lemon/suurballe.h
author Balazs Dezso <deba@inf.elte.hu>
Thu, 04 Mar 2010 15:20:59 +0100
changeset 951 41d7ac528c3a
parent 631 33c6b6e755cd
child 843 189760a7cdd0
child 924 c67e235c832f
permissions -rw-r--r--
Uniforming primal scale to 2 (#314)
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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_SUURBALLE_H
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#define LEMON_SUURBALLE_H
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///\ingroup shortest_path
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///\file
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///\brief An algorithm for finding arc-disjoint paths between two
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/// nodes having minimum total length.
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#include <vector>
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#include <limits>
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#include <lemon/bin_heap.h>
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#include <lemon/path.h>
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#include <lemon/list_graph.h>
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#include <lemon/maps.h>
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namespace lemon {
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  /// \addtogroup shortest_path
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  /// @{
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  /// \brief Algorithm for finding arc-disjoint paths between two nodes
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  /// having minimum total length.
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  ///
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  /// \ref lemon::Suurballe "Suurballe" implements an algorithm for
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  /// finding arc-disjoint paths having minimum total length (cost)
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  /// from a given source node to a given target node in a digraph.
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  ///
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  /// Note that this problem is a special case of the \ref min_cost_flow
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  /// "minimum cost flow problem". This implementation is actually an
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  /// efficient specialized version of the \ref CapacityScaling
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  /// "Successive Shortest Path" algorithm directly for this problem.
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  /// Therefore this class provides query functions for flow values and
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  /// node potentials (the dual solution) just like the minimum cost flow
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  /// algorithms.
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  ///
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  /// \tparam GR The digraph type the algorithm runs on.
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  /// \tparam LEN The type of the length map.
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  /// The default value is <tt>GR::ArcMap<int></tt>.
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  ///
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  /// \warning Length values should be \e non-negative \e integers.
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  ///
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  /// \note For finding node-disjoint paths this algorithm can be used
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  /// along with the \ref SplitNodes adaptor.
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#ifdef DOXYGEN
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  template <typename GR, typename LEN>
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#else
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  template < typename GR,
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             typename LEN = typename GR::template ArcMap<int> >
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#endif
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  class Suurballe
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  {
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    TEMPLATE_DIGRAPH_TYPEDEFS(GR);
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    typedef ConstMap<Arc, int> ConstArcMap;
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    typedef typename GR::template NodeMap<Arc> PredMap;
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  public:
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    /// The type of the digraph the algorithm runs on.
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    typedef GR Digraph;
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    /// The type of the length map.
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    typedef LEN LengthMap;
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    /// The type of the lengths.
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    typedef typename LengthMap::Value Length;
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#ifdef DOXYGEN
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    /// The type of the flow map.
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    typedef GR::ArcMap<int> FlowMap;
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    /// The type of the potential map.
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    typedef GR::NodeMap<Length> PotentialMap;
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#else
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    /// The type of the flow map.
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    typedef typename Digraph::template ArcMap<int> FlowMap;
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    /// The type of the potential map.
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    typedef typename Digraph::template NodeMap<Length> PotentialMap;
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#endif
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    /// The type of the path structures.
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    typedef SimplePath<GR> Path;
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  private:
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    // ResidualDijkstra is a special implementation of the
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    // Dijkstra algorithm for finding shortest paths in the
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    // residual network with respect to the reduced arc lengths
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    // and modifying the node potentials according to the
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    // distance of the nodes.
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    class ResidualDijkstra
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    {
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      typedef typename Digraph::template NodeMap<int> HeapCrossRef;
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      typedef BinHeap<Length, HeapCrossRef> Heap;
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    private:
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      // The digraph the algorithm runs on
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      const Digraph &_graph;
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      // The main maps
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      const FlowMap &_flow;
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      const LengthMap &_length;
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      PotentialMap &_potential;
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      // The distance map
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      PotentialMap _dist;
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      // The pred arc map
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      PredMap &_pred;
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      // The processed (i.e. permanently labeled) nodes
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      std::vector<Node> _proc_nodes;
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      Node _s;
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      Node _t;
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    public:
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      /// Constructor.
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      ResidualDijkstra( const Digraph &graph,
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                        const FlowMap &flow,
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                        const LengthMap &length,
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                        PotentialMap &potential,
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                        PredMap &pred,
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                        Node s, Node t ) :
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        _graph(graph), _flow(flow), _length(length), _potential(potential),
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        _dist(graph), _pred(pred), _s(s), _t(t) {}
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      /// \brief Run the algorithm. It returns \c true if a path is found
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      /// from the source node to the target node.
