lemon/matching.h
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 05 Nov 2009 10:01:02 +0100
changeset 779 c160bf9f18ef
parent 594 d657c71db7db
child 867 5b926cc36a4b
child 868 0513ccfea967
permissions -rw-r--r--
Merge
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2009
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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#ifndef LEMON_MAX_MATCHING_H
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#define LEMON_MAX_MATCHING_H
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#include <vector>
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#include <queue>
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#include <set>
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#include <limits>
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#include <lemon/core.h>
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#include <lemon/unionfind.h>
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#include <lemon/bin_heap.h>
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#include <lemon/maps.h>
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///\ingroup matching
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///\file
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///\brief Maximum matching algorithms in general graphs.
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namespace lemon {
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  /// \ingroup matching
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  ///
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  /// \brief Maximum cardinality matching in general graphs
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  ///
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  /// This class implements Edmonds' alternating forest matching algorithm
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  /// for finding a maximum cardinality matching in a general undirected graph.
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  /// It can be started from an arbitrary initial matching 
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  /// (the default is the empty one).
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  ///
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  /// The dual solution of the problem is a map of the nodes to
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  /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D),
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  /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds
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  /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph
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  /// with factor-critical components, the nodes in \c ODD/A form the
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  /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having
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  /// a perfect matching. The number of the factor-critical components
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  /// minus the number of barrier nodes is a lower bound on the
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  /// unmatched nodes, and the matching is optimal if and only if this bound is
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  /// tight. This decomposition can be obtained using \ref status() or
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  /// \ref statusMap() after running the algorithm.
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  ///
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  /// \tparam GR The undirected graph type the algorithm runs on.
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  template <typename GR>
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  class MaxMatching {
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  public:
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    /// The graph type of the algorithm
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    typedef GR Graph;
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    /// The type of the matching map
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    typedef typename Graph::template NodeMap<typename Graph::Arc>
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    MatchingMap;
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    ///\brief Status constants for Gallai-Edmonds decomposition.
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    ///
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    ///These constants are used for indicating the Gallai-Edmonds 
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    ///decomposition of a graph. The nodes with status \c EVEN (or \c D)
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    ///induce a subgraph with factor-critical components, the nodes with
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    ///status \c ODD (or \c A) form the canonical barrier, and the nodes
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    ///with status \c MATCHED (or \c C) induce a subgraph having a 
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    ///perfect matching.
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    enum Status {
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      EVEN = 1,       ///< = 1. (\c D is an alias for \c EVEN.)
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      D = 1,
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      MATCHED = 0,    ///< = 0. (\c C is an alias for \c MATCHED.)
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      C = 0,
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      ODD = -1,       ///< = -1. (\c A is an alias for \c ODD.)
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      A = -1,
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      UNMATCHED = -2  ///< = -2.
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    };
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    /// The type of the status map
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    typedef typename Graph::template NodeMap<Status> StatusMap;
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  private:
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    TEMPLATE_GRAPH_TYPEDEFS(Graph);
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    typedef UnionFindEnum<IntNodeMap> BlossomSet;
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    typedef ExtendFindEnum<IntNodeMap> TreeSet;
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    typedef RangeMap<Node> NodeIntMap;
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    typedef MatchingMap EarMap;
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    typedef std::vector<Node> NodeQueue;
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    const Graph& _graph;
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    MatchingMap* _matching;
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    StatusMap* _status;
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    EarMap* _ear;
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    IntNodeMap* _blossom_set_index;
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    BlossomSet* _blossom_set;
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    NodeIntMap* _blossom_rep;
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    IntNodeMap* _tree_set_index;
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    TreeSet* _tree_set;
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    NodeQueue _node_queue;
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    int _process, _postpone, _last;
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    int _node_num;
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  private:
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    void createStructures() {
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      _node_num = countNodes(_graph);
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      if (!_matching) {
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        _matching = new MatchingMap(_graph);
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      }
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      if (!_status) {
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        _status = new StatusMap(_graph);
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      }
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      if (!_ear) {
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        _ear = new EarMap(_graph);
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      }
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      if (!_blossom_set) {
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        _blossom_set_index = new IntNodeMap(_graph);
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        _blossom_set = new BlossomSet(*_blossom_set_index);
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      }
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      if (!_blossom_rep) {
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        _blossom_rep = new NodeIntMap(_node_num);
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      }
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      if (!_tree_set) {
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        _tree_set_index = new IntNodeMap(_graph);
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        _tree_set = new TreeSet(*_tree_set_index);
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      }
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      _node_queue.resize(_node_num);
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    }
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    void destroyStructures() {
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      if (_matching) {
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        delete _matching;
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      }
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      if (_status) {
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        delete _status;
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      }
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      if (_ear) {
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        delete _ear;
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      }
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      if (_blossom_set) {
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        delete _blossom_set;
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        delete _blossom_set_index;
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      }
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      if (_blossom_rep) {
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        delete _blossom_rep;
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      }
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      if (_tree_set) {
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        delete _tree_set_index;
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        delete _tree_set;
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      }
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    }
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    void processDense(const Node& n) {
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      _process = _postpone = _last = 0;
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      _node_queue[_last++] = n;
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      while (_process != _last) {
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        Node u = _node_queue[_process++];
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        for (OutArcIt a(_graph, u); a != INVALID; ++a) {
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          Node v = _graph.target(a);
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          if ((*_status)[v] == MATCHED) {
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            extendOnArc(a);
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          } else if ((*_status)[v] == UNMATCHED) {
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            augmentOnArc(a);
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            return;
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          }
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        }
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      }
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      while (_postpone != _last) {
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        Node u = _node_queue[_postpone++];
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        for (OutArcIt a(_graph, u); a != INVALID ; ++a) {
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          Node v = _graph.target(a);
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          if ((*_status)[v] == EVEN) {
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            if (_blossom_set->find(u) != _blossom_set->find(v)) {
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              shrinkOnEdge(a);
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            }
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          }
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          while (_process != _last) {
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            Node w = _node_queue[_process++];
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            for (OutArcIt b(_graph, w); b != INVALID; ++b) {
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              Node x = _graph.target(b);
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              if ((*_status)[x] == MATCHED) {
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                extendOnArc(b);
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              } else if ((*_status)[x] == UNMATCHED) {
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                augmentOnArc(b);
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                return;
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              }
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            }
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          }
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        }
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      }
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    }
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    void processSparse(const Node& n) {
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      _process = _last = 0;
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      _node_queue[_last++] = n;
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      while (_process != _last) {
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        Node u = _node_queue[_process++];
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        for (OutArcIt a(_graph, u); a != INVALID; ++a) {
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          Node v = _graph.target(a);
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          if ((*_status)[v] == EVEN) {
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            if (_blossom_set->find(u) != _blossom_set->find(v)) {
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              shrinkOnEdge(a);
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            }
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          } else if ((*_status)[v] == MATCHED) {
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            extendOnArc(a);
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          } else if ((*_status)[v] == UNMATCHED) {
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            augmentOnArc(a);
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            return;
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          }
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        }
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      }
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    }
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    void shrinkOnEdge(const Edge& e) {
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      Node nca = INVALID;
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      {
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        std::set<Node> left_set, right_set;
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        Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))];
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        left_set.insert(left);
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        Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))];
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        right_set.insert(right);
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        while (true) {
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          if ((*_matching)[left] == INVALID) break;
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          left = _graph.target((*_matching)[left]);
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          left = (*_blossom_rep)[_blossom_set->
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                                 find(_graph.target((*_ear)[left]))];
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          if (right_set.find(left) != right_set.end()) {
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            nca = left;
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            break;
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          }
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          left_set.insert(left);
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          if ((*_matching)[right] == INVALID) break;
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          right = _graph.target((*_matching)[right]);
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          right = (*_blossom_rep)[_blossom_set->
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                                  find(_graph.target((*_ear)[right]))];
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          if (left_set.find(right) != left_set.end()) {
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            nca = right;
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            break;
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          }
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          right_set.insert(right);
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        }
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        if (nca == INVALID) {
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          if ((*_matching)[left] == INVALID) {
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            nca = right;
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            while (left_set.find(nca) == left_set.end()) {
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              nca = _graph.target((*_matching)[nca]);
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              nca =(*_blossom_rep)[_blossom_set->
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                                   find(_graph.target((*_ear)[nca]))];
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            }
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          } else {
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            nca = left;
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            while (right_set.find(nca) == right_set.end()) {
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              nca = _graph.target((*_matching)[nca]);
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              nca = (*_blossom_rep)[_blossom_set->
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                                   find(_graph.target((*_ear)[nca]))];
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            }
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          }
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        }
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      }
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      {
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        Node node = _graph.u(e);
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        Arc arc = _graph.direct(e, true);
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        Node base = (*_blossom_rep)[_blossom_set->find(node)];
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        while (base != nca) {
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          (*_ear)[node] = arc;
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          Node n = node;
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          while (n != base) {
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            n = _graph.target((*_matching)[n]);
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            Arc a = (*_ear)[n];
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            n = _graph.target(a);
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            (*_ear)[n] = _graph.oppositeArc(a);
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          }
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          node = _graph.target((*_matching)[base]);
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          _tree_set->erase(base);
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          _tree_set->erase(node);
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          _blossom_set->insert(node, _blossom_set->find(base));
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          (*_status)[node] = EVEN;
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          _node_queue[_last++] = node;
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          arc = _graph.oppositeArc((*_ear)[node]);
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          node = _graph.target((*_ear)[node]);
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          base = (*_blossom_rep)[_blossom_set->find(node)];
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          _blossom_set->join(_graph.target(arc), base);
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        }
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      }
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      (*_blossom_rep)[_blossom_set->find(nca)] = nca;
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      {
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        Node node = _graph.v(e);
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        Arc arc = _graph.direct(e, false);
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        Node base = (*_blossom_rep)[_blossom_set->find(node)];
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        while (base != nca) {
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          (*_ear)[node] = arc;
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          Node n = node;
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          while (n != base) {
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            n = _graph.target((*_matching)[n]);
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            Arc a = (*_ear)[n];
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            n = _graph.target(a);
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            (*_ear)[n] = _graph.oppositeArc(a);
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          }
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          node = _graph.target((*_matching)[base]);
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          _tree_set->erase(base);
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          _tree_set->erase(node);
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          _blossom_set->insert(node, _blossom_set->find(base));
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          (*_status)[node] = EVEN;
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          _node_queue[_last++] = node;
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          arc = _graph.oppositeArc((*_ear)[node]);
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          node = _graph.target((*_ear)[node]);
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          base = (*_blossom_rep)[_blossom_set->find(node)];
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          _blossom_set->join(_graph.target(arc), base);
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        }
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      }
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      (*_blossom_rep)[_blossom_set->find(nca)] = nca;
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    }
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    void extendOnArc(const Arc& a) {
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      Node base = _graph.source(a);
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      Node odd = _graph.target(a);
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      (*_ear)[odd] = _graph.oppositeArc(a);
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      Node even = _graph.target((*_matching)[odd]);
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      (*_blossom_rep)[_blossom_set->insert(even)] = even;
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      (*_status)[odd] = ODD;
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      (*_status)[even] = EVEN;
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      int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]);
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      _tree_set->insert(odd, tree);
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      _tree_set->insert(even, tree);
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      _node_queue[_last++] = even;
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    }
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    void augmentOnArc(const Arc& a) {
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      Node even = _graph.source(a);
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      Node odd = _graph.target(a);
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      int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]);
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      (*_matching)[odd] = _graph.oppositeArc(a);
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      (*_status)[odd] = MATCHED;
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      Arc arc = (*_matching)[even];
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      (*_matching)[even] = a;
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      while (arc != INVALID) {
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        odd = _graph.target(arc);
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        arc = (*_ear)[odd];
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        even = _graph.target(arc);
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        (*_matching)[odd] = arc;
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        arc = (*_matching)[even];
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        (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]);
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      }
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      for (typename TreeSet::ItemIt it(*_tree_set, tree);
deba@327
   390
           it != INVALID; ++it) {
deba@327
   391
        if ((*_status)[it] == ODD) {
kpeter@581
   392
          (*_status)[it] = MATCHED;
deba@327
   393
        } else {
deba@327
   394
          int blossom = _blossom_set->find(it);
deba@327
   395
          for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom);
deba@327
   396
               jt != INVALID; ++jt) {
kpeter@581
   397
            (*_status)[jt] = MATCHED;
deba@327
   398
          }
deba@327
   399
          _blossom_set->eraseClass(blossom);
deba@327
   400
        }
deba@327
   401
      }
deba@327
   402
      _tree_set->eraseClass(tree);
deba@327
   403
deba@327
   404
    }
deba@326
   405
deba@326
   406
  public:
deba@326
   407
deba@327
   408
    /// \brief Constructor
deba@326
   409
    ///
deba@327
   410
    /// Constructor.
deba@327
   411
    MaxMatching(const Graph& graph)
deba@327
   412
      : _graph(graph), _matching(0), _status(0), _ear(0),
deba@327
   413
        _blossom_set_index(0), _blossom_set(0), _blossom_rep(0),
deba@327
   414
        _tree_set_index(0), _tree_set(0) {}
deba@327
   415
deba@327
   416
    ~MaxMatching() {
deba@327
   417
      destroyStructures();
deba@327
   418
    }
deba@327
   419
kpeter@590
   420
    /// \name Execution Control
alpar@330
   421
    /// The simplest way to execute the algorithm is to use the
kpeter@590
   422
    /// \c run() member function.\n
kpeter@590
   423
    /// If you need better control on the execution, you have to call
kpeter@590
   424
    /// one of the functions \ref init(), \ref greedyInit() or
kpeter@590
   425
    /// \ref matchingInit() first, then you can start the algorithm with
kpeter@590
   426
    /// \ref startSparse() or \ref startDense().
deba@327
   427
deba@327
   428
    ///@{
deba@327
   429
kpeter@590
   430
    /// \brief Set the initial matching to the empty matching.
deba@326
   431
    ///
kpeter@590
   432
    /// This function sets the initial matching to the empty matching.
deba@326
   433
    void init() {
deba@327
   434
      createStructures();
deba@327
   435
      for(NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581
   436
        (*_matching)[n] = INVALID;
kpeter@581
   437
        (*_status)[n] = UNMATCHED;
deba@326
   438
      }
deba@326
   439
    }
deba@326
   440
kpeter@590
   441
    /// \brief Find an initial matching in a greedy way.
deba@326
   442
    ///
kpeter@590
   443
    /// This function finds an initial matching in a greedy way.
deba@326
   444
    void greedyInit() {
deba@327
   445
      createStructures();
deba@327
   446
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581
   447
        (*_matching)[n] = INVALID;
kpeter@581
   448
        (*_status)[n] = UNMATCHED;
deba@326
   449
      }
deba@327
   450
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   451
        if ((*_matching)[n] == INVALID) {
deba@327
   452
          for (OutArcIt a(_graph, n); a != INVALID ; ++a) {
deba@327
   453
            Node v = _graph.target(a);
deba@327
   454
            if ((*_matching)[v] == INVALID && v != n) {
kpeter@581
   455
              (*_matching)[n] = a;
kpeter@581
   456
              (*_status)[n] = MATCHED;
kpeter@581
   457
              (*_matching)[v] = _graph.oppositeArc(a);
kpeter@581
   458
              (*_status)[v] = MATCHED;
deba@326
   459
              break;
deba@326
   460
            }
deba@326
   461
          }
deba@326
   462
        }
deba@326
   463
      }
deba@326
   464
    }
deba@326
   465
deba@327
   466
kpeter@590
   467
    /// \brief Initialize the matching from a map.
deba@326
   468
    ///
kpeter@590
   469
    /// This function initializes the matching from a \c bool valued edge
kpeter@590
   470
    /// map. This map should have the property that there are no two incident
kpeter@590
   471
    /// edges with \c true value, i.e. it really contains a matching.
kpeter@559
   472
    /// \return \c true if the map contains a matching.
deba@327
   473
    template <typename MatchingMap>
deba@327
   474
    bool matchingInit(const MatchingMap& matching) {
deba@327
   475
      createStructures();
deba@327
   476
deba@327
   477
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581
   478
        (*_matching)[n] = INVALID;
kpeter@581
   479
        (*_status)[n] = UNMATCHED;
deba@326
   480
      }
deba@327
   481
      for(EdgeIt e(_graph); e!=INVALID; ++e) {
deba@327
   482
        if (matching[e]) {
deba@327
   483
deba@327
   484
          Node u = _graph.u(e);
deba@327
   485
          if ((*_matching)[u] != INVALID) return false;
kpeter@581
   486
          (*_matching)[u] = _graph.direct(e, true);
kpeter@581
   487
          (*_status)[u] = MATCHED;
deba@327
   488
deba@327
   489
          Node v = _graph.v(e);
deba@327
   490
          if ((*_matching)[v] != INVALID) return false;
kpeter@581
   491
          (*_matching)[v] = _graph.direct(e, false);
kpeter@581
   492
          (*_status)[v] = MATCHED;
deba@327
   493
        }
deba@327
   494
      }
deba@327
   495
      return true;
deba@326
   496
    }
deba@326
   497
kpeter@590
   498
    /// \brief Start Edmonds' algorithm
deba@326
   499
    ///
kpeter@590
   500
    /// This function runs the original Edmonds' algorithm.
kpeter@590
   501
    ///
kpeter@651
   502
    /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be
kpeter@590
   503
    /// called before using this function.
deba@327
   504
    void startSparse() {
deba@327
   505
      for(NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   506
        if ((*_status)[n] == UNMATCHED) {
deba@327
   507
          (*_blossom_rep)[_blossom_set->insert(n)] = n;
deba@327
   508
          _tree_set->insert(n);
kpeter@581
   509
          (*_status)[n] = EVEN;
deba@327
   510
          processSparse(n);
deba@326
   511
        }
deba@326
   512
      }
deba@326
   513
    }
deba@326
   514
kpeter@590
   515
    /// \brief Start Edmonds' algorithm with a heuristic improvement 
kpeter@590
   516
    /// for dense graphs
deba@326
   517
    ///
kpeter@590
   518
    /// This function runs Edmonds' algorithm with a heuristic of postponing
alpar@330
   519
    /// shrinks, therefore resulting in a faster algorithm for dense graphs.
