DAGCycleDetector.h

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/**
 *
 *   Copyright (c) 2005-2021 by Pierre-Henri WUILLEMIN(@LIP6) & Christophe GONZALES(@AMU)
 *   info_at_agrum_dot_org
 *
 *  This library is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Lesser General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this library.  If not, see <http://www.gnu.org/licenses/>.
 *
 */


/** @file
 * @brief A class for detecting directed cycles in DAGs when trying to apply
 * many changes to the graph
 *
 * When trying to assess whether multiple changes applied to a given DAG would
 * induce cycles, use class DAGCycleDetector instead of trying to apply the
 * modifications to the DAG itself and check whether and exception is raised:
 * the class is designed to be fast for such modifications. However, the number
 * of modifications checked should be higher than at least 3 for this class to
 * be competitive.
 * @author Christophe GONZALES(@AMU) and Pierre-Henri WUILLEMIN(@LIP6)
 */
#ifndef GUM_DAG_CYCLE_DETECTOR_H
#define GUM_DAG_CYCLE_DETECTOR_H

#include <vector>

#include <agrum/tools/graphs/DAG.h>

namespace gum {

  /* ===========================================================================
   */
  // DAG CYCLE DETECTOR
  /* ===========================================================================
   */
  /** @class DAGCycleDetector
   * @ingroup graph_group
   * @brief A class for detecting directed cycles in DAGs when trying to apply
   * many changes to the graph
   *
   * When trying to assess whether multiple changes applied to a given DAG would
   * induce cycles, use class DAGCycleDetector instead of trying to apply the
   * modifications to the DAG itself and check whether and exception is raised:
   * the class is designed to be fast for such modifications. However, the
   *number
   * of modifications checked should be higher than at least 3 for this class to
   * be competitive.
   */
  class DAGCycleDetector {
    public:
    // the type of modification that can be applied to the graph
    enum class ChangeType
    {
      ARC_ADDITION,
      ARC_DELETION,
      ARC_REVERSAL
    };

    /// the base class indicating the possible changes
    class Change {
      public:
      Change(ChangeType type, NodeId tail, NodeId head) noexcept;
      Change(const Change& from) noexcept;
      Change(Change&& from) noexcept;
      virtual ~Change() noexcept;

      protected:
      Change& operator=(const Change& from) noexcept;
      Change& operator=(Change&& from) noexcept;

      public:
      // ##########################################################################
      /// @name Accessors/Modifiers
      // ##########################################################################
      /// @{

      /// returns the type of the operation
      ChangeType type() const noexcept;

      /// indicates the tail of the arc involved in the modification
      NodeId tail() const noexcept;

      /// indicates the head of the arc involved in the modification
      NodeId head() const noexcept;

      /// @}

      private:
      /// the type of modification
      ChangeType _type_;

      /// the tail of the arc to be modified
      NodeId _tail_;

      /// the head of the arc to be modified
      NodeId _head_;
    };

    /**
     * @class ArcAdd
     * @headerfile DAGCycleDetector.h <agrum/tools/graphs/DAGCycleDetector.h>
     * @brief the class to indicate that we wish to add a new arc
     * @ingroup graph_group
     */
    class ArcAdd: public Change {
      public:
      // ##########################################################################
      /// @name Constructors / Destructors
      // ##########################################################################
      /// @{
      /// default constructor
      ArcAdd(NodeId tail, NodeId head) noexcept;

      /// copy constructor
      ArcAdd(const ArcAdd& from) noexcept;

      /// move constructor
      ArcAdd(ArcAdd&& from) noexcept;

      /// destructor
      ~ArcAdd() noexcept;

      /// @}

      // ##########################################################################
      /// @name Operators
      // ##########################################################################
      /// @{

      /// copy operator
      ArcAdd& operator=(const ArcAdd& from) noexcept;

      /// move operator
      ArcAdd& operator=(ArcAdd&& from) noexcept;

      /// @}
    };

    /**
     * @class ArcDel
     * @headerfile DAGCycleDetector.h <agrum/tools/core/DAGCycleDetector.h>
     * @brief the class to indicate that we wish to remove an arc
     * @ingroup graph_group
     */
    class ArcDel: public Change {
      public:
      // ##########################################################################
      /// @name Constructors / Destructors
      // ##########################################################################
      /// @{
      /// default constructor
      ArcDel(NodeId tail, NodeId head) noexcept;

      /// copy constructor
      ArcDel(const ArcDel& from) noexcept;

      /// move constructor
      ArcDel(ArcDel&& from) noexcept;

      /// destructor
      ~ArcDel() noexcept;

      /// @}

      // ##########################################################################
      /// @name Operators
      // ##########################################################################
      /// @{

      /// copy operator
      ArcDel& operator=(const ArcDel& from) noexcept;

      /// move operator
      ArcDel& operator=(ArcDel&& from) noexcept;

      /// @}
    };