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      bool run() {
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        HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
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        Heap heap(heap_cross_ref);
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        heap.push(_s, 0);
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        _pred[_s] = INVALID;
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        _proc_nodes.clear();
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        // Process nodes
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        while (!heap.empty() && heap.top() != _t) {
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          Node u = heap.top(), v;
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          Length d = heap.prio() + _potential[u], nd;
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          _dist[u] = heap.prio();
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          heap.pop();
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          _proc_nodes.push_back(u);
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          // Traverse outgoing arcs
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          for (OutArcIt e(_graph, u); e != INVALID; ++e) {
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            if (_flow[e] == 0) {
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              v = _graph.target(e);
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              switch(heap.state(v)) {
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              case Heap::PRE_HEAP:
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                heap.push(v, d + _length[e] - _potential[v]);
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                _pred[v] = e;
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                break;
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              case Heap::IN_HEAP:
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                nd = d + _length[e] - _potential[v];
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                if (nd < heap[v]) {
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                  heap.decrease(v, nd);
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                  _pred[v] = e;
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                }
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                break;
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              case Heap::POST_HEAP:
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                break;
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              }
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            }
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          }
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          // Traverse incoming arcs
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          for (InArcIt e(_graph, u); e != INVALID; ++e) {
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            if (_flow[e] == 1) {
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              v = _graph.source(e);
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              switch(heap.state(v)) {
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              case Heap::PRE_HEAP:
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                heap.push(v, d - _length[e] - _potential[v]);
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                _pred[v] = e;
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                break;
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              case Heap::IN_HEAP:
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                nd = d - _length[e] - _potential[v];
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                if (nd < heap[v]) {
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                  heap.decrease(v, nd);
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                  _pred[v] = e;
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                }
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                break;
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              case Heap::POST_HEAP:
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                break;
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              }
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            }
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          }
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        }
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        if (heap.empty()) return false;
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        // Update potentials of processed nodes
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        Length t_dist = heap.prio();
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        for (int i = 0; i < int(_proc_nodes.size()); ++i)
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          _potential[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
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        return true;
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      }
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    }; //class ResidualDijkstra
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  private:
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    // The digraph the algorithm runs on
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    const Digraph &_graph;
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    // The length map
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    const LengthMap &_length;
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    // Arc map of the current flow
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    FlowMap *_flow;
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    bool _local_flow;
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    // Node map of the current potentials
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    PotentialMap *_potential;
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    bool _local_potential;
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    // The source node
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    Node _source;
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    // The target node
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    Node _target;
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    // Container to store the found paths
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    std::vector< SimplePath<Digraph> > paths;
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    int _path_num;
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    // The pred arc map
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    PredMap _pred;
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    // Implementation of the Dijkstra algorithm for finding augmenting
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    // shortest paths in the residual network
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    ResidualDijkstra *_dijkstra;
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  public:
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    /// \brief Constructor.
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    ///
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    /// Constructor.
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    ///
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    /// \param graph The digraph the algorithm runs on.
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    /// \param length The length (cost) values of the arcs.
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    Suurballe( const Digraph &graph,
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               const LengthMap &length ) :
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      _graph(graph), _length(length), _flow(0), _local_flow(false),
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      _potential(0), _local_potential(false), _pred(graph)
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    {
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      LEMON_ASSERT(std::numeric_limits<Length>::is_integer,
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        "The length type of Suurballe must be integer");
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    }
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    /// Destructor.
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    ~Suurballe() {
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      if (_local_flow) delete _flow;
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      if (_local_potential) delete _potential;
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      delete _dijkstra;
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    }
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    /// \brief Set the flow map.
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    ///
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    /// This function sets the flow map.
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    /// If it is not used before calling \ref run() or \ref init(),
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    /// an instance will be allocated automatically. The destructor
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    /// deallocates this automatically allocated map, of course.
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    ///
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    /// The found flow contains only 0 and 1 values, since it is the
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    /// union of the found arc-disjoint paths.
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    ///
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    /// \return <tt>(*this)</tt>
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    Suurballe& flowMap(FlowMap &map) {
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      if (_local_flow) {
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        delete _flow;
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        _local_flow = false;
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      }
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      _flow = &map;
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      return *this;
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    }
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    /// \brief Set the potential map.
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    ///
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    /// This function sets the potential map.
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    /// If it is not used before calling \ref run() or \ref init(),
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    /// an instance will be allocated automatically. The destructor
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    /// deallocates this automatically allocated map, of course.