kpeter@590
   520
    ///
kpeter@651
   521
    /// \pre \ref init(), \ref greedyInit() or \ref matchingInit() must be
kpeter@590
   522
    /// called before using this function.
deba@327
   523
    void startDense() {
deba@327
   524
      for(NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   525
        if ((*_status)[n] == UNMATCHED) {
deba@327
   526
          (*_blossom_rep)[_blossom_set->insert(n)] = n;
deba@327
   527
          _tree_set->insert(n);
kpeter@581
   528
          (*_status)[n] = EVEN;
deba@327
   529
          processDense(n);
deba@327
   530
        }
deba@327
   531
      }
deba@327
   532
    }
deba@327
   533
deba@327
   534
kpeter@590
   535
    /// \brief Run Edmonds' algorithm
deba@327
   536
    ///
kpeter@590
   537
    /// This function runs Edmonds' algorithm. An additional heuristic of 
kpeter@590
   538
    /// postponing shrinks is used for relatively dense graphs 
kpeter@590
   539
    /// (for which <tt>m>=2*n</tt> holds).
deba@326
   540
    void run() {
deba@327
   541
      if (countEdges(_graph) < 2 * countNodes(_graph)) {
deba@326
   542
        greedyInit();
deba@326
   543
        startSparse();
deba@326
   544
      } else {
deba@326
   545
        init();
deba@326
   546
        startDense();
deba@326
   547
      }
deba@326
   548
    }
deba@326
   549
deba@327
   550
    /// @}
deba@327
   551
kpeter@590
   552
    /// \name Primal Solution
kpeter@590
   553
    /// Functions to get the primal solution, i.e. the maximum matching.
deba@327
   554
deba@327
   555
    /// @{
deba@326
   556
kpeter@590
   557
    /// \brief Return the size (cardinality) of the matching.
deba@326
   558
    ///
kpeter@590
   559
    /// This function returns the size (cardinality) of the current matching. 
kpeter@590
   560
    /// After run() it returns the size of the maximum matching in the graph.
deba@327
   561
    int matchingSize() const {
deba@327
   562
      int size = 0;
deba@327
   563
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
   564
        if ((*_matching)[n] != INVALID) {
deba@327
   565
          ++size;
deba@326
   566
        }
deba@326
   567
      }
deba@327
   568
      return size / 2;
deba@326
   569
    }
deba@326
   570
kpeter@590
   571
    /// \brief Return \c true if the given edge is in the matching.
deba@327
   572
    ///
kpeter@590
   573
    /// This function returns \c true if the given edge is in the current 
kpeter@590
   574
    /// matching.
deba@327
   575
    bool matching(const Edge& edge) const {
deba@327
   576
      return edge == (*_matching)[_graph.u(edge)];
deba@327
   577
    }
deba@327
   578
kpeter@590
   579
    /// \brief Return the matching arc (or edge) incident to the given node.
deba@327
   580
    ///
kpeter@590
   581
    /// This function returns the matching arc (or edge) incident to the
kpeter@590
   582
    /// given node in the current matching or \c INVALID if the node is 
kpeter@590
   583
    /// not covered by the matching.
deba@327
   584
    Arc matching(const Node& n) const {
deba@327
   585
      return (*_matching)[n];
deba@327
   586
    }
deba@326
   587
kpeter@593
   588
    /// \brief Return a const reference to the matching map.
kpeter@593
   589
    ///
kpeter@593
   590
    /// This function returns a const reference to a node map that stores
kpeter@593
   591
    /// the matching arc (or edge) incident to each node.
kpeter@593
   592
    const MatchingMap& matchingMap() const {
kpeter@593
   593
      return *_matching;
kpeter@593
   594
    }
kpeter@593
   595
kpeter@590
   596
    /// \brief Return the mate of the given node.
deba@326
   597
    ///
kpeter@590
   598
    /// This function returns the mate of the given node in the current 
kpeter@590
   599
    /// matching or \c INVALID if the node is not covered by the matching.
deba@327
   600
    Node mate(const Node& n) const {
deba@327
   601
      return (*_matching)[n] != INVALID ?
deba@327
   602
        _graph.target((*_matching)[n]) : INVALID;
deba@326
   603
    }
deba@326
   604
deba@327
   605
    /// @}
deba@327
   606
kpeter@590
   607
    /// \name Dual Solution
kpeter@590
   608
    /// Functions to get the dual solution, i.e. the Gallai-Edmonds 
kpeter@590
   609
    /// decomposition.
deba@327
   610
deba@327
   611
    /// @{
deba@326
   612
kpeter@590
   613
    /// \brief Return the status of the given node in the Edmonds-Gallai
deba@326
   614
    /// decomposition.
deba@326
   615
    ///
kpeter@590
   616
    /// This function returns the \ref Status "status" of the given node
kpeter@590
   617
    /// in the Edmonds-Gallai decomposition.
kpeter@593
   618
    Status status(const Node& n) const {
deba@327
   619
      return (*_status)[n];
deba@326
   620
    }
deba@326
   621
kpeter@593
   622
    /// \brief Return a const reference to the status map, which stores
kpeter@593
   623
    /// the Edmonds-Gallai decomposition.
kpeter@593
   624
    ///
kpeter@593
   625
    /// This function returns a const reference to a node map that stores the
kpeter@593
   626
    /// \ref Status "status" of each node in the Edmonds-Gallai decomposition.
kpeter@593
   627
    const StatusMap& statusMap() const {
kpeter@593
   628
      return *_status;
kpeter@593
   629
    }
kpeter@593
   630
kpeter@590
   631
    /// \brief Return \c true if the given node is in the barrier.
deba@326
   632
    ///
kpeter@590
   633
    /// This function returns \c true if the given node is in the barrier.
deba@327
   634
    bool barrier(const Node& n) const {
deba@327
   635
      return (*_status)[n] == ODD;
deba@326
   636
    }
deba@326
   637
deba@327
   638
    /// @}
deba@326
   639
deba@326
   640
  };
deba@326
   641
deba@326
   642
  /// \ingroup matching
deba@326
   643
  ///
deba@326
   644
  /// \brief Weighted matching in general graphs
deba@326
   645
  ///
deba@326
   646
  /// This class provides an efficient implementation of Edmond's
deba@326
   647
  /// maximum weighted matching algorithm. The implementation is based
deba@326
   648
  /// on extensive use of priority queues and provides
kpeter@559
   649
  /// \f$O(nm\log n)\f$ time complexity.
deba@326
   650
  ///
kpeter@590
   651
  /// The maximum weighted matching problem is to find a subset of the 
kpeter@590
   652
  /// edges in an undirected graph with maximum overall weight for which 
kpeter@590
   653
  /// each node has at most one incident edge.
kpeter@590
   654
  /// It can be formulated with the following linear program.
deba@326
   655
  /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f]
deba@327
   656
  /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
deba@327
   657
      \quad \forall B\in\mathcal{O}\f] */
deba@326
   658
  /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326
   659
  /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@327
   660
  /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@327
   661
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
deba@327
   662
  /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
deba@327
   663
  /// subsets of the nodes.
deba@326
   664
  ///
deba@326
   665
  /// The algorithm calculates an optimal matching and a proof of the
deba@326
   666
  /// optimality. The solution of the dual problem can be used to check
deba@327
   667
  /// the result of the algorithm. The dual linear problem is the
kpeter@590
   668
  /// following.
deba@327
   669
  /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}
deba@327
   670
      z_B \ge w_{uv} \quad \forall uv\in E\f] */
deba@326
   671
  /// \f[y_u \ge 0 \quad \forall u \in V\f]
deba@326
   672
  /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@327
   673
  /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
deba@327
   674
      \frac{\vert B \vert - 1}{2}z_B\f] */
deba@326
   675
  ///
kpeter@590
   676
  /// The algorithm can be executed with the run() function. 
kpeter@590
   677
  /// After it the matching (the primal solution) and the dual solution
kpeter@590
   678
  /// can be obtained using the query functions and the 
kpeter@590
   679
  /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class, 
kpeter@590
   680
  /// which is able to iterate on the nodes of a blossom. 
kpeter@590
   681
  /// If the value type is integer, then the dual solution is multiplied
kpeter@590
   682
  /// by \ref MaxWeightedMatching::dualScale "4".
kpeter@590
   683
  ///
kpeter@593
   684
  /// \tparam GR The undirected graph type the algorithm runs on.
kpeter@590
   685
  /// \tparam WM The type edge weight map. The default type is 
kpeter@590
   686
  /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
kpeter@590
   687
#ifdef DOXYGEN
kpeter@590
   688
  template <typename GR, typename WM>
kpeter@590
   689
#else
kpeter@559
   690
  template <typename GR,
kpeter@559
   691
            typename WM = typename GR::template EdgeMap<int> >
kpeter@590
   692
#endif
deba@326
   693
  class MaxWeightedMatching {
deba@326
   694
  public:
deba@326
   695
kpeter@590
   696
    /// The graph type of the algorithm
kpeter@559
   697
    typedef GR Graph;
kpeter@590
   698
    /// The type of the edge weight map
kpeter@559
   699
    typedef WM WeightMap;
kpeter@590
   700
    /// The value type of the edge weights
deba@326
   701
    typedef typename WeightMap::Value Value;
deba@326
   702
kpeter@593
   703
    /// The type of the matching map
kpeter@590
   704
    typedef typename Graph::template NodeMap<typename Graph::Arc>
kpeter@590
   705
    MatchingMap;
kpeter@590
   706
deba@326
   707
    /// \brief Scaling factor for dual solution
deba@326
   708
    ///
kpeter@590
   709
    /// Scaling factor for dual solution. It is equal to 4 or 1
deba@326
   710
    /// according to the value type.
deba@326
   711
    static const int dualScale =
deba@326
   712
      std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326
   713
deba@326
   714
  private:
deba@326
   715
deba@326
   716
    TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326
   717
deba@326
   718
    typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326
   719
    typedef std::vector<Node> BlossomNodeList;
deba@326
   720
deba@326
   721
    struct BlossomVariable {
deba@326
   722
      int begin, end;
deba@326
   723
      Value value;
deba@326
   724
deba@326
   725
      BlossomVariable(int _begin, int _end, Value _value)
deba@326
   726
        : begin(_begin), end(_end), value(_value) {}
deba@326
   727
deba@326
   728
    };
deba@326
   729
deba@326
   730
    typedef std::vector<BlossomVariable> BlossomPotential;
deba@326
   731
deba@326
   732
    const Graph& _graph;
deba@326
   733
    const WeightMap& _weight;
deba@326
   734
deba@326
   735
    MatchingMap* _matching;
deba@326
   736
deba@326
   737
    NodePotential* _node_potential;
deba@326
   738
deba@326
   739
    BlossomPotential _blossom_potential;
deba@326
   740
    BlossomNodeList _blossom_node_list;
deba@326
   741
deba@326
   742
    int _node_num;
deba@326
   743
    int _blossom_num;
deba@326
   744
deba@326
   745
    typedef RangeMap<int> IntIntMap;
deba@326
   746
deba@326
   747
    enum Status {
deba@326
   748
      EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2
deba@326
   749
    };
deba@326
   750
deba@327
   751
    typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
deba@326
   752
    struct BlossomData {
deba@326
   753
      int tree;
deba@326
   754
      Status status;
deba@326
   755
      Arc pred, next;
deba@326
   756
      Value pot, offset;
deba@326
   757
      Node base;
deba@326
   758
    };
deba@326
   759
deba@327
   760
    IntNodeMap *_blossom_index;
deba@326
   761
    BlossomSet *_blossom_set;
deba@326
   762
    RangeMap<BlossomData>* _blossom_data;
deba@326
   763
deba@327
   764
    IntNodeMap *_node_index;
deba@327
   765
    IntArcMap *_node_heap_index;
deba@326
   766
deba@326
   767
    struct NodeData {
deba@326
   768
deba@327
   769
      NodeData(IntArcMap& node_heap_index)
deba@326
   770
        : heap(node_heap_index) {}
deba@326
   771
deba@326
   772
      int blossom;
deba@326
   773
      Value pot;
deba@327
   774
      BinHeap<Value, IntArcMap> heap;
deba@326
   775
      std::map<int, Arc> heap_index;
deba@326
   776
deba@326
   777
      int tree;
deba@326
   778
    };
deba@326
   779
deba@326
   780
    RangeMap<NodeData>* _node_data;
deba@326
   781
deba@326
   782
    typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326
   783
deba@326
   784
    IntIntMap *_tree_set_index;
deba@326
   785
    TreeSet *_tree_set;
deba@326
   786
deba@327
   787
    IntNodeMap *_delta1_index;
deba@327
   788
    BinHeap<Value, IntNodeMap> *_delta1;
deba@326
   789
deba@326
   790
    IntIntMap *_delta2_index;
deba@326
   791
    BinHeap<Value, IntIntMap> *_delta2;
deba@326
   792
deba@327
   793
    IntEdgeMap *_delta3_index;
deba@327
   794
    BinHeap<Value, IntEdgeMap> *_delta3;
deba@326
   795
deba@326
   796
    IntIntMap *_delta4_index;
deba@326
   797
    BinHeap<Value, IntIntMap> *_delta4;
deba@326
   798
deba@326
   799
    Value _delta_sum;
deba@326
   800
deba@326
   801
    void createStructures() {
deba@326
   802
      _node_num = countNodes(_graph);
deba@326
   803
      _blossom_num = _node_num * 3 / 2;
deba@326
   804
deba@326
   805
      if (!_matching) {
deba@326
   806
        _matching = new MatchingMap(_graph);
deba@326
   807
      }
deba@326
   808
      if (!_node_potential) {
deba@326
   809
        _node_potential = new NodePotential(_graph);
deba@326
   810
      }
deba@326
   811
      if (!_blossom_set) {
deba@327
   812
        _blossom_index = new IntNodeMap(_graph);
deba@326
   813
        _blossom_set = new BlossomSet(*_blossom_index);
deba@326
   814
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326
   815
      }
deba@326
   816
deba@326
   817
      if (!_node_index) {
deba@327
   818
        _node_index = new IntNodeMap(_graph);
deba@327
   819
        _node_heap_index = new IntArcMap(_graph);
deba@326
   820
        _node_data = new RangeMap<NodeData>(_node_num,
deba@326
   821
                                              NodeData(*_node_heap_index));
deba@326
   822
      }
deba@326
   823
deba@326
   824
      if (!_tree_set) {
deba@326
   825
        _tree_set_index = new IntIntMap(_blossom_num);
deba@326
   826
        _tree_set = new TreeSet(*_tree_set_index);
deba@326
   827
      }
deba@326
   828
      if (!_delta1) {
deba@327
   829
        _delta1_index = new IntNodeMap(_graph);
deba@327
   830
        _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index);
deba@326
   831
      }
deba@326
   832
      if (!_delta2) {
deba@326
   833
        _delta2_index = new IntIntMap(_blossom_num);
deba@326
   834
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@326
   835
      }
deba@326
   836
      if (!_delta3) {
deba@327
   837
        _delta3_index = new IntEdgeMap(_graph);
deba@327
   838
        _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
deba@326
   839
      }
deba@326
   840
      if (!_delta4) {
deba@326
   841
        _delta4_index = new IntIntMap(_blossom_num);
deba@326
   842
        _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@326
   843
      }
deba@326
   844
    }
deba@326
   845
deba@326
   846
    void destroyStructures() {
deba@326
   847
      _node_num = countNodes(_graph);
deba@326
   848
      _blossom_num = _node_num * 3 / 2;
deba@326
   849
deba@326
   850
      if (_matching) {
deba@326
   851
        delete _matching;
deba@326
   852
      }
deba@326
   853
      if (_node_potential) {
deba@326
   854
        delete _node_potential;
deba@326
   855
      }
deba@326
   856
      if (_blossom_set) {
deba@326
   857
        delete _blossom_index;
deba@326
   858
        delete _blossom_set;
deba@326
   859
        delete _blossom_data;
deba@326
   860
      }
deba@326
   861
deba@326
   862
      if (_node_index) {
deba@326
   863
        delete _node_index;
deba@326
   864
        delete _node_heap_index;
deba@326
   865
        delete _node_data;
deba@326
   866
      }
deba@326
   867
deba@326
   868
      if (_tree_set) {
deba@326
   869
        delete _tree_set_index;
deba@326
   870
        delete _tree_set;
deba@326
   871
      }
deba@326
   872
      if (_delta1) {
deba@326
   873
        delete _delta1_index;
deba@326
   874
        delete _delta1;
deba@326
   875
      }
deba@326
   876
      if (_delta2) {
deba@326
   877
        delete _delta2_index;
deba@326
   878
        delete _delta2;
deba@326
   879
      }
deba@326
   880
      if (_delta3) {
deba@326
   881
        delete _delta3_index;
deba@326
   882
        delete _delta3;
deba@326
   883
      }
deba@326
   884
      if (_delta4) {
deba@326
   885
        delete _delta4_index;
deba@326
   886
        delete _delta4;
deba@326
   887
      }
deba@326
   888
    }
deba@326
   889
deba@326
   890
    void matchedToEven(int blossom, int tree) {
deba@326
   891
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
   892
        _delta2->erase(blossom);
deba@326
   893
      }
deba@326
   894
deba@326
   895
      if (!_blossom_set->trivial(blossom)) {
deba@326
   896
        (*_blossom_data)[blossom].pot -=
deba@326
   897
          2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326
   898
      }
deba@326
   899
deba@326
   900
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
   901
           n != INVALID; ++n) {
deba@326
   902
deba@326
   903
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
   904
        int ni = (*_node_index)[n];
deba@326
   905
deba@326
   906
        (*_node_data)[ni].heap.clear();
deba@326
   907
        (*_node_data)[ni].heap_index.clear();
deba@326
   908
deba@326
   909
        (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
   910
deba@326
   911
        _delta1->push(n, (*_node_data)[ni].pot);
deba@326
   912
deba@326
   913
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
   914
          Node v = _graph.source(e);
deba@326
   915
          int vb = _blossom_set->find(v);
deba@326
   916
          int vi = (*_node_index)[v];
deba@326
   917
deba@326
   918
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
   919
            dualScale * _weight[e];
deba@326
   920
deba@326
   921
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
   922
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
   923
              _delta3->push(e, rw / 2);
deba@326
   924
            }
deba@326
   925
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
   926
            if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326
   927
              _delta3->push(e, rw);
deba@326
   928
            }
deba@326
   929
          } else {
deba@326
   930
            typename std::map<int, Arc>::iterator it =
deba@326
   931
              (*_node_data)[vi].heap_index.find(tree);
deba@326
   932
deba@326
   933
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
   934
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
   935
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
   936
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
   937
                it->second = e;
deba@326
   938
              }
deba@326
   939
            } else {
deba@326
   940
              (*_node_data)[vi].heap.push(e, rw);
deba@326
   941
