RhodeCode

/* -*- 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;

    }

  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 {

    }

    Node v(Edge edge) const {

    }

    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;

    }

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

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

      if (edge == INVALID) return INVALID;

      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);

      if (k < _dim) {

        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 = (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 = (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 {

    }

    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(); }

  check(!g.valid(n1), "Wrong validity check");

  check(g.valid(n2), "Wrong validity check");

  check(g.valid(n3), "Wrong validity check");

  check(!g.valid(e1), "Wrong validity check");

  check(g.valid(e2), "Wrong validity check");

  check(!g.valid(g.nodeFromId(-1)), "Wrong validity check");

  check(!g.valid(g.edgeFromId(-1)), "Wrong validity check");

  check(!g.valid(g.arcFromId(-1)), "Wrong validity check");

}

void checkGridGraph(int width, int height) {

  typedef GridGraph Graph;

  GRAPH_TYPEDEFS(Graph);

  Graph G(width, height);

  check(G.width() == width, "Wrong column number");

  check(G.height() == height, "Wrong row number");

  for (int i = 0; i < width; ++i) {

    for (int j = 0; j < height; ++j) {

      check(G.col(G(i, j)) == i, "Wrong column");

      check(G.row(G(i, j)) == j, "Wrong row");

      check(G.pos(G(i, j)).x == i, "Wrong column");

      check(G.pos(G(i, j)).y == j, "Wrong row");

    }

  }

  for (int j = 0; j < height; ++j) {

    for (int i = 0; i < width - 1; ++i) {

      check(G.source(G.right(G(i, j))) == G(i, j), "Wrong right");

      check(G.target(G.right(G(i, j))) == G(i + 1, j), "Wrong right");

    }

    check(G.right(G(width - 1, j)) == INVALID, "Wrong right");

  }

  for (int j = 0; j < height; ++j) {

    for (int i = 1; i < width; ++i) {

      check(G.source(G.left(G(i, j))) == G(i, j), "Wrong left");

      check(G.target(G.left(G(i, j))) == G(i - 1, j), "Wrong left");

    }

    check(G.left(G(0, j)) == INVALID, "Wrong left");

  }

  for (int i = 0; i < width; ++i) {

    for (int j = 0; j < height - 1; ++j) {

      check(G.source(G.up(G(i, j))) == G(i, j), "Wrong up");

      check(G.target(G.up(G(i, j))) == G(i, j + 1), "Wrong up");

    }

    check(G.up(G(i, height - 1)) == INVALID, "Wrong up");

  }

  for (int i = 0; i < width; ++i) {

    for (int j = 1; j < height; ++j) {

      check(G.source(G.down(G(i, j))) == G(i, j), "Wrong down");

      check(G.target(G.down(G(i, j))) == G(i, j - 1), "Wrong down");

    }

    check(G.down(G(i, 0)) == INVALID, "Wrong down");

  }

  checkGraphNodeList(G, width * height);

  checkGraphEdgeList(G, width * (height - 1) + (width - 1) * height);

  checkGraphArcList(G, 2 * (width * (height - 1) + (width - 1) * height));

  for (NodeIt n(G); n != INVALID; ++n) {

    int nb = 4;

    if (G.col(n) == 0) --nb;

    if (G.col(n) == width - 1) --nb;

    if (G.row(n) == 0) --nb;

    if (G.row(n) == height - 1) --nb;

    checkGraphOutArcList(G, n, nb);

    checkGraphInArcList(G, n, nb);

    checkGraphIncEdgeList(G, n, nb);

  }

  checkArcDirections(G);

  checkGraphConArcList(G, 2 * (width * (height - 1) + (width - 1) * height));

  checkGraphConEdgeList(G, width * (height - 1) + (width - 1) * height);

  checkNodeIds(G);

  checkArcIds(G);

  checkEdgeIds(G);

  checkGraphNodeMap(G);

  checkGraphArcMap(G);

  checkGraphEdgeMap(G);

}

void checkHypercubeGraph(int dim) {

  GRAPH_TYPEDEFS(HypercubeGraph);

  HypercubeGraph G(dim);

  checkGraphNodeList(G, 1 << dim);

  checkGraphArcList(G, dim * (1 << dim));

  Node n = G.nodeFromId(dim);

  for (NodeIt n(G); n != INVALID; ++n) {

    checkGraphIncEdgeList(G, n, dim);

    for (IncEdgeIt e(G, n); e != INVALID; ++e) {

      check( (G.u(e) == n &&

             (G.v(e) == n &&

             "Wrong edge or wrong dimension");

    }

    checkGraphOutArcList(G, n, dim);

    for (OutArcIt a(G, n); a != INVALID; ++a) {

      check(G.source(a) == n &&

            "Wrong arc or wrong dimension");

    }

    checkGraphInArcList(G, n, dim);

    for (InArcIt a(G, n); a != INVALID; ++a) {

      check(G.target(a) == n &&

            "Wrong arc or wrong dimension");

    }

  }

  checkGraphConArcList(G, (1 << dim) * dim);

  checkArcDirections(G);

  checkNodeIds(G);

  checkArcIds(G);

  checkEdgeIds(G);

  checkGraphNodeMap(G);

  checkGraphArcMap(G);

  checkGraphEdgeMap(G);

}

void checkGraphs() {

  { // Checking ListGraph

    checkGraph<ListGraph>();

    checkGraphValidityErase<ListGraph>();

  }

  { // Checking SmartGraph

    checkGraph<SmartGraph>();

    checkGraphValidity<SmartGraph>();

  }

  { // Checking FullGraph

    checkFullGraph(7);

    checkFullGraph(8);

  }

  { // Checking GridGraph

    checkGridGraph(5, 8);

    checkGridGraph(8, 5);

    checkGridGraph(5, 5);

    checkGridGraph(0, 0);

    checkGridGraph(1, 1);

  }

  { // Checking HypercubeGraph

    checkHypercubeGraph(1);

    checkHypercubeGraph(2);

    checkHypercubeGraph(3);

    checkHypercubeGraph(4);

  }

}

int main() {

  checkConcepts();

  checkGraphs();

  return 0;

}