    /** @class ArcReverse
     * @headerfile DAGCycleDetector.h <agrum/tools/graphs/DAGCycleDetector.h>
     * @brief the class to indicate that we wish to reverse an arc
     * @ingroup graph_group
     */
    class ArcReverse: public Change {
      public:
      // ##########################################################################
      /// @name Constructors / Destructors
      // ##########################################################################
      /// @{
      /// default constructor
      ArcReverse(NodeId tail, NodeId head) noexcept;

      /// copy constructor
      ArcReverse(const ArcReverse& from) noexcept;

      /// move constructor
      ArcReverse(ArcReverse&& from) noexcept;

      /// destructor
      ~ArcReverse() noexcept;

      /// @}

      // ##########################################################################
      /// @name Operators
      // ##########################################################################
      /// @{

      /// copy operator
      ArcReverse& operator=(const ArcReverse& from) noexcept;

      /// move operator
      ArcReverse& operator=(ArcReverse&& from) noexcept;

      /// @}
    };

    // ############################################################################
    /// @name Constructors / Destructors
    // ############################################################################
    /// @{

    /// default constructor
    DAGCycleDetector() noexcept;

    /// copy constructor
    DAGCycleDetector(const DAGCycleDetector& from);

    /// move constructor
    DAGCycleDetector(DAGCycleDetector&& from);

    /// destructor
    ~DAGCycleDetector();

    /// @}

    // ############################################################################
    /// @name Operators
    // ############################################################################
    /// @{

    /// copy operator
    DAGCycleDetector& operator=(const DAGCycleDetector& from);

    /// move operator
    DAGCycleDetector& operator=(DAGCycleDetector&& from);

    /// check the equality between two DAGCycleDetectors
    /** used essentally for debugging purposes */
    bool operator==(const DAGCycleDetector& from) const;

    /// check the inequality between two DAGCycleDetectors
    /** used essentally for debugging purposes */
    bool operator!=(const DAGCycleDetector& from) const;

    /// @}

    // ############################################################################
    /// @name Accessors/Modifiers
    // ############################################################################
    /// @{

    /// sets the initial DAG from which changes shall be applied
    void setDAG(const DAG& dag);

    /// adds a new arc to the current DAG
    /** worst case complexity: O(h^2) where h is the height of the DAG
     * @throws InvalidDirectedCycle if the arc would create a cycle in the dag
     */
    void addArc(NodeId x, NodeId y);

    /// removes an arc from the current DAG
    /** worst case complexity: O(h^2) where h is the height of the DAG */
    void eraseArc(NodeId x, NodeId y);

    /// reverses an arc from the DAG
    /**  worst case complexity: O(h^2) where h is the height of the DAG
     * @throws InvalidDirectedCycle if the arc reversal would create a cycle
     * in the dag */
    void reverseArc(NodeId x, NodeId y);

    /// indicates whether an arc addition would create a cycle
    /** worst case complexity: O(1) */
    bool hasCycleFromAddition(NodeId x, NodeId y) const noexcept;

    /// indicates wether an arc reversal would create a cycle
    /** worst case complexity: O(1) */
    bool hasCycleFromReversal(NodeId x, NodeId y) const noexcept;

    /// indicates whether an arc deletion would create a cycle
    /** worst case complexity: O(1) */
    bool hasCycleFromDeletion(NodeId x, NodeId y) const noexcept;

    /// indicates whether a set of modifications would create a cycle
    /** the Boolean returned corresponds to the existence (or not) of a cycle
     * on the graph resulting from the whole sequence of modifications. This
     * means, for instance, that if, among modifs, there exists an arc (X,Y)
     * addition involving a cycle but also the same arc (X,Y) deletion, the
     * final
     * graph obtained does not contains a cycle (due to the deletion) and
     * the method will thus return false. */
    bool hasCycleFromModifications(const std::vector< Change >& modifs) const;

    /// @}

    private:
    /// the initial dag from which modifications are applied
    DiGraph _dag_;

    /// the set of ancestors of each node in the dag
    /** for each ancestor, we keep track of the number of paths leading to it */
    NodeProperty< NodeProperty< Size > > _ancestors_;

    /// the set of descendants of each node in the dag
    /** for each ancestor, we keep track of the number of paths leading to it */
    NodeProperty< NodeProperty< Size > > _descendants_;

    /// adds a weighted nodeset to another (weights are added)
    void _addWeightedSet_(NodeProperty< Size >&       nodeset,
                          const NodeProperty< Size >& set_to_add,
                          Size                        multiplier) const;

    /// removes a weighted nodeset from another (weights are subtracted)
    void _delWeightedSet_(NodeProperty< Size >&       nodeset,
                          const NodeProperty< Size >& set_to_del,
                          Size                        multiplier) const;

    /** @brief put into a weighted nodeset the nodes of another weighted set
     * that
     * belong to a set of arc extremities */
    void _restrictWeightedSet_(NodeProperty< Size >&       result_set,
                               const NodeProperty< Size >& set_to_restrict,
                               const NodeSet&              extrmities) const;
  };

} /* namespace gum */

#ifndef GUM_NO_INLINE
#  include <agrum/tools/graphs/algorithms/DAGCycleDetector_inl.h>
#endif   // GUM_NOINLINE

#endif   // GUM_DAG_CYCLE_DETECTOR_H