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
   942
            }
deba@326
   943
deba@326
   944
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
   945
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
   946
deba@326
   947
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
   948
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
   949
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
   950
                               (*_blossom_data)[vb].offset);
deba@326
   951
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
   952
                           (*_blossom_data)[vb].offset){
deba@326
   953
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
   954
                                   (*_blossom_data)[vb].offset);
deba@326
   955
                }
deba@326
   956
              }
deba@326
   957
            }
deba@326
   958
          }
deba@326
   959
        }
deba@326
   960
      }
deba@326
   961
      (*_blossom_data)[blossom].offset = 0;
deba@326
   962
    }
deba@326
   963
deba@326
   964
    void matchedToOdd(int blossom) {
deba@326
   965
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
   966
        _delta2->erase(blossom);
deba@326
   967
      }
deba@326
   968
      (*_blossom_data)[blossom].offset += _delta_sum;
deba@326
   969
      if (!_blossom_set->trivial(blossom)) {
deba@326
   970
        _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326
   971
                     (*_blossom_data)[blossom].offset);
deba@326
   972
      }
deba@326
   973
    }
deba@326
   974
deba@326
   975
    void evenToMatched(int blossom, int tree) {
deba@326
   976
      if (!_blossom_set->trivial(blossom)) {
deba@326
   977
        (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326
   978
      }
deba@326
   979
deba@326
   980
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
   981
           n != INVALID; ++n) {
deba@326
   982
        int ni = (*_node_index)[n];
deba@326
   983
        (*_node_data)[ni].pot -= _delta_sum;
deba@326
   984
deba@326
   985
        _delta1->erase(n);
deba@326
   986
deba@326
   987
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
   988
          Node v = _graph.source(e);
deba@326
   989
          int vb = _blossom_set->find(v);
deba@326
   990
          int vi = (*_node_index)[v];
deba@326
   991
deba@326
   992
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
   993
            dualScale * _weight[e];
deba@326
   994
deba@326
   995
          if (vb == blossom) {
deba@326
   996
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
   997
              _delta3->erase(e);
deba@326
   998
            }
deba@326
   999
          } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1000
deba@326
  1001
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1002
              _delta3->erase(e);
deba@326
  1003
            }
deba@326
  1004
deba@326
  1005
            int vt = _tree_set->find(vb);
deba@326
  1006
deba@326
  1007
            if (vt != tree) {
deba@326
  1008
deba@326
  1009
              Arc r = _graph.oppositeArc(e);
deba@326
  1010
deba@326
  1011
              typename std::map<int, Arc>::iterator it =
deba@326
  1012
                (*_node_data)[ni].heap_index.find(vt);
deba@326
  1013
deba@326
  1014
              if (it != (*_node_data)[ni].heap_index.end()) {
deba@326
  1015
                if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326
  1016
                  (*_node_data)[ni].heap.replace(it->second, r);
deba@326
  1017
                  (*_node_data)[ni].heap.decrease(r, rw);
deba@326
  1018
                  it->second = r;
deba@326
  1019
                }
deba@326
  1020
              } else {
deba@326
  1021
                (*_node_data)[ni].heap.push(r, rw);
deba@326
  1022
                (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326
  1023
              }
deba@326
  1024
deba@326
  1025
              if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326
  1026
                _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326
  1027
deba@326
  1028
                if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326
  1029
                  _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1030
                               (*_blossom_data)[blossom].offset);
deba@326
  1031
                } else if ((*_delta2)[blossom] >
deba@326
  1032
                           _blossom_set->classPrio(blossom) -
deba@326
  1033
                           (*_blossom_data)[blossom].offset){
deba@326
  1034
                  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1035
                                   (*_blossom_data)[blossom].offset);
deba@326
  1036
                }
deba@326
  1037
              }
deba@326
  1038
            }
deba@326
  1039
deba@326
  1040
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
  1041
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1042
              _delta3->erase(e);
deba@326
  1043
            }
deba@326
  1044
          } else {
deba@326
  1045
deba@326
  1046
            typename std::map<int, Arc>::iterator it =
deba@326
  1047
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  1048
deba@326
  1049
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  1050
              (*_node_data)[vi].heap.erase(it->second);
deba@326
  1051
              (*_node_data)[vi].heap_index.erase(it);
deba@326
  1052
              if ((*_node_data)[vi].heap.empty()) {
deba@326
  1053
                _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326
  1054
              } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326
  1055
                _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326
  1056
              }
deba@326
  1057
deba@326
  1058
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  1059
                if (_blossom_set->classPrio(vb) ==
deba@326
  1060
                    std::numeric_limits<Value>::max()) {
deba@326
  1061
                  _delta2->erase(vb);
deba@326
  1062
                } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326
  1063
                           (*_blossom_data)[vb].offset) {
deba@326
  1064
                  _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326
  1065
                                   (*_blossom_data)[vb].offset);
deba@326
  1066
                }
deba@326
  1067
              }
deba@326
  1068
            }
deba@326
  1069
          }
deba@326
  1070
        }
deba@326
  1071
      }
deba@326
  1072
    }
deba@326
  1073
deba@326
  1074
    void oddToMatched(int blossom) {
deba@326
  1075
      (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326
  1076
deba@326
  1077
      if (_blossom_set->classPrio(blossom) !=
deba@326
  1078
          std::numeric_limits<Value>::max()) {
deba@326
  1079
        _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1080
                       (*_blossom_data)[blossom].offset);
deba@326
  1081
      }
deba@326
  1082
deba@326
  1083
      if (!_blossom_set->trivial(blossom)) {
deba@326
  1084
        _delta4->erase(blossom);
deba@326
  1085
      }
deba@326
  1086
    }
deba@326
  1087
deba@326
  1088
    void oddToEven(int blossom, int tree) {
deba@326
  1089
      if (!_blossom_set->trivial(blossom)) {
deba@326
  1090
        _delta4->erase(blossom);
deba@326
  1091
        (*_blossom_data)[blossom].pot -=
deba@326
  1092
          2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326
  1093
      }
deba@326
  1094
deba@326
  1095
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  1096
           n != INVALID; ++n) {
deba@326
  1097
        int ni = (*_node_index)[n];
deba@326
  1098
deba@326
  1099
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  1100
deba@326
  1101
        (*_node_data)[ni].heap.clear();
deba@326
  1102
        (*_node_data)[ni].heap_index.clear();
deba@326
  1103
        (*_node_data)[ni].pot +=
deba@326
  1104
          2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
  1105
deba@326
  1106
        _delta1->push(n, (*_node_data)[ni].pot);
deba@326
  1107
deba@326
  1108
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1109
          Node v = _graph.source(e);
deba@326
  1110
          int vb = _blossom_set->find(v);
deba@326
  1111
          int vi = (*_node_index)[v];
deba@326
  1112
deba@326
  1113
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  1114
            dualScale * _weight[e];
deba@326
  1115
deba@326
  1116
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1117
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
  1118
              _delta3->push(e, rw / 2);
deba@326
  1119
            }
deba@326
  1120
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
  1121
            if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326
  1122
              _delta3->push(e, rw);
deba@326
  1123
            }
deba@326
  1124
          } else {
deba@326
  1125
deba@326
  1126
            typename std::map<int, Arc>::iterator it =
deba@326
  1127
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  1128
deba@326
  1129
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  1130
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
  1131
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
  1132
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
  1133
                it->second = e;
deba@326
  1134
              }
deba@326
  1135
            } else {
deba@326
  1136
              (*_node_data)[vi].heap.push(e, rw);
deba@326
  1137
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
  1138
            }
deba@326
  1139
deba@326
  1140
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
  1141
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
  1142
deba@326
  1143
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  1144
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
  1145
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
  1146
                               (*_blossom_data)[vb].offset);
deba@326
  1147
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
  1148
                           (*_blossom_data)[vb].offset) {
deba@326
  1149
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
  1150
                                   (*_blossom_data)[vb].offset);
deba@326
  1151
                }
deba@326
  1152
              }
deba@326
  1153
            }
deba@326
  1154
          }
deba@326
  1155
        }
deba@326
  1156
      }
deba@326
  1157
      (*_blossom_data)[blossom].offset = 0;
deba@326
  1158
    }
deba@326
  1159
deba@326
  1160
deba@326
  1161
    void matchedToUnmatched(int blossom) {
deba@326
  1162
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  1163
        _delta2->erase(blossom);
deba@326
  1164
      }
deba@326
  1165
deba@326
  1166
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  1167
           n != INVALID; ++n) {
deba@326
  1168
        int ni = (*_node_index)[n];
deba@326
  1169
deba@326
  1170
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  1171
deba@326
  1172
        (*_node_data)[ni].heap.clear();
deba@326
  1173
        (*_node_data)[ni].heap_index.clear();
deba@326
  1174
deba@326
  1175
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1176
          Node v = _graph.target(e);
deba@326
  1177
          int vb = _blossom_set->find(v);
deba@326
  1178
          int vi = (*_node_index)[v];
deba@326
  1179
deba@326
  1180
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  1181
            dualScale * _weight[e];
deba@326
  1182
deba@326
  1183
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1184
            if (_delta3->state(e) != _delta3->IN_HEAP) {
deba@326
  1185
              _delta3->push(e, rw);
deba@326
  1186
            }
deba@326
  1187
          }
deba@326
  1188
        }
deba@326
  1189
      }
deba@326
  1190
    }
deba@326
  1191
deba@326
  1192
    void unmatchedToMatched(int blossom) {
deba@326
  1193
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  1194
           n != INVALID; ++n) {
deba@326
  1195
        int ni = (*_node_index)[n];
deba@326
  1196
deba@326
  1197
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1198
          Node v = _graph.source(e);
deba@326
  1199
          int vb = _blossom_set->find(v);
deba@326
  1200
          int vi = (*_node_index)[v];
deba@326
  1201
deba@326
  1202
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  1203
            dualScale * _weight[e];
deba@326
  1204
deba@326
  1205
          if (vb == blossom) {
deba@326
  1206
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1207
              _delta3->erase(e);
deba@326
  1208
            }
deba@326
  1209
          } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  1210
deba@326
  1211
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1212
              _delta3->erase(e);
deba@326
  1213
            }
deba@326
  1214
deba@326
  1215
            int vt = _tree_set->find(vb);
deba@326
  1216
deba@326
  1217
            Arc r = _graph.oppositeArc(e);
deba@326
  1218
deba@326
  1219
            typename std::map<int, Arc>::iterator it =
deba@326
  1220
              (*_node_data)[ni].heap_index.find(vt);
deba@326
  1221
deba@326
  1222
            if (it != (*_node_data)[ni].heap_index.end()) {
deba@326
  1223
              if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326
  1224
                (*_node_data)[ni].heap.replace(it->second, r);
deba@326
  1225
                (*_node_data)[ni].heap.decrease(r, rw);
deba@326
  1226
                it->second = r;
deba@326
  1227
              }
deba@326
  1228
            } else {
deba@326
  1229
              (*_node_data)[ni].heap.push(r, rw);
deba@326
  1230
              (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326
  1231
            }
deba@326
  1232
deba@326
  1233
            if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326
  1234
              _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326
  1235
deba@326
  1236
              if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326
  1237
                _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1238
                             (*_blossom_data)[blossom].offset);
deba@326
  1239
              } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)-
deba@326
  1240
                         (*_blossom_data)[blossom].offset){
deba@326
  1241
                _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326
  1242
                                 (*_blossom_data)[blossom].offset);
deba@326
  1243
              }
deba@326
  1244
            }
deba@326
  1245
deba@326
  1246
          } else if ((*_blossom_data)[vb].status == UNMATCHED) {
deba@326
  1247
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  1248
              _delta3->erase(e);
deba@326
  1249
            }
deba@326
  1250
          }
deba@326
  1251
        }
deba@326
  1252
      }
deba@326
  1253
    }
deba@326
  1254
deba@326
  1255
    void alternatePath(int even, int tree) {
deba@326
  1256
      int odd;
deba@326
  1257
deba@326
  1258
      evenToMatched(even, tree);
deba@326
  1259
      (*_blossom_data)[even].status = MATCHED;
deba@326
  1260
deba@326
  1261
      while ((*_blossom_data)[even].pred != INVALID) {
deba@326
  1262
        odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326
  1263
        (*_blossom_data)[odd].status = MATCHED;
deba@326
  1264
        oddToMatched(odd);
deba@326
  1265
        (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326
  1266
deba@326
  1267
        even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326
  1268
        (*_blossom_data)[even].status = MATCHED;
deba@326
  1269
        evenToMatched(even, tree);
deba@326
  1270
        (*_blossom_data)[even].next =
deba@326
  1271
          _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326
  1272
      }
deba@326
  1273
deba@326
  1274
    }
deba@326
  1275
deba@326
  1276
    void destroyTree(int tree) {
deba@326
  1277
      for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326
  1278
        if ((*_blossom_data)[b].status == EVEN) {
deba@326
  1279
          (*_blossom_data)[b].status = MATCHED;
deba@326
  1280
          evenToMatched(b, tree);
deba@326
  1281
        } else if ((*_blossom_data)[b].status == ODD) {
deba@326
  1282
          (*_blossom_data)[b].status = MATCHED;
deba@326
  1283
          oddToMatched(b);
deba@326
  1284
        }
deba@326
  1285
      }
deba@326
  1286
      _tree_set->eraseClass(tree);
deba@326
  1287
    }
deba@326
  1288
deba@326
  1289
deba@326
  1290
    void unmatchNode(const Node& node) {
deba@326
  1291
      int blossom = _blossom_set->find(node);
deba@326
  1292
      int tree = _tree_set->find(blossom);
deba@326
  1293
deba@326
  1294
      alternatePath(blossom, tree);
deba@326
  1295
      destroyTree(tree);
deba@326
  1296
deba@326
  1297
      (*_blossom_data)[blossom].status = UNMATCHED;
deba@326
  1298
      (*_blossom_data)[blossom].base = node;
deba@326
  1299
      matchedToUnmatched(blossom);
deba@326
  1300
    }
deba@326
  1301
deba@326
  1302
deba@327
  1303
    void augmentOnEdge(const Edge& edge) {
deba@327
  1304
deba@327
  1305
      int left = _blossom_set->find(_graph.u(edge));
deba@327
  1306
      int right = _blossom_set->find(_graph.v(edge));
deba@326
  1307
deba@326
  1308
      if ((*_blossom_data)[left].status == EVEN) {
deba@326
  1309
        int left_tree = _tree_set->find(left);
deba@326
  1310
        alternatePath(left, left_tree);
deba@326
  1311
        destroyTree(left_tree);
deba@326
  1312
      } else {
deba@326
  1313
        (*_blossom_data)[left].status = MATCHED;
deba@326
  1314
        unmatchedToMatched(left);
deba@326
  1315
      }
deba@326
  1316
deba@326
  1317
      if ((*_blossom_data)[right].status == EVEN) {
deba@326
  1318
        int right_tree = _tree_set->find(right);
deba@326
  1319
        alternatePath(right, right_tree);
deba@326
  1320
        destroyTree(right_tree);
deba@326
  1321
      } else {
deba@326
  1322
        (*_blossom_data)[right].status = MATCHED;
deba@326
  1323
        unmatchedToMatched(right);
deba@326
  1324
      }
deba@326
  1325
deba@327
  1326
      (*_blossom_data)[left].next = _graph.direct(edge, true);
deba@327
  1327
      (*_blossom_data)[right].next = _graph.direct(edge, false);
deba@326
  1328
    }
deba@326
  1329
deba@326
  1330
    void extendOnArc(const Arc& arc) {
deba@326
  1331
      int base = _blossom_set->find(_graph.target(arc));
deba@326
  1332
      int tree = _tree_set->find(base);
deba@326
  1333
deba@326
  1334
      int odd = _blossom_set->find(_graph.source(arc));
deba@326
  1335
      _tree_set->insert(odd, tree);
deba@326
  1336
      (*_blossom_data)[odd].status = ODD;
deba@326
  1337
      matchedToOdd(odd);
deba@326
  1338
      (*_blossom_data)[odd].pred = arc;
deba@326
  1339
deba@326
  1340
      int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326
  1341
      (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326
  1342
      _tree_set->insert(even, tree);
deba@326
  1343
      (*_blossom_data)[even].status = EVEN;
deba@326
  1344
      matchedToEven(even, tree);
deba@326
  1345
    }
deba@326
  1346
deba@327
  1347
    void shrinkOnEdge(const Edge& edge, int tree) {
deba@326
  1348
      int nca = -1;
deba@326
  1349