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    ///
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    /// The node potentials provide the dual solution of the underlying
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    /// \ref min_cost_flow "minimum cost flow problem".
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    ///
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    /// \return <tt>(*this)</tt>
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    Suurballe& potentialMap(PotentialMap &map) {
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      if (_local_potential) {
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        delete _potential;
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        _local_potential = false;
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      }
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      _potential = &map;
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      return *this;
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    }
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    /// \name Execution Control
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    /// The simplest way to execute the algorithm is to call the run()
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    /// function.
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    /// \n
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    /// If you only need the flow that is the union of the found
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    /// arc-disjoint paths, you may call init() and findFlow().
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    /// @{
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    /// \brief Run the algorithm.
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    ///
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    /// This function runs the algorithm.
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    ///
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    /// \param s The source node.
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    /// \param t The target node.
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    /// \param k The number of paths to be found.
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    ///
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    /// \return \c k if there are at least \c k arc-disjoint paths from
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    /// \c s to \c t in the digraph. Otherwise it returns the number of
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    /// arc-disjoint paths found.
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    ///
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    /// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
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    /// just a shortcut of the following code.
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    /// \code
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    ///   s.init(s);
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    ///   s.findFlow(t, k);
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    ///   s.findPaths();
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    /// \endcode
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    int run(const Node& s, const Node& t, int k = 2) {
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      init(s);
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      findFlow(t, k);
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      findPaths();
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      return _path_num;
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    }
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    /// \brief Initialize the algorithm.
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    ///
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    /// This function initializes the algorithm.
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    ///
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    /// \param s The source node.
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    void init(const Node& s) {
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      _source = s;
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      // Initialize maps
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      if (!_flow) {
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        _flow = new FlowMap(_graph);
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        _local_flow = true;
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      }
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      if (!_potential) {
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        _potential = new PotentialMap(_graph);
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        _local_potential = true;
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      }
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      for (ArcIt e(_graph); e != INVALID; ++e) (*_flow)[e] = 0;
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      for (NodeIt n(_graph); n != INVALID; ++n) (*_potential)[n] = 0;
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    }
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    /// \brief Execute the algorithm to find an optimal flow.
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    ///
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    /// This function executes the successive shortest path algorithm to
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    /// find a minimum cost flow, which is the union of \c k (or less)
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    /// arc-disjoint paths.
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    ///
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    /// \param t The target node.
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    /// \param k The number of paths to be found.
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    ///
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    /// \return \c k if there are at least \c k arc-disjoint paths from
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    /// the source node to the given node \c t in the digraph.
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    /// Otherwise it returns the number of arc-disjoint paths found.
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    ///
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    /// \pre \ref init() must be called before using this function.
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    int findFlow(const Node& t, int k = 2) {
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      _target = t;
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      _dijkstra =
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        new ResidualDijkstra( _graph, *_flow, _length, *_potential, _pred,
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                              _source, _target );
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      // Find shortest paths
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      _path_num = 0;
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      while (_path_num < k) {
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        // Run Dijkstra
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        if (!_dijkstra->run()) break;
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        ++_path_num;
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        // Set the flow along the found shortest path
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        Node u = _target;
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        Arc e;
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        while ((e = _pred[u]) != INVALID) {
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          if (u == _graph.target(e)) {
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            (*_flow)[e] = 1;
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            u = _graph.source(e);
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          } else {
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            (*_flow)[e] = 0;
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            u = _graph.target(e);
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          }
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        }
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      }
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      return _path_num;
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    }
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    /// \brief Compute the paths from the flow.
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    ///
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    /// This function computes the paths from the found minimum cost flow,
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    /// which is the union of some arc-disjoint paths.
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    ///
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    /// \pre \ref init() and \ref findFlow() must be called before using
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    /// this function.
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   413
    void findPaths() {
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      FlowMap res_flow(_graph);
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      for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
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   416
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      paths.clear();
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   418
      paths.resize(_path_num);
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      for (int i = 0; i < _path_num; ++i) {
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        Node n = _source;
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   421
        while (n != _target) {
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          OutArcIt e(_graph, n);
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   423
          for ( ; res_flow[e] == 0; ++e) ;
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          n = _graph.target(e);
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          paths[i].addBack(e);
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          res_flow[e] = 0;
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   427
        }
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   428
      }
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   429
    }
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   430
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   431
    /// @}
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   433
    /// \name Query Functions
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   434
    /// The results of the algorithm can be obtained using these
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    /// functions.
