc;
1.138 +
1.139 + protected:
1.140 + int _id;
1.141 +
1.142 + Edge(int id) : _id(id) {}
1.143 +
1.144 + public:
1.145 + Edge() {}
1.146 + Edge (Invalid) : _id(-1) {}
1.147 + bool operator==(const Edge edge) const {return _id == edge._id;}
1.148 + bool operator!=(const Edge edge) const {return _id != edge._id;}
1.149 + bool operator<(const Edge edge) const {return _id < edge._id;}
1.150 + };
1.151 +
1.152 + class Arc {
1.153 + friend class HypercubeGraphBase;
1.154 +
1.155 + protected:
1.156 + int _id;
1.157 +
1.158 + Arc(int id) : _id(id) {}
1.159 +
1.160 + public:
1.161 + Arc() {}
1.162 + Arc (Invalid) : _id(-1) {}
1.163 + operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; }
1.164 + bool operator==(const Arc arc) const {return _id == arc._id;}
1.165 + bool operator!=(const Arc arc) const {return _id != arc._id;}
1.166 + bool operator<(const Arc arc) const {return _id < arc._id;}
1.167 + };
1.168 +
1.169 + void first(Node& node) const {
1.170 + node._id = _node_num - 1;
1.171 + }
1.172 +
1.173 + static void next(Node& node) {
1.174 + --node._id;
1.175 + }
1.176 +
1.177 + void first(Edge& edge) const {
1.178 + edge._id = _edge_num - 1;
1.179 + }
1.180 +
1.181 + static void next(Edge& edge) {
1.182 + --edge._id;
1.183 + }
1.184 +
1.185 + void first(Arc& arc) const {
1.186 + arc._id = 2 * _edge_num - 1;
1.187 + }
1.188 +
1.189 + static void next(Arc& arc) {
1.190 + --arc._id;
1.191 + }
1.192 +
1.193 + void firstInc(Edge& edge, bool& dir, const Node& node) const {
1.194 + edge._id = node._id >> 1;
1.195 + dir = (node._id & 1) == 0;
1.196 + }
1.197 +
1.198 + void nextInc(Edge& edge, bool& dir) const {
1.199 + Node n = dir ? u(edge) : v(edge);
1.200 + int k = (edge._id >> _dim-1) + 1;
1.201 + if (k < _dim) {
1.202 + edge._id = (k << _dim-1) |
1.203 + ((n._id >> k+1) << k) | (n._id & ((1 << k) - 1));
1.204 + dir = ((n._id >> k) & 1) == 0;
1.205 + } else {
1.206 + edge._id = -1;
1.207 + dir = true;
1.208 + }
1.209 + }
1.210 +
1.211 + void firstOut(Arc& arc, const Node& node) const {
1.212 + arc._id = ((node._id >> 1) << 1) | (~node._id & 1);
1.213 + }
1.214 +
1.215 + void nextOut(Arc& arc) const {
1.216 + Node n = (arc._id & 1) == 1 ? u(arc) : v(arc);
1.217 + int k = (arc._id >> _dim) + 1;
1.218 + if (k < _dim) {
1.219 + arc._id = (k << _dim-1) |
1.220 + ((n._id >> k+1) << k) | (n._id & ((1 << k) - 1));
1.221 + arc._id = (arc._id << 1) | (~(n._id >> k) & 1);
1.222 + } else {
1.223 + arc._id = -1;
1.224 + }
1.225 + }
1.226 +
1.227 + void firstIn(Arc& arc, const Node& node) const {
1.228 + arc._id = ((node._id >> 1) << 1) | (node._id & 1);
1.229 + }
1.230 +
1.231 + void nextIn(Arc& arc) const {
1.232 + Node n = (arc._id & 1) == 1 ? v(arc) : u(arc);
1.233 + int k = (arc._id >> _dim) + 1;
1.234 + if (k < _dim) {
1.235 + arc._id = (k << _dim-1) |
1.236 + ((n._id >> k+1) << k) | (n._id & ((1 << k) - 1));
1.237 + arc._id = (arc._id << 1) | ((n._id >> k) & 1);
1.238 + } else {
1.239 + arc._id = -1;
1.240 + }
1.241 + }
1.242 +
1.243 + static bool direction(Arc arc) {
1.244 + return (arc._id & 1) == 1;
1.245 + }