      std::vector<int> left_path, right_path;
deba@326
  1350
deba@326
  1351
      {
deba@326
  1352
        std::set<int> left_set, right_set;
deba@326
  1353
        int left = _blossom_set->find(_graph.u(edge));
deba@326
  1354
        left_path.push_back(left);
deba@326
  1355
        left_set.insert(left);
deba@326
  1356
deba@326
  1357
        int right = _blossom_set->find(_graph.v(edge));
deba@326
  1358
        right_path.push_back(right);
deba@326
  1359
        right_set.insert(right);
deba@326
  1360
deba@326
  1361
        while (true) {
deba@326
  1362
deba@326
  1363
          if ((*_blossom_data)[left].pred == INVALID) break;
deba@326
  1364
deba@326
  1365
          left =
deba@326
  1366
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  1367
          left_path.push_back(left);
deba@326
  1368
          left =
deba@326
  1369
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  1370
          left_path.push_back(left);
deba@326
  1371
deba@326
  1372
          left_set.insert(left);
deba@326
  1373
deba@326
  1374
          if (right_set.find(left) != right_set.end()) {
deba@326
  1375
            nca = left;
deba@326
  1376
            break;
deba@326
  1377
          }
deba@326
  1378
deba@326
  1379
          if ((*_blossom_data)[right].pred == INVALID) break;
deba@326
  1380
deba@326
  1381
          right =
deba@326
  1382
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  1383
          right_path.push_back(right);
deba@326
  1384
          right =
deba@326
  1385
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  1386
          right_path.push_back(right);
deba@326
  1387
deba@326
  1388
          right_set.insert(right);
deba@326
  1389
deba@326
  1390
          if (left_set.find(right) != left_set.end()) {
deba@326
  1391
            nca = right;
deba@326
  1392
            break;
deba@326
  1393
          }
deba@326
  1394
deba@326
  1395
        }
deba@326
  1396
deba@326
  1397
        if (nca == -1) {
deba@326
  1398
          if ((*_blossom_data)[left].pred == INVALID) {
deba@326
  1399
            nca = right;
deba@326
  1400
            while (left_set.find(nca) == left_set.end()) {
deba@326
  1401
              nca =
deba@326
  1402
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1403
              right_path.push_back(nca);
deba@326
  1404
              nca =
deba@326
  1405
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1406
              right_path.push_back(nca);
deba@326
  1407
            }
deba@326
  1408
          } else {
deba@326
  1409
            nca = left;
deba@326
  1410
            while (right_set.find(nca) == right_set.end()) {
deba@326
  1411
              nca =
deba@326
  1412
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1413
              left_path.push_back(nca);
deba@326
  1414
              nca =
deba@326
  1415
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  1416
              left_path.push_back(nca);
deba@326
  1417
            }
deba@326
  1418
          }
deba@326
  1419
        }
deba@326
  1420
      }
deba@326
  1421
deba@326
  1422
      std::vector<int> subblossoms;
deba@326
  1423
      Arc prev;
deba@326
  1424
deba@326
  1425
      prev = _graph.direct(edge, true);
deba@326
  1426
      for (int i = 0; left_path[i] != nca; i += 2) {
deba@326
  1427
        subblossoms.push_back(left_path[i]);
deba@326
  1428
        (*_blossom_data)[left_path[i]].next = prev;
deba@326
  1429
        _tree_set->erase(left_path[i]);
deba@326
  1430
deba@326
  1431
        subblossoms.push_back(left_path[i + 1]);
deba@326
  1432
        (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326
  1433
        oddToEven(left_path[i + 1], tree);
deba@326
  1434
        _tree_set->erase(left_path[i + 1]);
deba@326
  1435
        prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326
  1436
      }
deba@326
  1437
deba@326
  1438
      int k = 0;
deba@326
  1439
      while (right_path[k] != nca) ++k;
deba@326
  1440
deba@326
  1441
      subblossoms.push_back(nca);
deba@326
  1442
      (*_blossom_data)[nca].next = prev;
deba@326
  1443
deba@326
  1444
      for (int i = k - 2; i >= 0; i -= 2) {
deba@326
  1445
        subblossoms.push_back(right_path[i + 1]);
deba@326
  1446
        (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326
  1447
        oddToEven(right_path[i + 1], tree);
deba@326
  1448
        _tree_set->erase(right_path[i + 1]);
deba@326
  1449
deba@326
  1450
        (*_blossom_data)[right_path[i + 1]].next =
deba@326
  1451
          (*_blossom_data)[right_path[i + 1]].pred;
deba@326
  1452
deba@326
  1453
        subblossoms.push_back(right_path[i]);
deba@326
  1454
        _tree_set->erase(right_path[i]);
deba@326
  1455
      }
deba@326
  1456
deba@326
  1457
      int surface =
deba@326
  1458
        _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326
  1459
deba@326
  1460
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  1461
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  1462
          (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326
  1463
        }
deba@326
  1464
        (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326
  1465
      }
deba@326
  1466
deba@326
  1467
      (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326
  1468
      (*_blossom_data)[surface].offset = 0;
deba@326
  1469
      (*_blossom_data)[surface].status = EVEN;
deba@326
  1470
      (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326
  1471
      (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326
  1472
deba@326
  1473
      _tree_set->insert(surface, tree);
deba@326
  1474
      _tree_set->erase(nca);
deba@326
  1475
    }
deba@326
  1476
deba@326
  1477
    void splitBlossom(int blossom) {
deba@326
  1478
      Arc next = (*_blossom_data)[blossom].next;
deba@326
  1479
      Arc pred = (*_blossom_data)[blossom].pred;
deba@326
  1480
deba@326
  1481
      int tree = _tree_set->find(blossom);
deba@326
  1482
deba@326
  1483
      (*_blossom_data)[blossom].status = MATCHED;
deba@326
  1484
      oddToMatched(blossom);
deba@326
  1485
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  1486
        _delta2->erase(blossom);
deba@326
  1487
      }
deba@326
  1488
deba@326
  1489
      std::vector<int> subblossoms;
deba@326
  1490
      _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  1491
deba@326
  1492
      Value offset = (*_blossom_data)[blossom].offset;
deba@326
  1493
      int b = _blossom_set->find(_graph.source(pred));
deba@326
  1494
      int d = _blossom_set->find(_graph.source(next));
deba@326
  1495
deba@326
  1496
      int ib = -1, id = -1;
deba@326
  1497
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  1498
        if (subblossoms[i] == b) ib = i;
deba@326
  1499
        if (subblossoms[i] == d) id = i;
deba@326
  1500
deba@326
  1501
        (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326
  1502
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  1503
          (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326
  1504
        }
deba@326
  1505
        if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326
  1506
            std::numeric_limits<Value>::max()) {
deba@326
  1507
          _delta2->push(subblossoms[i],
deba@326
  1508
                        _blossom_set->classPrio(subblossoms[i]) -
deba@326
  1509
                        (*_blossom_data)[subblossoms[i]].offset);
deba@326
  1510
        }
deba@326
  1511
      }
deba@326
  1512
deba@326
  1513
      if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326
  1514
        for (int i = (id + 1) % subblossoms.size();
deba@326
  1515
             i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  1516
          int sb = subblossoms[i];
deba@326
  1517
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1518
          (*_blossom_data)[sb].next =
deba@326
  1519
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1520
        }
deba@326
  1521
deba@326
  1522
        for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  1523
          int sb = subblossoms[i];
deba@326
  1524
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1525
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  1526
deba@326
  1527
          (*_blossom_data)[sb].status = ODD;
deba@326
  1528
          matchedToOdd(sb);
deba@326
  1529
          _tree_set->insert(sb, tree);
deba@326
  1530
          (*_blossom_data)[sb].pred = pred;
deba@326
  1531
          (*_blossom_data)[sb].next =
deba@326
  1532
                           _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1533
deba@326
  1534
          pred = (*_blossom_data)[ub].next;
deba@326
  1535
deba@326
  1536
          (*_blossom_data)[tb].status = EVEN;
deba@326
  1537
          matchedToEven(tb, tree);
deba@326
  1538
          _tree_set->insert(tb, tree);
deba@326
  1539
          (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326
  1540
        }
deba@326
  1541
deba@326
  1542
        (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326
  1543
        matchedToOdd(subblossoms[id]);
deba@326
  1544
        _tree_set->insert(subblossoms[id], tree);
deba@326
  1545
        (*_blossom_data)[subblossoms[id]].next = next;
deba@326
  1546
        (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326
  1547
deba@326
  1548
      } else {
deba@326
  1549
deba@326
  1550
        for (int i = (ib + 1) % subblossoms.size();
deba@326
  1551
             i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  1552
          int sb = subblossoms[i];
deba@326
  1553
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1554
          (*_blossom_data)[sb].next =
deba@326
  1555
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1556
        }
deba@326
  1557
deba@326
  1558
        for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  1559
          int sb = subblossoms[i];
deba@326
  1560
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  1561
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  1562
deba@326
  1563
          (*_blossom_data)[sb].status = ODD;
deba@326
  1564
          matchedToOdd(sb);
deba@326
  1565
          _tree_set->insert(sb, tree);
deba@326
  1566
          (*_blossom_data)[sb].next = next;
deba@326
  1567
          (*_blossom_data)[sb].pred =
deba@326
  1568
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  1569
deba@326
  1570
          (*_blossom_data)[tb].status = EVEN;
deba@326
  1571
          matchedToEven(tb, tree);
deba@326
  1572
          _tree_set->insert(tb, tree);
deba@326
  1573
          (*_blossom_data)[tb].pred =
deba@326
  1574
            (*_blossom_data)[tb].next =
deba@326
  1575
            _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326
  1576
          next = (*_blossom_data)[ub].next;
deba@326
  1577
        }
deba@326
  1578
deba@326
  1579
        (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326
  1580
        matchedToOdd(subblossoms[ib]);
deba@326
  1581
        _tree_set->insert(subblossoms[ib], tree);
deba@326
  1582
        (*_blossom_data)[subblossoms[ib]].next = next;
deba@326
  1583
        (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326
  1584
      }
deba@326
  1585
      _tree_set->erase(blossom);
deba@326
  1586
    }
deba@326
  1587
deba@326
  1588
    void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326
  1589
      if (_blossom_set->trivial(blossom)) {
deba@326
  1590
        int bi = (*_node_index)[base];
deba@326
  1591
        Value pot = (*_node_data)[bi].pot;
deba@326
  1592
kpeter@581
  1593
        (*_matching)[base] = matching;
deba@326
  1594
        _blossom_node_list.push_back(base);
kpeter@581
  1595
        (*_node_potential)[base] = pot;
deba@326
  1596
      } else {
deba@326
  1597
deba@326
  1598
        Value pot = (*_blossom_data)[blossom].pot;
deba@326
  1599
        int bn = _blossom_node_list.size();
deba@326
  1600
deba@326
  1601
        std::vector<int> subblossoms;
deba@326
  1602
        _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  1603
        int b = _blossom_set->find(base);
deba@326
  1604
        int ib = -1;
deba@326
  1605
        for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  1606
          if (subblossoms[i] == b) { ib = i; break; }
deba@326
  1607
        }
deba@326
  1608
deba@326
  1609
        for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326
  1610
          int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326
  1611
          int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326
  1612
deba@326
  1613
          Arc m = (*_blossom_data)[tb].next;
deba@326
  1614
          extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326
  1615
          extractBlossom(tb, _graph.source(m), m);
deba@326
  1616
        }
deba@326
  1617
        extractBlossom(subblossoms[ib], base, matching);
deba@326
  1618
deba@326
  1619
        int en = _blossom_node_list.size();
deba@326
  1620
deba@326
  1621
        _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326
  1622
      }
deba@326
  1623
    }
deba@326
  1624
deba@326
  1625
    void extractMatching() {
deba@326
  1626
      std::vector<int> blossoms;
deba@326
  1627
      for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326
  1628
        blossoms.push_back(c);
deba@326
  1629
      }
deba@326
  1630
deba@326
  1631
      for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326
  1632
        if ((*_blossom_data)[blossoms[i]].status == MATCHED) {
deba@326
  1633
deba@326
  1634
          Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326
  1635
          (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326
  1636
          for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326
  1637
               n != INVALID; ++n) {
deba@326
  1638
            (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326
  1639
          }
deba@326
  1640
deba@326
  1641
          Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326
  1642
          Node base = _graph.source(matching);
deba@326
  1643
          extractBlossom(blossoms[i], base, matching);
deba@326
  1644
        } else {
deba@326
  1645
          Node base = (*_blossom_data)[blossoms[i]].base;
deba@326
  1646
          extractBlossom(blossoms[i], base, INVALID);
deba@326
  1647
        }
deba@326
  1648
      }
deba@326
  1649
    }
deba@326
  1650
deba@326
  1651
  public:
deba@326
  1652
deba@326
  1653
    /// \brief Constructor
deba@326
  1654
    ///
deba@326
  1655
    /// Constructor.
deba@326
  1656
    MaxWeightedMatching(const Graph& graph, const WeightMap& weight)
deba@326
  1657
      : _graph(graph), _weight(weight), _matching(0),
deba@326
  1658
        _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326
  1659
        _node_num(0), _blossom_num(0),
deba@326
  1660
deba@326
  1661
        _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326
  1662
        _node_index(0), _node_heap_index(0), _node_data(0),
deba@326
  1663
        _tree_set_index(0), _tree_set(0),
deba@326
  1664
deba@326
  1665
        _delta1_index(0), _delta1(0),
deba@326
  1666
        _delta2_index(0), _delta2(0),
deba@326
  1667
        _delta3_index(0), _delta3(0),
deba@326
  1668
        _delta4_index(0), _delta4(0),
deba@326
  1669
deba@326
  1670
        _delta_sum() {}
deba@326
  1671
deba@326
  1672
    ~MaxWeightedMatching() {
deba@326
  1673
      destroyStructures();
deba@326
  1674
    }
deba@326
  1675
kpeter@590
  1676
    /// \name Execution Control
alpar@330
  1677
    /// The simplest way to execute the algorithm is to use the
kpeter@590
  1678
    /// \ref run() member function.
deba@326
  1679
deba@326
  1680
    ///@{
deba@326
  1681
deba@326
  1682
    /// \brief Initialize the algorithm
deba@326
  1683
    ///
kpeter@590
  1684
    /// This function initializes the algorithm.
deba@326
  1685
    void init() {
deba@326
  1686
      createStructures();
deba@326
  1687
deba@326
  1688
      for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@581
  1689
        (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
deba@326
  1690
      }
deba@326
  1691
      for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@581
  1692
        (*_delta1_index)[n] = _delta1->PRE_HEAP;
deba@326
  1693
      }
deba@326
  1694
      for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@581
  1695
        (*_delta3_index)[e] = _delta3->PRE_HEAP;
deba@326
  1696
      }
deba@326
  1697
      for (int i = 0; i < _blossom_num; ++i) {
kpeter@581
  1698
        (*_delta2_index)[i] = _delta2->PRE_HEAP;
kpeter@581
  1699
        (*_delta4_index)[i] = _delta4->PRE_HEAP;
deba@326
  1700
      }
deba@326
  1701
deba@326
  1702
      int index = 0;
deba@326
  1703
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1704
        Value max = 0;
deba@326
  1705
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  1706
          if (_graph.target(e) == n) continue;
deba@326
  1707
          if ((dualScale * _weight[e]) / 2 > max) {
deba@326
  1708
            max = (dualScale * _weight[e]) / 2;
deba@326
  1709
          }
deba@326
  1710
        }
kpeter@581
  1711
        (*_node_index)[n] = index;
deba@326
  1712
        (*_node_data)[index].pot = max;
deba@326
  1713
        _delta1->push(n, max);
deba@326
  1714
        int blossom =
deba@326
  1715
          _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326
  1716
deba@326
  1717
        _tree_set->insert(blossom);
deba@326
  1718
deba@326
  1719
        (*_blossom_data)[blossom].status = EVEN;
deba@326
  1720
        (*_blossom_data)[blossom].pred = INVALID;
deba@326
  1721
        (*_blossom_data)[blossom].next = INVALID;
deba@326
  1722
        (*_blossom_data)[blossom].pot = 0;
deba@326
  1723
        (*_blossom_data)[blossom].offset = 0;
deba@326
  1724
        ++index;
deba@326
  1725
      }
deba@326
  1726
      for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326
  1727
        int si = (*_node_index)[_graph.u(e)];
deba@326
  1728
        int ti = (*_node_index)[_graph.v(e)];
deba@326
  1729
        if (_graph.u(e) != _graph.v(e)) {
deba@326
  1730
          _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326
  1731
                            dualScale * _weight[e]) / 2);
deba@326
  1732
        }
deba@326
  1733
      }
deba@326
  1734
    }
deba@326
  1735
kpeter@590
  1736
    /// \brief Start the algorithm
deba@326
  1737
    ///
kpeter@590
  1738
    /// This function starts the algorithm.
kpeter@590
  1739
    ///
kpeter@590
  1740
    /// \pre \ref init() must be called before using this function.
deba@326
  1741
    void start() {
deba@326
  1742
      enum OpType {
deba@326
  1743
        D1, D2, D3, D4
deba@326
  1744
      };
deba@326
  1745
deba@326
  1746
      int unmatched = _node_num;
deba@326
  1747
      while (unmatched > 0) {
deba@326
  1748
        Value d1 = !_delta1->empty() ?
deba@326
  1749
          _delta1->prio() : std::numeric_limits<Value>::max();
deba@326
  1750
deba@326
  1751
        Value d2 = !_delta2->empty() ?
deba@326
  1752
          _delta2->prio() : std::numeric_limits<Value>::max();
deba@326
  1753
deba@326
  1754
        Value d3 = !_delta3->empty() ?
deba@326
  1755
          _delta3->prio() : std::numeric_limits<Value>::max();
deba@326
  1756
deba@326
  1757
        Value d4 = !_delta4->empty() ?