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    /// \n The algorithm should be executed before using them.
alpar@357
   437
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    /// @{
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    /// \brief Return the total length of the found paths.
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    ///
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    /// This function returns the total length of the found paths, i.e.
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   443
    /// the total cost of the found flow.
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   444
    /// The complexity of the function is O(e).
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    ///
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   446
    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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   448
    Length totalLength() const {
kpeter@670
   449
      Length c = 0;
kpeter@670
   450
      for (ArcIt e(_graph); e != INVALID; ++e)
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   451
        c += (*_flow)[e] * _length[e];
kpeter@670
   452
      return c;
kpeter@670
   453
    }
kpeter@670
   454
kpeter@670
   455
    /// \brief Return the flow value on the given arc.
kpeter@670
   456
    ///
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   457
    /// This function returns the flow value on the given arc.
kpeter@670
   458
    /// It is \c 1 if the arc is involved in one of the found arc-disjoint
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   459
    /// paths, otherwise it is \c 0.
kpeter@670
   460
    ///
kpeter@670
   461
    /// \pre \ref run() or \ref findFlow() must be called before using
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   462
    /// this function.
kpeter@670
   463
    int flow(const Arc& arc) const {
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   464
      return (*_flow)[arc];
kpeter@670
   465
    }
kpeter@670
   466
kpeter@670
   467
    /// \brief Return a const reference to an arc map storing the
alpar@357
   468
    /// found flow.
alpar@357
   469
    ///
kpeter@670
   470
    /// This function returns a const reference to an arc map storing
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   471
    /// the flow that is the union of the found arc-disjoint paths.
alpar@357
   472
    ///
kpeter@358
   473
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@358
   474
    /// this function.
alpar@357
   475
    const FlowMap& flowMap() const {
alpar@357
   476
      return *_flow;
alpar@357
   477
    }
alpar@357
   478
kpeter@358
   479
    /// \brief Return the potential of the given node.
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   480
    ///
kpeter@358
   481
    /// This function returns the potential of the given node.
kpeter@670
   482
    /// The node potentials provide the dual solution of the
kpeter@670
   483
    /// underlying \ref min_cost_flow "minimum cost flow problem".
alpar@357
   484
    ///
kpeter@358
   485
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@358
   486
    /// this function.
alpar@357
   487
    Length potential(const Node& node) const {
alpar@357
   488
      return (*_potential)[node];
alpar@357
   489
    }
alpar@357
   490
kpeter@670
   491
    /// \brief Return a const reference to a node map storing the
kpeter@670
   492
    /// found potentials (the dual solution).
alpar@357
   493
    ///
kpeter@670
   494
    /// This function returns a const reference to a node map storing
kpeter@670
   495
    /// the found potentials that provide the dual solution of the
kpeter@670
   496
    /// underlying \ref min_cost_flow "minimum cost flow problem".
alpar@357
   497
    ///
kpeter@358
   498
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@358
   499
    /// this function.
kpeter@670
   500
    const PotentialMap& potentialMap() const {
kpeter@670
   501
      return *_potential;
alpar@357
   502
    }
alpar@357
   503
kpeter@358
   504
    /// \brief Return the number of the found paths.
alpar@357
   505
    ///
kpeter@358
   506
    /// This function returns the number of the found paths.
alpar@357
   507
    ///
kpeter@358
   508
    /// \pre \ref run() or \ref findFlow() must be called before using
kpeter@358
   509
    /// this function.
alpar@357
   510
    int pathNum() const {
alpar@357
   511
      return _path_num;
alpar@357
   512
    }
alpar@357
   513
kpeter@358
   514
    /// \brief Return a const reference to the specified path.
alpar@357
   515
    ///
kpeter@358
   516
    /// This function returns a const reference to the specified path.
alpar@357
   517
    ///
kpeter@670
   518
    /// \param i The function returns the <tt>i</tt>-th path.
alpar@357
   519
    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
alpar@357
   520
    ///
kpeter@358
   521
    /// \pre \ref run() or \ref findPaths() must be called before using
kpeter@358
   522
    /// this function.
alpar@357
   523
    Path path(int i) const {
alpar@357
   524
      return paths[i];
alpar@357
   525
    }
alpar@357
   526
alpar@357
   527
    /// @}
alpar@357
   528
alpar@357
   529
  }; //class Suurballe
alpar@357
   530
alpar@357
   531
  ///@}
alpar@357
   532
alpar@357
   533
} //namespace lemon
alpar@357
   534
alpar@357
   535
#endif //LEMON_SUURBALLE_H