1.246 +
1.247 + static Arc direct(Edge edge, bool dir) {
1.248 + return Arc((edge._id << 1) | (dir ? 1 : 0));
1.249 + }
1.250 +
1.251 + int dimension() const {
1.252 + return _dim;
1.253 + }
1.254 +
1.255 + bool projection(Node node, int n) const {
1.256 + return static_cast<bool>(node._id & (1 << n));
1.257 + }
1.258 +
1.259 + int dimension(Edge edge) const {
1.260 + return edge._id >> _dim-1;
1.261 + }
1.262 +
1.263 + int dimension(Arc arc) const {
1.264 + return arc._id >> _dim;
1.265 + }
1.266 +
1.267 + int index(Node node) const {
1.268 + return node._id;
1.269 + }
1.270 +
1.271 + Node operator()(int ix) const {
1.272 + return Node(ix);
1.273 + }
1.274 +
1.275 + private:
1.276 + int _dim;
1.277 + int _node_num, _edge_num;
1.278 + };
1.279 +
1.280 +
1.281 + typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase;
1.282 +
1.283 + /// \ingroup graphs
1.284 + ///
1.285 + /// \brief Hypercube graph class
1.286 + ///
1.287 + /// This class implements a special graph type. The nodes of the graph
1.288 + /// are indiced with integers with at most \c dim binary digits.
1.289 + /// Two nodes are connected in the graph if and only if their indices
1.290 + /// differ only on one position in the binary form.
1.291 + ///
1.292 + /// \note The type of the indices is chosen to \c int for efficiency
1.293 + /// reasons. Thus the maximum dimension of this implementation is 26
1.294 + /// (assuming that the size of \c int is 32 bit).
1.295 + ///
1.296 + /// This graph type is fully conform to the \ref concepts::Graph
1.297 + /// "Graph" concept, and it also has an important extra feature
1.298 + /// that its maps are real \ref concepts::ReferenceMap
1.299 + /// "reference map"s.
1.300 + class HypercubeGraph : public ExtendedHypercubeGraphBase {
1.301 + public:
1.302 +
1.303 + typedef ExtendedHypercubeGraphBase Parent;
1.304 +
1.305 + /// \brief Constructs a hypercube graph with \c dim dimensions.
1.306 + ///
1.307 + /// Constructs a hypercube graph with \c dim dimensions.
1.308 + HypercubeGraph(int dim) { construct(dim); }
1.309 +
1.310 + /// \brief The number of dimensions.
1.311 + ///
1.312 + /// Gives back the number of dimensions.
1.313 + int dimension() const {
1.314 + return Parent::dimension();
1.315 + }
1.316 +
1.317 + /// \brief Returns \c true if the n'th bit of the node is one.
1.318 + ///
1.319 + /// Returns \c true if the n'th bit of the node is one.
1.320 + bool projection(Node node, int n) const {
1.321 + return Parent::projection(node, n);
1.322 + }
1.323 +
1.324 + /// \brief The dimension id of an edge.
1.325 + ///
1.326 + /// Gives back the dimension id of the given edge.
1.327 + /// It is in the [0..dim-1] range.
1.328 + int dimension(Edge edge) const {
1.329 + return Parent::dimension(edge);
1.330 + }
1.331 +
1.332 + /// \brief The dimension id of an arc.
1.333 + ///
1.334 + /// Gives back the dimension id of the given arc.
1.335 + /// It is in the [0..dim-1] range.
1.336 + int dimension(Arc arc) const {
1.337 + return Parent::dimension(arc);
1.338 + }
1.339 +
1.340 + /// \brief The index of a node.