deba@326
  1758
          _delta4->prio() : std::numeric_limits<Value>::max();
deba@326
  1759
deba@326
  1760
        _delta_sum = d1; OpType ot = D1;
deba@326
  1761
        if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; }
deba@326
  1762
        if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@326
  1763
        if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326
  1764
deba@326
  1765
deba@326
  1766
        switch (ot) {
deba@326
  1767
        case D1:
deba@326
  1768
          {
deba@326
  1769
            Node n = _delta1->top();
deba@326
  1770
            unmatchNode(n);
deba@326
  1771
            --unmatched;
deba@326
  1772
          }
deba@326
  1773
          break;
deba@326
  1774
        case D2:
deba@326
  1775
          {
deba@326
  1776
            int blossom = _delta2->top();
deba@326
  1777
            Node n = _blossom_set->classTop(blossom);
deba@326
  1778
            Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326
  1779
            extendOnArc(e);
deba@326
  1780
          }
deba@326
  1781
          break;
deba@326
  1782
        case D3:
deba@326
  1783
          {
deba@326
  1784
            Edge e = _delta3->top();
deba@326
  1785
deba@326
  1786
            int left_blossom = _blossom_set->find(_graph.u(e));
deba@326
  1787
            int right_blossom = _blossom_set->find(_graph.v(e));
deba@326
  1788
deba@326
  1789
            if (left_blossom == right_blossom) {
deba@326
  1790
              _delta3->pop();
deba@326
  1791
            } else {
deba@326
  1792
              int left_tree;
deba@326
  1793
              if ((*_blossom_data)[left_blossom].status == EVEN) {
deba@326
  1794
                left_tree = _tree_set->find(left_blossom);
deba@326
  1795
              } else {
deba@326
  1796
                left_tree = -1;
deba@326
  1797
                ++unmatched;
deba@326
  1798
              }
deba@326
  1799
              int right_tree;
deba@326
  1800
              if ((*_blossom_data)[right_blossom].status == EVEN) {
deba@326
  1801
                right_tree = _tree_set->find(right_blossom);
deba@326
  1802
              } else {
deba@326
  1803
                right_tree = -1;
deba@326
  1804
                ++unmatched;
deba@326
  1805
              }
deba@326
  1806
deba@326
  1807
              if (left_tree == right_tree) {
deba@327
  1808
                shrinkOnEdge(e, left_tree);
deba@326
  1809
              } else {
deba@327
  1810
                augmentOnEdge(e);
deba@326
  1811
                unmatched -= 2;
deba@326
  1812
              }
deba@326
  1813
            }
deba@326
  1814
          } break;
deba@326
  1815
        case D4:
deba@326
  1816
          splitBlossom(_delta4->top());
deba@326
  1817
          break;
deba@326
  1818
        }
deba@326
  1819
      }
deba@326
  1820
      extractMatching();
deba@326
  1821
    }
deba@326
  1822
kpeter@590
  1823
    /// \brief Run the algorithm.
deba@326
  1824
    ///
kpeter@590
  1825
    /// This method runs the \c %MaxWeightedMatching algorithm.
deba@326
  1826
    ///
deba@326
  1827
    /// \note mwm.run() is just a shortcut of the following code.
deba@326
  1828
    /// \code
deba@326
  1829
    ///   mwm.init();
deba@326
  1830
    ///   mwm.start();
deba@326
  1831
    /// \endcode
deba@326
  1832
    void run() {
deba@326
  1833
      init();
deba@326
  1834
      start();
deba@326
  1835
    }
deba@326
  1836
deba@326
  1837
    /// @}
deba@326
  1838
kpeter@590
  1839
    /// \name Primal Solution
kpeter@590
  1840
    /// Functions to get the primal solution, i.e. the maximum weighted 
kpeter@590
  1841
    /// matching.\n
kpeter@590
  1842
    /// Either \ref run() or \ref start() function should be called before
kpeter@590
  1843
    /// using them.
deba@326
  1844
deba@326
  1845
    /// @{
deba@326
  1846
kpeter@590
  1847
    /// \brief Return the weight of the matching.
deba@326
  1848
    ///
kpeter@590
  1849
    /// This function returns the weight of the found matching.
kpeter@590
  1850
    ///
kpeter@590
  1851
    /// \pre Either run() or start() must be called before using this function.
kpeter@593
  1852
    Value matchingWeight() const {
deba@326
  1853
      Value sum = 0;
deba@326
  1854
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1855
        if ((*_matching)[n] != INVALID) {
deba@326
  1856
          sum += _weight[(*_matching)[n]];
deba@326
  1857
        }
deba@326
  1858
      }
deba@326
  1859
      return sum /= 2;
deba@326
  1860
    }
deba@326
  1861
kpeter@590
  1862
    /// \brief Return the size (cardinality) of the matching.
deba@326
  1863
    ///
kpeter@590
  1864
    /// This function returns the size (cardinality) of the found matching.
kpeter@590
  1865
    ///
kpeter@590
  1866
    /// \pre Either run() or start() must be called before using this function.
deba@327
  1867
    int matchingSize() const {
deba@327
  1868
      int num = 0;
deba@327
  1869
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@327
  1870
        if ((*_matching)[n] != INVALID) {
deba@327
  1871
          ++num;
deba@327
  1872
        }
deba@327
  1873
      }
deba@327
  1874
      return num /= 2;
deba@327
  1875
    }
deba@327
  1876
kpeter@590
  1877
    /// \brief Return \c true if the given edge is in the matching.
deba@327
  1878
    ///
kpeter@590
  1879
    /// This function returns \c true if the given edge is in the found 
kpeter@590
  1880
    /// matching.
kpeter@590
  1881
    ///
kpeter@590
  1882
    /// \pre Either run() or start() must be called before using this function.
deba@327
  1883
    bool matching(const Edge& edge) const {
deba@327
  1884
      return edge == (*_matching)[_graph.u(edge)];
deba@326
  1885
    }
deba@326
  1886
kpeter@590
  1887
    /// \brief Return the matching arc (or edge) incident to the given node.
deba@326
  1888
    ///
kpeter@590
  1889
    /// This function returns the matching arc (or edge) incident to the
kpeter@590
  1890
    /// given node in the found matching or \c INVALID if the node is 
kpeter@590
  1891
    /// not covered by the matching.
kpeter@590
  1892
    ///
kpeter@590
  1893
    /// \pre Either run() or start() must be called before using this function.
deba@326
  1894
    Arc matching(const Node& node) const {
deba@326
  1895
      return (*_matching)[node];
deba@326
  1896
    }
deba@326
  1897
kpeter@593
  1898
    /// \brief Return a const reference to the matching map.
kpeter@593
  1899
    ///
kpeter@593
  1900
    /// This function returns a const reference to a node map that stores
kpeter@593
  1901
    /// the matching arc (or edge) incident to each node.
kpeter@593
  1902
    const MatchingMap& matchingMap() const {
kpeter@593
  1903
      return *_matching;
kpeter@593
  1904
    }
kpeter@593
  1905
kpeter@590
  1906
    /// \brief Return the mate of the given node.
deba@326
  1907
    ///
kpeter@590
  1908
    /// This function returns the mate of the given node in the found 
kpeter@590
  1909
    /// matching or \c INVALID if the node is not covered by the matching.
kpeter@590
  1910
    ///
kpeter@590
  1911
    /// \pre Either run() or start() must be called before using this function.
deba@326
  1912
    Node mate(const Node& node) const {
deba@326
  1913
      return (*_matching)[node] != INVALID ?
deba@326
  1914
        _graph.target((*_matching)[node]) : INVALID;
deba@326
  1915
    }
deba@326
  1916
deba@326
  1917
    /// @}
deba@326
  1918
kpeter@590
  1919
    /// \name Dual Solution
kpeter@590
  1920
    /// Functions to get the dual solution.\n
kpeter@590
  1921
    /// Either \ref run() or \ref start() function should be called before
kpeter@590
  1922
    /// using them.
deba@326
  1923
deba@326
  1924
    /// @{
deba@326
  1925
kpeter@590
  1926
    /// \brief Return the value of the dual solution.
deba@326
  1927
    ///
kpeter@590
  1928
    /// This function returns the value of the dual solution. 
kpeter@590
  1929
    /// It should be equal to the primal value scaled by \ref dualScale 
kpeter@590
  1930
    /// "dual scale".
kpeter@590
  1931
    ///
kpeter@590
  1932
    /// \pre Either run() or start() must be called before using this function.
deba@326
  1933
    Value dualValue() const {
deba@326
  1934
      Value sum = 0;
deba@326
  1935
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  1936
        sum += nodeValue(n);
deba@326
  1937
      }
deba@326
  1938
      for (int i = 0; i < blossomNum(); ++i) {
deba@326
  1939
        sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326
  1940
      }
deba@326
  1941
      return sum;
deba@326
  1942
    }
deba@326
  1943
kpeter@590
  1944
    /// \brief Return the dual value (potential) of the given node.
deba@326
  1945
    ///
kpeter@590
  1946
    /// This function returns the dual value (potential) of the given node.
kpeter@590
  1947
    ///
kpeter@590
  1948
    /// \pre Either run() or start() must be called before using this function.
deba@326
  1949
    Value nodeValue(const Node& n) const {
deba@326
  1950
      return (*_node_potential)[n];
deba@326
  1951
    }
deba@326
  1952
kpeter@590
  1953
    /// \brief Return the number of the blossoms in the basis.
deba@326
  1954
    ///
kpeter@590
  1955
    /// This function returns the number of the blossoms in the basis.
kpeter@590
  1956
    ///
kpeter@590
  1957
    /// \pre Either run() or start() must be called before using this function.
deba@326
  1958
    /// \see BlossomIt
deba@326
  1959
    int blossomNum() const {
deba@326
  1960
      return _blossom_potential.size();
deba@326
  1961
    }
deba@326
  1962
kpeter@590
  1963
    /// \brief Return the number of the nodes in the given blossom.
deba@326
  1964
    ///
kpeter@590
  1965
    /// This function returns the number of the nodes in the given blossom.
kpeter@590
  1966
    ///
kpeter@590
  1967
    /// \pre Either run() or start() must be called before using this function.
kpeter@590
  1968
    /// \see BlossomIt
deba@326
  1969
    int blossomSize(int k) const {
deba@326
  1970
      return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326
  1971
    }
deba@326
  1972
kpeter@590
  1973
    /// \brief Return the dual value (ptential) of the given blossom.
deba@326
  1974
    ///
kpeter@590
  1975
    /// This function returns the dual value (ptential) of the given blossom.
kpeter@590
  1976
    ///
kpeter@590
  1977
    /// \pre Either run() or start() must be called before using this function.
deba@326
  1978
    Value blossomValue(int k) const {
deba@326
  1979
      return _blossom_potential[k].value;
deba@326
  1980
    }
deba@326
  1981
kpeter@590
  1982
    /// \brief Iterator for obtaining the nodes of a blossom.
deba@326
  1983
    ///
kpeter@590
  1984
    /// This class provides an iterator for obtaining the nodes of the 
kpeter@590
  1985
    /// given blossom. It lists a subset of the nodes.
kpeter@590
  1986
    /// Before using this iterator, you must allocate a 
kpeter@590
  1987
    /// MaxWeightedMatching class and execute it.
deba@326
  1988
    class BlossomIt {
deba@326
  1989
    public:
deba@326
  1990
deba@326
  1991
      /// \brief Constructor.
deba@326
  1992
      ///
kpeter@590
  1993
      /// Constructor to get the nodes of the given variable.
kpeter@590
  1994
      ///
kpeter@590
  1995
      /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or 
kpeter@590
  1996
      /// \ref MaxWeightedMatching::start() "algorithm.start()" must be 
kpeter@590
  1997
      /// called before initializing this iterator.
deba@326
  1998
      BlossomIt(const MaxWeightedMatching& algorithm, int variable)
deba@326
  1999
        : _algorithm(&algorithm)
deba@326
  2000
      {
deba@326
  2001
        _index = _algorithm->_blossom_potential[variable].begin;
deba@326
  2002
        _last = _algorithm->_blossom_potential[variable].end;
deba@326
  2003
      }
deba@326
  2004
kpeter@590
  2005
      /// \brief Conversion to \c Node.
deba@326
  2006
      ///
kpeter@590
  2007
      /// Conversion to \c Node.
deba@326
  2008
      operator Node() const {
deba@327
  2009
        return _algorithm->_blossom_node_list[_index];
deba@326
  2010
      }
deba@326
  2011
deba@326
  2012
      /// \brief Increment operator.
deba@326
  2013
      ///
deba@326
  2014
      /// Increment operator.
deba@326
  2015
      BlossomIt& operator++() {
deba@326
  2016
        ++_index;
deba@326
  2017
        return *this;
deba@326
  2018
      }
deba@326
  2019
deba@327
  2020
      /// \brief Validity checking
deba@327
  2021
      ///
deba@327
  2022
      /// Checks whether the iterator is invalid.
deba@327
  2023
      bool operator==(Invalid) const { return _index == _last; }
deba@327
  2024
deba@327
  2025
      /// \brief Validity checking
deba@327
  2026
      ///
deba@327
  2027
      /// Checks whether the iterator is valid.
deba@327
  2028
      bool operator!=(Invalid) const { return _index != _last; }
deba@326
  2029
deba@326
  2030
    private:
deba@326
  2031
      const MaxWeightedMatching* _algorithm;
deba@326
  2032
      int _last;
deba@326
  2033
      int _index;
deba@326
  2034
    };
deba@326
  2035
deba@326
  2036
    /// @}
deba@326
  2037
deba@326
  2038
  };
deba@326
  2039
deba@326
  2040
  /// \ingroup matching
deba@326
  2041
  ///
deba@326
  2042
  /// \brief Weighted perfect matching in general graphs
deba@326
  2043
  ///
deba@326
  2044
  /// This class provides an efficient implementation of Edmond's
deba@327
  2045
  /// maximum weighted perfect matching algorithm. The implementation
deba@326
  2046
  /// is based on extensive use of priority queues and provides
kpeter@559
  2047
  /// \f$O(nm\log n)\f$ time complexity.
deba@326
  2048
  ///
kpeter@590
  2049
  /// The maximum weighted perfect matching problem is to find a subset of 
kpeter@590
  2050
  /// the edges in an undirected graph with maximum overall weight for which 
kpeter@590
  2051
  /// each node has exactly one incident edge.
kpeter@590
  2052
  /// It can be formulated with the following linear program.
deba@326
  2053
  /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f]
deba@327
  2054
  /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2}
deba@327
  2055
      \quad \forall B\in\mathcal{O}\f] */
deba@326
  2056
  /// \f[x_e \ge 0\quad \forall e\in E\f]
deba@326
  2057
  /// \f[\max \sum_{e\in E}x_ew_e\f]
deba@327
  2058
  /// where \f$\delta(X)\f$ is the set of edges incident to a node in
deba@327
  2059
  /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in
deba@327
  2060
  /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality
deba@327
  2061
  /// subsets of the nodes.
deba@326
  2062
  ///
deba@326
  2063
  /// The algorithm calculates an optimal matching and a proof of the
deba@326
  2064
  /// optimality. The solution of the dual problem can be used to check
deba@327
  2065
  /// the result of the algorithm. The dual linear problem is the
kpeter@590
  2066
  /// following.
deba@327
  2067
  /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge
deba@327
  2068
      w_{uv} \quad \forall uv\in E\f] */
deba@326
  2069
  /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f]
deba@327
  2070
  /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}}
deba@327
  2071
      \frac{\vert B \vert - 1}{2}z_B\f] */
deba@326
  2072
  ///
kpeter@590
  2073
  /// The algorithm can be executed with the run() function. 
kpeter@590
  2074
  /// After it the matching (the primal solution) and the dual solution
kpeter@590
  2075
  /// can be obtained using the query functions and the 
kpeter@590
  2076
  /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class, 
kpeter@590
  2077
  /// which is able to iterate on the nodes of a blossom. 
kpeter@590
  2078
  /// If the value type is integer, then the dual solution is multiplied
kpeter@590
  2079
  /// by \ref MaxWeightedMatching::dualScale "4".
kpeter@590
  2080
  ///
kpeter@593
  2081
  /// \tparam GR The undirected graph type the algorithm runs on.
kpeter@590
  2082
  /// \tparam WM The type edge weight map. The default type is 
kpeter@590
  2083
  /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>".
kpeter@590
  2084
#ifdef DOXYGEN
kpeter@590
  2085
  template <typename GR, typename WM>
kpeter@590
  2086
#else
kpeter@559
  2087
  template <typename GR,
kpeter@559
  2088
            typename WM = typename GR::template EdgeMap<int> >
kpeter@590
  2089
#endif
deba@326
  2090
  class MaxWeightedPerfectMatching {
deba@326
  2091
  public:
deba@326
  2092
kpeter@590
  2093
    /// The graph type of the algorithm
kpeter@559
  2094
    typedef GR Graph;
kpeter@590
  2095
    /// The type of the edge weight map
kpeter@559
  2096
    typedef WM WeightMap;
kpeter@590
  2097
    /// The value type of the edge weights
deba@326
  2098
    typedef typename WeightMap::Value Value;
deba@326
  2099
deba@326
  2100
    /// \brief Scaling factor for dual solution
deba@326
  2101
    ///
deba@326
  2102
    /// Scaling factor for dual solution, it is equal to 4 or 1
deba@326
  2103
    /// according to the value type.
deba@326
  2104
    static const int dualScale =
deba@326
  2105
      std::numeric_limits<Value>::is_integer ? 4 : 1;
deba@326
  2106
kpeter@593
  2107
    /// The type of the matching map
deba@326
  2108
    typedef typename Graph::template NodeMap<typename Graph::Arc>
deba@326
  2109
    MatchingMap;
deba@326
  2110
deba@326
  2111
  private:
deba@326
  2112
deba@326
  2113
    TEMPLATE_GRAPH_TYPEDEFS(Graph);
deba@326
  2114
deba@326
  2115
    typedef typename Graph::template NodeMap<Value> NodePotential;
deba@326
  2116
    typedef std::vector<Node> BlossomNodeList;
deba@326
  2117
deba@326
  2118
    struct BlossomVariable {
deba@326
  2119
      int begin, end;
deba@326
  2120
      Value value;
deba@326
  2121
deba@326
  2122
      BlossomVariable(int _begin, int _end, Value _value)
deba@326
  2123
        : begin(_begin), end(_end), value(_value) {}
deba@326
  2124
deba@326
  2125
    };
deba@326
  2126
deba@326
  2127
    typedef std::vector<BlossomVariable> BlossomPotential;
deba@326
  2128
deba@326
  2129
    const Graph& _graph;
deba@326
  2130
    const WeightMap& _weight;
deba@326
  2131
deba@326
  2132
    MatchingMap* _matching;
deba@326
  2133
deba@326
  2134
    NodePotential* _node_potential;
deba@326
  2135
deba@326
  2136
    BlossomPotential _blossom_potential;
deba@326
  2137
    BlossomNodeList _blossom_node_list;
deba@326
  2138
deba@326
  2139
    int _node_num;
deba@326
  2140
    int _blossom_num;
deba@326
  2141
deba@326
  2142
    typedef RangeMap<int> IntIntMap;
deba@326
  2143
deba@326
  2144
    enum Status {
deba@326
  2145
      EVEN = -1, MATCHED = 0, ODD = 1
deba@326
  2146
    };
deba@326
  2147
deba@327
  2148
    typedef HeapUnionFind<Value, IntNodeMap> BlossomSet;
deba@326
  2149
    struct BlossomData {
deba@326
  2150
      int tree;
deba@326
  2151
      Status status;
deba@326
  2152
      Arc pred, next;
deba@326
  2153
      Value pot, offset;
deba@326
  2154
    };
deba@326
  2155
deba@327
  2156
    IntNodeMap *_blossom_index;
deba@326
  2157
    BlossomSet *_blossom_set;
deba@326
  2158
    RangeMap<BlossomData>* _blossom_data;
deba@326
  2159
deba@327
  2160
    IntNodeMap *_node_index;
deba@327
  2161
    IntArcMap *_node_heap_index;
deba@326
  2162
deba@326
  2163
    struct NodeData {
deba@326
  2164
deba@327
  2165
      NodeData(IntArcMap& node_heap_index)
deba@326
  2166
        : heap(node_heap_index) {}
deba@326
  2167
deba@326
  2168
      int blossom;
deba@326
  2169
      Value pot;
deba@327
  2170
      BinHeap<Value, IntArcMap> heap;
deba@326
  2171
      std::map<int, Arc> heap_index;
deba@326
  2172
deba@326
  2173
      int tree;
deba@326
  2174
    };
deba@326
  2175
deba@326
  2176
    RangeMap<NodeData>* _node_data;
deba@326
  2177
deba@326
  2178
    typedef ExtendFindEnum<IntIntMap> TreeSet;
deba@326
  2179
deba@326
  2180
    IntIntMap *_tree_set_index;
deba@326
  2181
    TreeSet *_tree_set;
deba@326
  2182
deba@326
  2183
    IntIntMap *_delta2_index;
deba@326
  2184
    BinHeap<Value, IntIntMap> *_delta2;
deba@326
  2185
deba@327
  2186
    IntEdgeMap *_delta3_index;
deba@327
  2187
    BinHeap<Value, IntEdgeMap> *_delta3;
deba@326
  2188
deba@326
  2189
    IntIntMap *_delta4_index;
deba@326
  2190
    BinHeap<Value, IntIntMap> *_delta4;
deba@326
  2191
deba@326
  2192
    Value _delta_sum;
deba@326
  2193
deba@326
  2194
    void createStructures() {
deba@326
  2195
      _node_num = countNodes(_graph);
deba@326
  2196
      _blossom_num = _node_num * 3 / 2;
deba@326
  2197
deba@326
  2198
      if (!_matching) {
deba@326
  2199
        _matching = new MatchingMap(_graph);
deba@326
  2200
      }
deba@326
  2201
      if (!_node_potential) {
deba@326
  2202
        _node_potential = new NodePotential(_graph);
deba@326
  2203
      }
deba@326
  2204
      if (!_blossom_set) {
deba@327
  2205
        _blossom_index = new IntNodeMap(_graph);
deba@326
  2206
        _blossom_set = new BlossomSet(*_blossom_index);
deba@326
  2207
        _blossom_data = new RangeMap<BlossomData>(_blossom_num);
deba@326
  2208
      }
deba@326
  2209
deba@326
  2210
      if (!_node_index) {
deba@327
  2211
        _node_index = new IntNodeMap(_graph);
deba@327
  2212
        _node_heap_index = new IntArcMap(_graph);
deba@326
  2213
        _node_data = new RangeMap<NodeData>(_node_num,
deba@327
  2214
                                            NodeData(*_node_heap_index));
deba@326
  2215
      }
deba@326
  2216
deba@326
  2217
      if (!_tree_set) {
deba@326
  2218
        _tree_set_index = new IntIntMap(_blossom_num);
deba@326
  2219
        _tree_set = new TreeSet(*_tree_set_index);
deba@326
  2220
      }
deba@326
  2221
      if (!_delta2) {
deba@326
  2222
        _delta2_index = new IntIntMap(_blossom_num);
deba@326
  2223
        _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index);
deba@326
  2224
      }
deba@326
  2225
      if (!_delta3) {
deba@327
  2226
        _delta3_index = new IntEdgeMap(_graph);
deba@327
  2227
        _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index);
deba@326
  2228
      }
deba@326
  2229
      if (!_delta4) {
deba@326
  2230
        _delta4_index = new IntIntMap(_blossom_num);
deba@326
  2231
        _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index);
deba@326
  2232
      }
deba@326
  2233
    }
deba@326
  2234
deba@326
  2235
    void destroyStructures() {
deba@326
  2236
      _node_num = countNodes(_graph);
deba@326
  2237
      _blossom_num = _node_num * 3 / 2;
deba@326
  2238
deba@326
  2239
      if (_matching) {
deba@326
  2240
        delete _matching;
deba@326
  2241
      }
deba@326
  2242
      if (_node_potential) {
deba@326
  2243
        delete _node_potential;
deba@326
  2244
      }
deba@326
  2245
      if (_blossom_set) {
deba@326
  2246
        delete _blossom_index;
deba@326
  2247
        delete _blossom_set;
deba@326
  2248
        delete _blossom_data;
deba@326
  2249
      }
deba@326
  2250
deba@326
  2251
      if (_node_index) {
deba@326
  2252
        delete _node_index;
deba@326
  2253
        delete _node_heap_index;
deba@326
  2254
        delete _node_data;
deba@326
  2255
      }
deba@326
  2256
deba@326
  2257
      if (_tree_set) {
deba@326
  2258
        delete _tree_set_index;
deba@326
  2259
        delete _tree_set;
deba@326
  2260
      }
deba@326
  2261
      if (_delta2) {
deba@326
  2262
        delete _delta2_index;
deba@326
  2263
        delete _delta2;
deba@326
  2264
      }
deba@326
  2265
      if (_delta3) {
deba@326
  2266
        delete _delta3_index;
deba@326
  2267
        delete _delta3;
deba@326
  2268
      }
deba@326
  2269
      if (_delta4) {
deba@326
  2270
        delete _delta4_index;
deba@326
  2271
        delete _delta4;
deba@326
  2272
      }
deba@326
  2273
    }
deba@326
  2274
deba@326
  2275
    void matchedToEven(int blossom, int tree) {
deba@326
  2276
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  2277
        _delta2->erase(blossom);
deba@326
  2278
      }
deba@326
  2279
deba@326
  2280
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2281
        (*_blossom_data)[blossom].pot -=
deba@326
  2282
          2 * (_delta_sum - (*_blossom_data)[blossom].offset);
deba@326
  2283
      }
deba@326
  2284
deba@326
  2285
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  2286
           n != INVALID; ++n) {
deba@326
  2287
deba@326
  2288
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  2289
        int ni = (*_node_index)[n];
deba@326
  2290
deba@326
  2291
        (*_node_data)[ni].heap.clear();
deba@326
  2292
        (*_node_data)[ni].heap_index.clear();
deba@326
  2293
deba@326
  2294
        (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
  2295
deba@326
  2296
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2297
          Node v = _graph.source(e);
deba@326
  2298
          int vb = _blossom_set->find(v);
deba@326
  2299
          int vi = (*_node_index)[v];
deba@326
  2300
deba@326
  2301
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  2302
            dualScale * _weight[e];
deba@326
  2303
deba@326
  2304
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  2305
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
  2306
              _delta3->push(e, rw / 2);
deba@326
  2307
            }
deba@326
  2308
          } else {
deba@326
  2309
            typename std::map<int, Arc>::iterator it =
deba@326
  2310
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  2311
deba@326
  2312
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  2313
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
  2314
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
  2315
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
  2316
                it->second = e;
deba@326
  2317
              }
deba@326
  2318
            } else {
deba@326
  2319
              (*_node_data)[vi].heap.push(e, rw);
deba@326
  2320
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
  2321
            }
deba@326
  2322
deba@326
  2323
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
  2324
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
  2325
deba@326
  2326
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  2327
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
  2328
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
  2329
                               (*_blossom_data)[vb].offset);
deba@326
  2330
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
  2331
                           (*_blossom_data)[vb].offset){
deba@326
  2332
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
  2333
                                   (*_blossom_data)[vb].offset);
deba@326
  2334
                }
deba@326
  2335
              }
deba@326
  2336
            }
deba@326
  2337
          }
deba@326
  2338
        }
deba@326
  2339
      }
deba@326
  2340
      (*_blossom_data)[blossom].offset = 0;
deba@326
  2341
    }
deba@326
  2342
deba@326
  2343
    void matchedToOdd(int blossom) {
deba@326
  2344
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  2345
        _delta2->erase(blossom);
deba@326
  2346
      }
deba@326
  2347
      (*_blossom_data)[blossom].offset += _delta_sum;
deba@326
  2348
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2349
        _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 +
deba@326
  2350
                     (*_blossom_data)[blossom].offset);
deba@326
  2351
      }
deba@326
  2352
    }
deba@326
  2353
deba@326
  2354
    void evenToMatched(int blossom, int tree) {
deba@326
  2355
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2356
        (*_blossom_data)[blossom].pot += 2 * _delta_sum;
deba@326
  2357
      }
deba@326
  2358
deba@326
  2359
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  2360
           n != INVALID; ++n) {
deba@326
  2361
        int ni = (*_node_index)[n];
deba@326
  2362
        (*_node_data)[ni].pot -= _delta_sum;
deba@326
  2363
deba@326
  2364
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2365
          Node v = _graph.source(e);
deba@326
  2366
          int vb = _blossom_set->find(v);
deba@326
  2367
          int vi = (*_node_index)[v];
deba@326
  2368
deba@326
  2369
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  2370
            dualScale * _weight[e];
deba@326
  2371
deba@326
  2372
          if (vb == blossom) {
deba@326
  2373
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  2374
              _delta3->erase(e);
deba@326
  2375
            }
deba@326
  2376
          } else if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  2377
deba@326
  2378
            if (_delta3->state(e) == _delta3->IN_HEAP) {
deba@326
  2379
              _delta3->erase(e);
deba@326
  2380
            }
deba@326
  2381
deba@326
  2382
            int vt = _tree_set->find(vb);
deba@326
  2383
deba@326
  2384
            if (vt != tree) {
deba@326
  2385
deba@326
  2386
              Arc r = _graph.oppositeArc(e);
deba@326
  2387
deba@326
  2388
              typename std::map<int, Arc>::iterator it =
deba@326
  2389
                (*_node_data)[ni].heap_index.find(vt);
deba@326
  2390
deba@326
  2391
              if (it != (*_node_data)[ni].heap_index.end()) {
deba@326
  2392
                if ((*_node_data)[ni].heap[it->second] > rw) {
deba@326
  2393
                  (*_node_data)[ni].heap.replace(it->second, r);
deba@326
  2394
                  (*_node_data)[ni].heap.decrease(r, rw);
deba@326
  2395
                  it->second = r;
deba@326
  2396
                }
deba@326
  2397
              } else {
deba@326
  2398
                (*_node_data)[ni].heap.push(r, rw);
deba@326
  2399
                (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r));
deba@326
  2400
              }
deba@326
  2401
deba@326
  2402
              if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) {
deba@326
  2403
                _blossom_set->decrease(n, (*_node_data)[ni].heap.prio());
deba@326
  2404
deba@326
  2405
                if (_delta2->state(blossom) != _delta2->IN_HEAP) {
deba@326
  2406
                  _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  2407
                               (*_blossom_data)[blossom].offset);
deba@326
  2408
                } else if ((*_delta2)[blossom] >
deba@326
  2409
                           _blossom_set->classPrio(blossom) -
deba@326
  2410
                           (*_blossom_data)[blossom].offset){
deba@326
  2411
                  _delta2->decrease(blossom, _blossom_set->classPrio(blossom) -
deba@326
  2412
                                   (*_blossom_data)[blossom].offset);
deba@326
  2413
                }
deba@326
  2414
              }
deba@326
  2415
            }
deba@326
  2416
          } else {
deba@326
  2417
deba@326
  2418
            typename std::map<int, Arc>::iterator it =
deba@326
  2419
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  2420
deba@326
  2421
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  2422
              (*_node_data)[vi].heap.erase(it->second);
deba@326
  2423
              (*_node_data)[vi].heap_index.erase(it);
deba@326
  2424
              if ((*_node_data)[vi].heap.empty()) {
deba@326
  2425
                _blossom_set->increase(v, std::numeric_limits<Value>::max());
deba@326
  2426
              } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) {
deba@326
  2427
                _blossom_set->increase(v, (*_node_data)[vi].heap.prio());
deba@326
  2428
              }
deba@326
  2429
deba@326
  2430
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  2431
                if (_blossom_set->classPrio(vb) ==
deba@326
  2432
                    std::numeric_limits<Value>::max()) {
deba@326
  2433
                  _delta2->erase(vb);
deba@326
  2434
                } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) -
deba@326
  2435
                           (*_blossom_data)[vb].offset) {
deba@326
  2436
                  _delta2->increase(vb, _blossom_set->classPrio(vb) -
deba@326
  2437
                                   (*_blossom_data)[vb].offset);
deba@326
  2438
                }
deba@326
  2439
              }
deba@326
  2440
            }
deba@326
  2441
          }
deba@326
  2442
        }
deba@326
  2443
      }
deba@326
  2444
    }
deba@326
  2445
deba@326
  2446
    void oddToMatched(int blossom) {
deba@326
  2447
      (*_blossom_data)[blossom].offset -= _delta_sum;
deba@326
  2448
deba@326
  2449
      if (_blossom_set->classPrio(blossom) !=
deba@326
  2450
          std::numeric_limits<Value>::max()) {
deba@326
  2451
        _delta2->push(blossom, _blossom_set->classPrio(blossom) -
deba@326
  2452
                       (*_blossom_data)[blossom].offset);
deba@326
  2453
      }
deba@326
  2454
deba@326
  2455
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2456
        _delta4->erase(blossom);
deba@326
  2457
      }
deba@326
  2458
    }
deba@326
  2459
deba@326
  2460
    void oddToEven(int blossom, int tree) {
deba@326
  2461
      if (!_blossom_set->trivial(blossom)) {
deba@326
  2462
        _delta4->erase(blossom);
deba@326
  2463
        (*_blossom_data)[blossom].pot -=
deba@326
  2464
          2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset);
deba@326
  2465
      }
deba@326
  2466
deba@326
  2467
      for (typename BlossomSet::ItemIt n(*_blossom_set, blossom);
deba@326
  2468
           n != INVALID; ++n) {
deba@326
  2469
        int ni = (*_node_index)[n];
deba@326
  2470
deba@326
  2471
        _blossom_set->increase(n, std::numeric_limits<Value>::max());
deba@326
  2472
deba@326
  2473
        (*_node_data)[ni].heap.clear();
deba@326
  2474
        (*_node_data)[ni].heap_index.clear();
deba@326
  2475
        (*_node_data)[ni].pot +=
deba@326
  2476
          2 * _delta_sum - (*_blossom_data)[blossom].offset;
deba@326
  2477
deba@326
  2478
        for (InArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2479
          Node v = _graph.source(e);
deba@326
  2480
          int vb = _blossom_set->find(v);
deba@326
  2481
          int vi = (*_node_index)[v];
deba@326
  2482
deba@326
  2483
          Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot -
deba@326
  2484
            dualScale * _weight[e];
deba@326
  2485
deba@326
  2486
          if ((*_blossom_data)[vb].status == EVEN) {
deba@326
  2487
            if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) {
deba@326
  2488
              _delta3->push(e, rw / 2);
deba@326
  2489
            }
deba@326
  2490
          } else {
deba@326
  2491
deba@326
  2492
            typename std::map<int, Arc>::iterator it =
deba@326
  2493
              (*_node_data)[vi].heap_index.find(tree);
deba@326
  2494
deba@326
  2495
            if (it != (*_node_data)[vi].heap_index.end()) {
deba@326
  2496
              if ((*_node_data)[vi].heap[it->second] > rw) {
deba@326
  2497
                (*_node_data)[vi].heap.replace(it->second, e);
deba@326
  2498
                (*_node_data)[vi].heap.decrease(e, rw);
deba@326
  2499
                it->second = e;
deba@326
  2500
              }
deba@326
  2501
            } else {
deba@326
  2502
              (*_node_data)[vi].heap.push(e, rw);
deba@326
  2503
              (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e));
deba@326
  2504
            }
deba@326
  2505
deba@326
  2506
            if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) {
deba@326
  2507
              _blossom_set->decrease(v, (*_node_data)[vi].heap.prio());
deba@326
  2508
deba@326
  2509
              if ((*_blossom_data)[vb].status == MATCHED) {
deba@326
  2510
                if (_delta2->state(vb) != _delta2->IN_HEAP) {
deba@326
  2511