1.341 + ///
1.342 + /// Gives back the index of the given node.
1.343 + /// The lower bits of the integer describes the node.
1.344 + int index(Node node) const {
1.345 + return Parent::index(node);
1.346 + }
1.347 +
1.348 + /// \brief Gives back a node by its index.
1.349 + ///
1.350 + /// Gives back a node by its index.
1.351 + Node operator()(int ix) const {
1.352 + return Parent::operator()(ix);
1.353 + }
1.354 +
1.355 + /// \brief Number of nodes.
1.356 + int nodeNum() const { return Parent::nodeNum(); }
1.357 + /// \brief Number of edges.
1.358 + int edgeNum() const { return Parent::edgeNum(); }
1.359 + /// \brief Number of arcs.
1.360 + int arcNum() const { return Parent::arcNum(); }
1.361 +
1.362 + /// \brief Linear combination map.
1.363 + ///
1.364 + /// This map makes possible to give back a linear combination
1.365 + /// for each node. It works like the \c std::accumulate function,
1.366 + /// so it accumulates the \c bf binary function with the \c fv first
1.367 + /// value. The map accumulates only on that positions (dimensions)
1.368 + /// where the index of the node is one. The values that have to be
1.369 + /// accumulated should be given by the \c begin and \c end iterators
1.370 + /// and the length of this range should be equal to the dimension
1.371 + /// number of the graph.
1.372 + ///
1.373 + ///\code
1.374 + /// const int DIM = 3;
1.375 + /// HypercubeGraph graph(DIM);
1.376 + /// dim2::Point<double> base[DIM];
1.377 + /// for (int k = 0; k < DIM; ++k) {
1.378 + /// base[k].x = rnd();
1.379 + /// base[k].y = rnd();
1.380 + /// }
1.381 + /// HypercubeGraph::HyperMap<dim2::Point<double> >
1.382 + /// pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0));
1.383 + ///\endcode
1.384 + ///
1.385 + /// \see HypercubeGraph
1.386 + template <typename T, typename BF = std::plus<T> >
1.387 + class HyperMap {
1.388 + public:
1.389 +
1.390 + /// \brief The key type of the map
1.391 + typedef Node Key;
1.392 + /// \brief The value type of the map
1.393 + typedef T Value;
1.394 +
1.395 + /// \brief Constructor for HyperMap.
1.396 + ///
1.397 + /// Construct a HyperMap for the given graph. The values that have
1.398 + /// to be accumulated should be given by the \c begin and \c end
1.399 + /// iterators and the length of this range should be equal to the
1.400 + /// dimension number of the graph.
1.401 + ///
1.402 + /// This map accumulates the \c bf binary function with the \c fv
1.403 + /// first value on that positions (dimensions) where the index of
1.404 + /// the node is one.
1.405 + template <typename It>
1.406 + HyperMap(const Graph& graph, It begin, It end,
1.407 + T fv = 0, const BF& bf = BF())
1.408 + : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf)
1.409 + {
1.410 + LEMON_ASSERT(_values.size() == graph.dimension(),
1.411 + "Wrong size of range");
1.412 + }
1.413 +
1.414 + /// \brief The partial accumulated value.
1.415 + ///
1.416 + /// Gives back the partial accumulated value.
1.417 + Value operator[](const Key& k) const {
1.418 + Value val = _first_value;
1.419 + int id = _graph.index(k);
1.420 + int n = 0;
1.421 + while (id != 0) {
1.422 + if (id & 1) {
1.423 + val = _bin_func(val, _values[n]);
1.424 + }
1.425 + id >>= 1;
1.426 + ++n;
1.427 + }
1.428 + return val;
1.429 + }
1.430 +
1.431 + private:
1.432 + const Graph& _graph;
1.433 + std::vector<T> _values;
1.434 + T _first_value;
1.435 + BF _bin_func;
1.436 + };
1.437 +
1.438 + };
1.439 +
1.440 +}
1.441 +
1.442 +#endif