                  _delta2->push(vb, _blossom_set->classPrio(vb) -
deba@326
  2512
                               (*_blossom_data)[vb].offset);
deba@326
  2513
                } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) -
deba@326
  2514
                           (*_blossom_data)[vb].offset) {
deba@326
  2515
                  _delta2->decrease(vb, _blossom_set->classPrio(vb) -
deba@326
  2516
                                   (*_blossom_data)[vb].offset);
deba@326
  2517
                }
deba@326
  2518
              }
deba@326
  2519
            }
deba@326
  2520
          }
deba@326
  2521
        }
deba@326
  2522
      }
deba@326
  2523
      (*_blossom_data)[blossom].offset = 0;
deba@326
  2524
    }
deba@326
  2525
deba@326
  2526
    void alternatePath(int even, int tree) {
deba@326
  2527
      int odd;
deba@326
  2528
deba@326
  2529
      evenToMatched(even, tree);
deba@326
  2530
      (*_blossom_data)[even].status = MATCHED;
deba@326
  2531
deba@326
  2532
      while ((*_blossom_data)[even].pred != INVALID) {
deba@326
  2533
        odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred));
deba@326
  2534
        (*_blossom_data)[odd].status = MATCHED;
deba@326
  2535
        oddToMatched(odd);
deba@326
  2536
        (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred;
deba@326
  2537
deba@326
  2538
        even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred));
deba@326
  2539
        (*_blossom_data)[even].status = MATCHED;
deba@326
  2540
        evenToMatched(even, tree);
deba@326
  2541
        (*_blossom_data)[even].next =
deba@326
  2542
          _graph.oppositeArc((*_blossom_data)[odd].pred);
deba@326
  2543
      }
deba@326
  2544
deba@326
  2545
    }
deba@326
  2546
deba@326
  2547
    void destroyTree(int tree) {
deba@326
  2548
      for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) {
deba@326
  2549
        if ((*_blossom_data)[b].status == EVEN) {
deba@326
  2550
          (*_blossom_data)[b].status = MATCHED;
deba@326
  2551
          evenToMatched(b, tree);
deba@326
  2552
        } else if ((*_blossom_data)[b].status == ODD) {
deba@326
  2553
          (*_blossom_data)[b].status = MATCHED;
deba@326
  2554
          oddToMatched(b);
deba@326
  2555
        }
deba@326
  2556
      }
deba@326
  2557
      _tree_set->eraseClass(tree);
deba@326
  2558
    }
deba@326
  2559
deba@327
  2560
    void augmentOnEdge(const Edge& edge) {
deba@327
  2561
deba@327
  2562
      int left = _blossom_set->find(_graph.u(edge));
deba@327
  2563
      int right = _blossom_set->find(_graph.v(edge));
deba@326
  2564
deba@326
  2565
      int left_tree = _tree_set->find(left);
deba@326
  2566
      alternatePath(left, left_tree);
deba@326
  2567
      destroyTree(left_tree);
deba@326
  2568
deba@326
  2569
      int right_tree = _tree_set->find(right);
deba@326
  2570
      alternatePath(right, right_tree);
deba@326
  2571
      destroyTree(right_tree);
deba@326
  2572
deba@327
  2573
      (*_blossom_data)[left].next = _graph.direct(edge, true);
deba@327
  2574
      (*_blossom_data)[right].next = _graph.direct(edge, false);
deba@326
  2575
    }
deba@326
  2576
deba@326
  2577
    void extendOnArc(const Arc& arc) {
deba@326
  2578
      int base = _blossom_set->find(_graph.target(arc));
deba@326
  2579
      int tree = _tree_set->find(base);
deba@326
  2580
deba@326
  2581
      int odd = _blossom_set->find(_graph.source(arc));
deba@326
  2582
      _tree_set->insert(odd, tree);
deba@326
  2583
      (*_blossom_data)[odd].status = ODD;
deba@326
  2584
      matchedToOdd(odd);
deba@326
  2585
      (*_blossom_data)[odd].pred = arc;
deba@326
  2586
deba@326
  2587
      int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next));
deba@326
  2588
      (*_blossom_data)[even].pred = (*_blossom_data)[even].next;
deba@326
  2589
      _tree_set->insert(even, tree);
deba@326
  2590
      (*_blossom_data)[even].status = EVEN;
deba@326
  2591
      matchedToEven(even, tree);
deba@326
  2592
    }
deba@326
  2593
deba@327
  2594
    void shrinkOnEdge(const Edge& edge, int tree) {
deba@326
  2595
      int nca = -1;
deba@326
  2596
      std::vector<int> left_path, right_path;
deba@326
  2597
deba@326
  2598
      {
deba@326
  2599
        std::set<int> left_set, right_set;
deba@326
  2600
        int left = _blossom_set->find(_graph.u(edge));
deba@326
  2601
        left_path.push_back(left);
deba@326
  2602
        left_set.insert(left);
deba@326
  2603
deba@326
  2604
        int right = _blossom_set->find(_graph.v(edge));
deba@326
  2605
        right_path.push_back(right);
deba@326
  2606
        right_set.insert(right);
deba@326
  2607
deba@326
  2608
        while (true) {
deba@326
  2609
deba@326
  2610
          if ((*_blossom_data)[left].pred == INVALID) break;
deba@326
  2611
deba@326
  2612
          left =
deba@326
  2613
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  2614
          left_path.push_back(left);
deba@326
  2615
          left =
deba@326
  2616
            _blossom_set->find(_graph.target((*_blossom_data)[left].pred));
deba@326
  2617
          left_path.push_back(left);
deba@326
  2618
deba@326
  2619
          left_set.insert(left);
deba@326
  2620
deba@326
  2621
          if (right_set.find(left) != right_set.end()) {
deba@326
  2622
            nca = left;
deba@326
  2623
            break;
deba@326
  2624
          }
deba@326
  2625
deba@326
  2626
          if ((*_blossom_data)[right].pred == INVALID) break;
deba@326
  2627
deba@326
  2628
          right =
deba@326
  2629
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  2630
          right_path.push_back(right);
deba@326
  2631
          right =
deba@326
  2632
            _blossom_set->find(_graph.target((*_blossom_data)[right].pred));
deba@326
  2633
          right_path.push_back(right);
deba@326
  2634
deba@326
  2635
          right_set.insert(right);
deba@326
  2636
deba@326
  2637
          if (left_set.find(right) != left_set.end()) {
deba@326
  2638
            nca = right;
deba@326
  2639
            break;
deba@326
  2640
          }
deba@326
  2641
deba@326
  2642
        }
deba@326
  2643
deba@326
  2644
        if (nca == -1) {
deba@326
  2645
          if ((*_blossom_data)[left].pred == INVALID) {
deba@326
  2646
            nca = right;
deba@326
  2647
            while (left_set.find(nca) == left_set.end()) {
deba@326
  2648
              nca =
deba@326
  2649
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2650
              right_path.push_back(nca);
deba@326
  2651
              nca =
deba@326
  2652
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2653
              right_path.push_back(nca);
deba@326
  2654
            }
deba@326
  2655
          } else {
deba@326
  2656
            nca = left;
deba@326
  2657
            while (right_set.find(nca) == right_set.end()) {
deba@326
  2658
              nca =
deba@326
  2659
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2660
              left_path.push_back(nca);
deba@326
  2661
              nca =
deba@326
  2662
                _blossom_set->find(_graph.target((*_blossom_data)[nca].pred));
deba@326
  2663
              left_path.push_back(nca);
deba@326
  2664
            }
deba@326
  2665
          }
deba@326
  2666
        }
deba@326
  2667
      }
deba@326
  2668
deba@326
  2669
      std::vector<int> subblossoms;
deba@326
  2670
      Arc prev;
deba@326
  2671
deba@326
  2672
      prev = _graph.direct(edge, true);
deba@326
  2673
      for (int i = 0; left_path[i] != nca; i += 2) {
deba@326
  2674
        subblossoms.push_back(left_path[i]);
deba@326
  2675
        (*_blossom_data)[left_path[i]].next = prev;
deba@326
  2676
        _tree_set->erase(left_path[i]);
deba@326
  2677
deba@326
  2678
        subblossoms.push_back(left_path[i + 1]);
deba@326
  2679
        (*_blossom_data)[left_path[i + 1]].status = EVEN;
deba@326
  2680
        oddToEven(left_path[i + 1], tree);
deba@326
  2681
        _tree_set->erase(left_path[i + 1]);
deba@326
  2682
        prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred);
deba@326
  2683
      }
deba@326
  2684
deba@326
  2685
      int k = 0;
deba@326
  2686
      while (right_path[k] != nca) ++k;
deba@326
  2687
deba@326
  2688
      subblossoms.push_back(nca);
deba@326
  2689
      (*_blossom_data)[nca].next = prev;
deba@326
  2690
deba@326
  2691
      for (int i = k - 2; i >= 0; i -= 2) {
deba@326
  2692
        subblossoms.push_back(right_path[i + 1]);
deba@326
  2693
        (*_blossom_data)[right_path[i + 1]].status = EVEN;
deba@326
  2694
        oddToEven(right_path[i + 1], tree);
deba@326
  2695
        _tree_set->erase(right_path[i + 1]);
deba@326
  2696
deba@326
  2697
        (*_blossom_data)[right_path[i + 1]].next =
deba@326
  2698
          (*_blossom_data)[right_path[i + 1]].pred;
deba@326
  2699
deba@326
  2700
        subblossoms.push_back(right_path[i]);
deba@326
  2701
        _tree_set->erase(right_path[i]);
deba@326
  2702
      }
deba@326
  2703
deba@326
  2704
      int surface =
deba@326
  2705
        _blossom_set->join(subblossoms.begin(), subblossoms.end());
deba@326
  2706
deba@326
  2707
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  2708
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  2709
          (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum;
deba@326
  2710
        }
deba@326
  2711
        (*_blossom_data)[subblossoms[i]].status = MATCHED;
deba@326
  2712
      }
deba@326
  2713
deba@326
  2714
      (*_blossom_data)[surface].pot = -2 * _delta_sum;
deba@326
  2715
      (*_blossom_data)[surface].offset = 0;
deba@326
  2716
      (*_blossom_data)[surface].status = EVEN;
deba@326
  2717
      (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred;
deba@326
  2718
      (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred;
deba@326
  2719
deba@326
  2720
      _tree_set->insert(surface, tree);
deba@326
  2721
      _tree_set->erase(nca);
deba@326
  2722
    }
deba@326
  2723
deba@326
  2724
    void splitBlossom(int blossom) {
deba@326
  2725
      Arc next = (*_blossom_data)[blossom].next;
deba@326
  2726
      Arc pred = (*_blossom_data)[blossom].pred;
deba@326
  2727
deba@326
  2728
      int tree = _tree_set->find(blossom);
deba@326
  2729
deba@326
  2730
      (*_blossom_data)[blossom].status = MATCHED;
deba@326
  2731
      oddToMatched(blossom);
deba@326
  2732
      if (_delta2->state(blossom) == _delta2->IN_HEAP) {
deba@326
  2733
        _delta2->erase(blossom);
deba@326
  2734
      }
deba@326
  2735
deba@326
  2736
      std::vector<int> subblossoms;
deba@326
  2737
      _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  2738
deba@326
  2739
      Value offset = (*_blossom_data)[blossom].offset;
deba@326
  2740
      int b = _blossom_set->find(_graph.source(pred));
deba@326
  2741
      int d = _blossom_set->find(_graph.source(next));
deba@326
  2742
deba@326
  2743
      int ib = -1, id = -1;
deba@326
  2744
      for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  2745
        if (subblossoms[i] == b) ib = i;
deba@326
  2746
        if (subblossoms[i] == d) id = i;
deba@326
  2747
deba@326
  2748
        (*_blossom_data)[subblossoms[i]].offset = offset;
deba@326
  2749
        if (!_blossom_set->trivial(subblossoms[i])) {
deba@326
  2750
          (*_blossom_data)[subblossoms[i]].pot -= 2 * offset;
deba@326
  2751
        }
deba@326
  2752
        if (_blossom_set->classPrio(subblossoms[i]) !=
deba@326
  2753
            std::numeric_limits<Value>::max()) {
deba@326
  2754
          _delta2->push(subblossoms[i],
deba@326
  2755
                        _blossom_set->classPrio(subblossoms[i]) -
deba@326
  2756
                        (*_blossom_data)[subblossoms[i]].offset);
deba@326
  2757
        }
deba@326
  2758
      }
deba@326
  2759
deba@326
  2760
      if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) {
deba@326
  2761
        for (int i = (id + 1) % subblossoms.size();
deba@326
  2762
             i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  2763
          int sb = subblossoms[i];
deba@326
  2764
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2765
          (*_blossom_data)[sb].next =
deba@326
  2766
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2767
        }
deba@326
  2768
deba@326
  2769
        for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  2770
          int sb = subblossoms[i];
deba@326
  2771
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2772
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  2773
deba@326
  2774
          (*_blossom_data)[sb].status = ODD;
deba@326
  2775
          matchedToOdd(sb);
deba@326
  2776
          _tree_set->insert(sb, tree);
deba@326
  2777
          (*_blossom_data)[sb].pred = pred;
deba@326
  2778
          (*_blossom_data)[sb].next =
deba@326
  2779
                           _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2780
deba@326
  2781
          pred = (*_blossom_data)[ub].next;
deba@326
  2782
deba@326
  2783
          (*_blossom_data)[tb].status = EVEN;
deba@326
  2784
          matchedToEven(tb, tree);
deba@326
  2785
          _tree_set->insert(tb, tree);
deba@326
  2786
          (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next;
deba@326
  2787
        }
deba@326
  2788
deba@326
  2789
        (*_blossom_data)[subblossoms[id]].status = ODD;
deba@326
  2790
        matchedToOdd(subblossoms[id]);
deba@326
  2791
        _tree_set->insert(subblossoms[id], tree);
deba@326
  2792
        (*_blossom_data)[subblossoms[id]].next = next;
deba@326
  2793
        (*_blossom_data)[subblossoms[id]].pred = pred;
deba@326
  2794
deba@326
  2795
      } else {
deba@326
  2796
deba@326
  2797
        for (int i = (ib + 1) % subblossoms.size();
deba@326
  2798
             i != id; i = (i + 2) % subblossoms.size()) {
deba@326
  2799
          int sb = subblossoms[i];
deba@326
  2800
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2801
          (*_blossom_data)[sb].next =
deba@326
  2802
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2803
        }
deba@326
  2804
deba@326
  2805
        for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) {
deba@326
  2806
          int sb = subblossoms[i];
deba@326
  2807
          int tb = subblossoms[(i + 1) % subblossoms.size()];
deba@326
  2808
          int ub = subblossoms[(i + 2) % subblossoms.size()];
deba@326
  2809
deba@326
  2810
          (*_blossom_data)[sb].status = ODD;
deba@326
  2811
          matchedToOdd(sb);
deba@326
  2812
          _tree_set->insert(sb, tree);
deba@326
  2813
          (*_blossom_data)[sb].next = next;
deba@326
  2814
          (*_blossom_data)[sb].pred =
deba@326
  2815
            _graph.oppositeArc((*_blossom_data)[tb].next);
deba@326
  2816
deba@326
  2817
          (*_blossom_data)[tb].status = EVEN;
deba@326
  2818
          matchedToEven(tb, tree);
deba@326
  2819
          _tree_set->insert(tb, tree);
deba@326
  2820
          (*_blossom_data)[tb].pred =
deba@326
  2821
            (*_blossom_data)[tb].next =
deba@326
  2822
            _graph.oppositeArc((*_blossom_data)[ub].next);
deba@326
  2823
          next = (*_blossom_data)[ub].next;
deba@326
  2824
        }
deba@326
  2825
deba@326
  2826
        (*_blossom_data)[subblossoms[ib]].status = ODD;
deba@326
  2827
        matchedToOdd(subblossoms[ib]);
deba@326
  2828
        _tree_set->insert(subblossoms[ib], tree);
deba@326
  2829
        (*_blossom_data)[subblossoms[ib]].next = next;
deba@326
  2830
        (*_blossom_data)[subblossoms[ib]].pred = pred;
deba@326
  2831
      }
deba@326
  2832
      _tree_set->erase(blossom);
deba@326
  2833
    }
deba@326
  2834
deba@326
  2835
    void extractBlossom(int blossom, const Node& base, const Arc& matching) {
deba@326
  2836
      if (_blossom_set->trivial(blossom)) {
deba@326
  2837
        int bi = (*_node_index)[base];
deba@326
  2838
        Value pot = (*_node_data)[bi].pot;
deba@326
  2839
kpeter@581
  2840
        (*_matching)[base] = matching;
deba@326
  2841
        _blossom_node_list.push_back(base);
kpeter@581
  2842
        (*_node_potential)[base] = pot;
deba@326
  2843
      } else {
deba@326
  2844
deba@326
  2845
        Value pot = (*_blossom_data)[blossom].pot;
deba@326
  2846
        int bn = _blossom_node_list.size();
deba@326
  2847
deba@326
  2848
        std::vector<int> subblossoms;
deba@326
  2849
        _blossom_set->split(blossom, std::back_inserter(subblossoms));
deba@326
  2850
        int b = _blossom_set->find(base);
deba@326
  2851
        int ib = -1;
deba@326
  2852
        for (int i = 0; i < int(subblossoms.size()); ++i) {
deba@326
  2853
          if (subblossoms[i] == b) { ib = i; break; }
deba@326
  2854
        }
deba@326
  2855
deba@326
  2856
        for (int i = 1; i < int(subblossoms.size()); i += 2) {
deba@326
  2857
          int sb = subblossoms[(ib + i) % subblossoms.size()];
deba@326
  2858
          int tb = subblossoms[(ib + i + 1) % subblossoms.size()];
deba@326
  2859
deba@326
  2860
          Arc m = (*_blossom_data)[tb].next;
deba@326
  2861
          extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m));
deba@326
  2862
          extractBlossom(tb, _graph.source(m), m);
deba@326
  2863
        }
deba@326
  2864
        extractBlossom(subblossoms[ib], base, matching);
deba@326
  2865
deba@326
  2866
        int en = _blossom_node_list.size();
deba@326
  2867
deba@326
  2868
        _blossom_potential.push_back(BlossomVariable(bn, en, pot));
deba@326
  2869
      }
deba@326
  2870
    }
deba@326
  2871
deba@326
  2872
    void extractMatching() {
deba@326
  2873
      std::vector<int> blossoms;
deba@326
  2874
      for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) {
deba@326
  2875
        blossoms.push_back(c);
deba@326
  2876
      }
deba@326
  2877
deba@326
  2878
      for (int i = 0; i < int(blossoms.size()); ++i) {
deba@326
  2879
deba@326
  2880
        Value offset = (*_blossom_data)[blossoms[i]].offset;
deba@326
  2881
        (*_blossom_data)[blossoms[i]].pot += 2 * offset;
deba@326
  2882
        for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]);
deba@326
  2883
             n != INVALID; ++n) {
deba@326
  2884
          (*_node_data)[(*_node_index)[n]].pot -= offset;
deba@326
  2885
        }
deba@326
  2886
deba@326
  2887
        Arc matching = (*_blossom_data)[blossoms[i]].next;
deba@326
  2888
        Node base = _graph.source(matching);
deba@326
  2889
        extractBlossom(blossoms[i], base, matching);
deba@326
  2890
      }
deba@326
  2891
    }
deba@326
  2892
deba@326
  2893
  public:
deba@326
  2894
deba@326
  2895
    /// \brief Constructor
deba@326
  2896
    ///
deba@326
  2897
    /// Constructor.
deba@326
  2898
    MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight)
deba@326
  2899
      : _graph(graph), _weight(weight), _matching(0),
deba@326
  2900
        _node_potential(0), _blossom_potential(), _blossom_node_list(),
deba@326
  2901
        _node_num(0), _blossom_num(0),
deba@326
  2902
deba@326
  2903
        _blossom_index(0), _blossom_set(0), _blossom_data(0),
deba@326
  2904
        _node_index(0), _node_heap_index(0), _node_data(0),
deba@326
  2905
        _tree_set_index(0), _tree_set(0),
deba@326
  2906
deba@326
  2907
        _delta2_index(0), _delta2(0),
deba@326
  2908
        _delta3_index(0), _delta3(0),
deba@326
  2909
        _delta4_index(0), _delta4(0),
deba@326
  2910
deba@326
  2911
        _delta_sum() {}
deba@326
  2912
deba@326
  2913
    ~MaxWeightedPerfectMatching() {
deba@326
  2914
      destroyStructures();
deba@326
  2915
    }
deba@326
  2916
kpeter@590
  2917
    /// \name Execution Control
alpar@330
  2918
    /// The simplest way to execute the algorithm is to use the
kpeter@590
  2919
    /// \ref run() member function.
deba@326
  2920
deba@326
  2921
    ///@{
deba@326
  2922
deba@326
  2923
    /// \brief Initialize the algorithm
deba@326
  2924
    ///
kpeter@590
  2925
    /// This function initializes the algorithm.
deba@326
  2926
    void init() {
deba@326
  2927
      createStructures();
deba@326
  2928
deba@326
  2929
      for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@581
  2930
        (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP;
deba@326
  2931
      }
deba@326
  2932
      for (EdgeIt e(_graph); e != INVALID; ++e) {
kpeter@581
  2933
        (*_delta3_index)[e] = _delta3->PRE_HEAP;
deba@326
  2934
      }
deba@326
  2935
      for (int i = 0; i < _blossom_num; ++i) {
kpeter@581
  2936
        (*_delta2_index)[i] = _delta2->PRE_HEAP;
kpeter@581
  2937
        (*_delta4_index)[i] = _delta4->PRE_HEAP;
deba@326
  2938
      }
deba@326
  2939
deba@326
  2940
      int index = 0;
deba@326
  2941
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  2942
        Value max = - std::numeric_limits<Value>::max();
deba@326
  2943
        for (OutArcIt e(_graph, n); e != INVALID; ++e) {
deba@326
  2944
          if (_graph.target(e) == n) continue;
deba@326
  2945
          if ((dualScale * _weight[e]) / 2 > max) {
deba@326
  2946
            max = (dualScale * _weight[e]) / 2;
deba@326
  2947
          }
deba@326
  2948
        }
kpeter@581
  2949
        (*_node_index)[n] = index;
deba@326
  2950
        (*_node_data)[index].pot = max;
deba@326
  2951
        int blossom =
deba@326
  2952
          _blossom_set->insert(n, std::numeric_limits<Value>::max());
deba@326
  2953
deba@326
  2954
        _tree_set->insert(blossom);
deba@326
  2955
deba@326
  2956
        (*_blossom_data)[blossom].status = EVEN;
deba@326
  2957
        (*_blossom_data)[blossom].pred = INVALID;
deba@326
  2958
        (*_blossom_data)[blossom].next = INVALID;
deba@326
  2959
        (*_blossom_data)[blossom].pot = 0;
deba@326
  2960
        (*_blossom_data)[blossom].offset = 0;
deba@326
  2961
        ++index;
deba@326
  2962
      }
deba@326
  2963
      for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@326
  2964
        int si = (*_node_index)[_graph.u(e)];
deba@326
  2965
        int ti = (*_node_index)[_graph.v(e)];
deba@326
  2966
        if (_graph.u(e) != _graph.v(e)) {
deba@326
  2967
          _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot -
deba@326
  2968
                            dualScale * _weight[e]) / 2);
deba@326
  2969
        }
deba@326
  2970
      }
deba@326
  2971
    }
deba@326
  2972
kpeter@590
  2973
    /// \brief Start the algorithm
deba@326
  2974
    ///
kpeter@590
  2975
    /// This function starts the algorithm.
kpeter@590
  2976
    ///
kpeter@590
  2977
    /// \pre \ref init() must be called before using this function.
deba@326
  2978
    bool start() {
deba@326
  2979
      enum OpType {
deba@326
  2980
        D2, D3, D4
deba@326
  2981
      };
deba@326
  2982
deba@326
  2983
      int unmatched = _node_num;
deba@326
  2984
      while (unmatched > 0) {
deba@326
  2985
        Value d2 = !_delta2->empty() ?
deba@326
  2986
          _delta2->prio() : std::numeric_limits<Value>::max();
deba@326
  2987
deba@326
  2988
        Value d3 = !_delta3->empty() ?
deba@326
  2989
          _delta3->prio() : std::numeric_limits<Value>::max();
deba@326
  2990
deba@326
  2991
        Value d4 = !_delta4->empty() ?
deba@326
  2992
          _delta4->prio() : std::numeric_limits<Value>::max();
deba@326
  2993
deba@326
  2994
        _delta_sum = d2; OpType ot = D2;
deba@326
  2995
        if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; }
deba@326
  2996
        if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; }
deba@326
  2997
deba@326
  2998
        if (_delta_sum == std::numeric_limits<Value>::max()) {
deba@326
  2999
          return false;
deba@326
  3000
        }
deba@326
  3001
deba@326
  3002
        switch (ot) {
deba@326
  3003
        case D2:
deba@326
  3004
          {
deba@326
  3005
            int blossom = _delta2->top();
deba@326
  3006
            Node n = _blossom_set->classTop(blossom);
deba@326
  3007
            Arc e = (*_node_data)[(*_node_index)[n]].heap.top();
deba@326
  3008
            extendOnArc(e);
deba@326
  3009
          }
deba@326
  3010
          break;
deba@326
  3011
        case D3:
deba@326
  3012
          {
deba@326
  3013
            Edge e = _delta3->top();
deba@326
  3014
deba@326
  3015
            int left_blossom = _blossom_set->find(_graph.u(e));
deba@326
  3016
            int right_blossom = _blossom_set->find(_graph.v(e));
deba@326
  3017
deba@326
  3018
            if (left_blossom == right_blossom) {
deba@326
  3019
              _delta3->pop();
deba@326
  3020
            } else {
deba@326
  3021
              int left_tree = _tree_set->find(left_blossom);
deba@326
  3022
              int right_tree = _tree_set->find(right_blossom);
deba@326
  3023
deba@326
  3024
              if (left_tree == right_tree) {
deba@327
  3025
                shrinkOnEdge(e, left_tree);
deba@326
  3026
              } else {
deba@327
  3027
                augmentOnEdge(e);
deba@326
  3028
                unmatched -= 2;
deba@326
  3029
              }
deba@326
  3030
            }
deba@326
  3031
          } break;
deba@326
  3032
        case D4:
deba@326
  3033
          splitBlossom(_delta4->top());
deba@326
  3034
          break;
deba@326
  3035
        }
deba@326
  3036
      }
deba@326
  3037
      extractMatching();
deba@326
  3038
      return true;
deba@326
  3039
    }
deba@326
  3040
kpeter@590
  3041
    /// \brief Run the algorithm.
deba@326
  3042
    ///
kpeter@590
  3043
    /// This method runs the \c %MaxWeightedPerfectMatching algorithm.
deba@326
  3044
    ///
kpeter@590
  3045
    /// \note mwpm.run() is just a shortcut of the following code.
deba@326
  3046
    /// \code
kpeter@590
  3047
    ///   mwpm.init();
kpeter@590
  3048
    ///   mwpm.start();
deba@326
  3049
    /// \endcode
deba@326
  3050
    bool run() {
deba@326
  3051
      init();
deba@326
  3052
      return start();
deba@326
  3053
    }
deba@326
  3054
deba@326
  3055
    /// @}
deba@326
  3056
kpeter@590
  3057
    /// \name Primal Solution
kpeter@590
  3058
    /// Functions to get the primal solution, i.e. the maximum weighted 
kpeter@590
  3059
    /// perfect matching.\n
kpeter@590
  3060
    /// Either \ref run() or \ref start() function should be called before
kpeter@590
  3061
    /// using them.
deba@326
  3062
deba@326
  3063
    /// @{
deba@326
  3064
kpeter@590
  3065
    /// \brief Return the weight of the matching.
deba@326
  3066
    ///
kpeter@590
  3067
    /// This function returns the weight of the found matching.
kpeter@590
  3068
    ///
kpeter@590
  3069
    /// \pre Either run() or start() must be called before using this function.
kpeter@593
  3070
    Value matchingWeight() const {
deba@326
  3071
      Value sum = 0;
deba@326
  3072
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  3073
        if ((*_matching)[n] != INVALID) {
deba@326
  3074
          sum += _weight[(*_matching)[n]];
deba@326
  3075
        }
deba@326
  3076
      }
deba@326
  3077
      return sum /= 2;
deba@326
  3078
    }
deba@326
  3079
kpeter@590
  3080
    /// \brief Return \c true if the given edge is in the matching.
deba@326
  3081
    ///
kpeter@590
  3082
    /// This function returns \c true if the given edge is in the found 
kpeter@590
  3083
    /// matching.
kpeter@590
  3084
    ///
kpeter@590
  3085
    /// \pre Either run() or start() must be called before using this function.
deba@327
  3086
    bool matching(const Edge& edge) const {
deba@327
  3087
      return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge;
deba@326
  3088
    }
deba@326
  3089
kpeter@590
  3090
    /// \brief Return the matching arc (or edge) incident to the given node.
deba@326
  3091
    ///
kpeter@590
  3092
    /// This function returns the matching arc (or edge) incident to the
kpeter@590
  3093
    /// given node in the found matching or \c INVALID if the node is 
kpeter@590
  3094
    /// not covered by the matching.
kpeter@590
  3095
    ///
kpeter@590
  3096
    /// \pre Either run() or start() must be called before using this function.
deba@326
  3097
    Arc matching(const Node& node) const {
deba@326
  3098
      return (*_matching)[node];
deba@326
  3099
    }
deba@326
  3100
kpeter@593
  3101
    /// \brief Return a const reference to the matching map.
kpeter@593
  3102
    ///
kpeter@593
  3103
    /// This function returns a const reference to a node map that stores
kpeter@593
  3104
    /// the matching arc (or edge) incident to each node.
kpeter@593
  3105
    const MatchingMap& matchingMap() const {
kpeter@593
  3106
      return *_matching;
kpeter@593
  3107
    }
kpeter@593
  3108
kpeter@590
  3109
    /// \brief Return the mate of the given node.
deba@326
  3110
    ///
kpeter@590
  3111
    /// This function returns the mate of the given node in the found 
kpeter@590
  3112
    /// matching or \c INVALID if the node is not covered by the matching.
kpeter@590
  3113
    ///
kpeter@590
  3114
    /// \pre Either run() or start() must be called before using this function.
deba@326
  3115
    Node mate(const Node& node) const {
deba@326
  3116
      return _graph.target((*_matching)[node]);
deba@326
  3117
    }
deba@326
  3118
deba@326
  3119
    /// @}
deba@326
  3120
kpeter@590
  3121
    /// \name Dual Solution
kpeter@590
  3122
    /// Functions to get the dual solution.\n
kpeter@590
  3123
    /// Either \ref run() or \ref start() function should be called before
kpeter@590
  3124
    /// using them.
deba@326
  3125
deba@326
  3126
    /// @{
deba@326
  3127
kpeter@590
  3128
    /// \brief Return the value of the dual solution.
deba@326
  3129
    ///
kpeter@590
  3130
    /// This function returns the value of the dual solution. 
kpeter@590
  3131
    /// It should be equal to the primal value scaled by \ref dualScale 
kpeter@590
  3132
    /// "dual scale".
kpeter@590
  3133
    ///
kpeter@590
  3134
    /// \pre Either run() or start() must be called before using this function.
deba@326
  3135
    Value dualValue() const {
deba@326
  3136
      Value sum = 0;
deba@326
  3137
      for (NodeIt n(_graph); n != INVALID; ++n) {
deba@326
  3138
        sum += nodeValue(n);
deba@326
  3139
      }
deba@326
  3140
      for (int i = 0; i < blossomNum(); ++i) {
deba@326
  3141
        sum += blossomValue(i) * (blossomSize(i) / 2);
deba@326
  3142
      }
deba@326
  3143
      return sum;
deba@326
  3144
    }
deba@326
  3145
kpeter@590
  3146
    /// \brief Return the dual value (potential) of the given node.
deba@326
  3147
    ///
kpeter@590
  3148
    /// This function returns the dual value (potential) of the given node.
kpeter@590
  3149
    ///
kpeter@590
  3150
    /// \pre Either run() or start() must be called before using this function.
deba@326
  3151
    Value nodeValue(const Node& n) const {
deba@326
  3152
      return (*_node_potential)[n];
deba@326
  3153
    }
deba@326
  3154
kpeter@590
  3155
    /// \brief Return the number of the blossoms in the basis.
deba@326
  3156
    ///
kpeter@590
  3157
    /// This function returns the number of the blossoms in the basis.
kpeter@590
  3158
    ///
kpeter@590
  3159
    /// \pre Either run() or start() must be called before using this function.
deba@326
  3160
    /// \see BlossomIt
deba@326
  3161
    int blossomNum() const {
deba@326
  3162
      return _blossom_potential.size();
deba@326
  3163
    }
deba@326
  3164
kpeter@590
  3165
    /// \brief Return the number of the nodes in the given blossom.
deba@326
  3166
    ///
kpeter@590
  3167
    /// This function returns the number of the nodes in the given blossom.
kpeter@590
  3168
    ///
kpeter@590
  3169
    /// \pre Either run() or start() must be called before using this function.
kpeter@590
  3170
    /// \see BlossomIt
deba@326
  3171
    int blossomSize(int k) const {
deba@326
  3172
      return _blossom_potential[k].end - _blossom_potential[k].begin;
deba@326
  3173
    }
deba@326
  3174
kpeter@590
  3175
    /// \brief Return the dual value (ptential) of the given blossom.
deba@326
  3176
    ///
kpeter@590
  3177
    /// This function returns the dual value (ptential) of the given blossom.
kpeter@590
  3178
    ///
kpeter@590
  3179
    /// \pre Either run() or start() must be called before using this function.
deba@326
  3180
    Value blossomValue(int k) const {
deba@326
  3181
      return _blossom_potential[k].value;
deba@326
  3182
    }
deba@326
  3183
kpeter@590
  3184
    /// \brief Iterator for obtaining the nodes of a blossom.
deba@326
  3185
    ///
kpeter@590
  3186
    /// This class provides an iterator for obtaining the nodes of the 
kpeter@590
  3187
    /// given blossom. It lists a subset of the nodes.
kpeter@590
  3188
    /// Before using this iterator, you must allocate a 
kpeter@590
  3189
    /// MaxWeightedPerfectMatching class and execute it.
deba@326
  3190
    class BlossomIt {
deba@326
  3191
    public:
deba@326
  3192
deba@326
  3193
      /// \brief Constructor.
deba@326
  3194
      ///
kpeter@590
  3195
      /// Constructor to get the nodes of the given variable.
kpeter@590
  3196
      ///
kpeter@590
  3197
      /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()" 
kpeter@590
  3198
      /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()" 
kpeter@590
  3199
      /// must be called before initializing this iterator.
deba@326
  3200
      BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable)
deba@326
  3201
        : _algorithm(&algorithm)
deba@326
  3202
      {
deba@326
  3203
        _index = _algorithm->_blossom_potential[variable].begin;
deba@326
  3204
        _last = _algorithm->_blossom_potential[variable].end;
deba@326
  3205
      }
deba@326
  3206
kpeter@590
  3207
      /// \brief Conversion to \c Node.
deba@326
  3208
      ///
kpeter@590
  3209
      /// Conversion to \c Node.
deba@326
  3210
      operator Node() const {
deba@327
  3211
        return _algorithm->_blossom_node_list[_index];
deba@326
  3212
      }
deba@326
  3213
deba@326
  3214
      /// \brief Increment operator.
deba@326
  3215
      ///
deba@326
  3216
      /// Increment operator.
deba@326
  3217
      BlossomIt& operator++() {
deba@326
  3218
        ++_index;
deba@326
  3219
        return *this;
deba@326
  3220
      }
deba@326
  3221
deba@327
  3222
      /// \brief Validity checking
deba@327
  3223
      ///
kpeter@590
  3224
      /// This function checks whether the iterator is invalid.
deba@327
  3225
      bool operator==(Invalid) const { return _index == _last; }
deba@327
  3226
deba@327
  3227
      /// \brief Validity checking
deba@327
  3228
      ///
kpeter@590
  3229
      /// This function checks whether the iterator is valid.
deba@327
  3230
      bool operator!=(Invalid) const { return _index != _last; }
deba@326
  3231
deba@326
  3232
    private:
deba@326
  3233
      const MaxWeightedPerfectMatching* _algorithm;
deba@326
  3234
      int _last;
deba@326
  3235
      int _index;
deba@326
  3236
    };
deba@326
  3237
deba@326
  3238
    /// @}
deba@326
  3239
deba@326
  3240
  };
deba@326
  3241
deba@326
  3242
} //END OF NAMESPACE LEMON
deba@326
  3243
deba@326
  3244
#endif //LEMON_MAX_MATCHING_H