lemon/suurballe.h
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 17 Apr 2009 18:14:35 +0200
changeset 610 dacc2cee2b4c
parent 440 88ed40ad0d4f
child 559 c5fd2d996909
permissions -rw-r--r--
Slightly modify the interface of Circulation and Preflow (#266)
in order to synchronize them to the interface of NetworkSimplex.

Circulation:
- The "delta" notation is replaced by "supply".
- lowerCapMap(), upperCapMap() are renamed to lowerMap() and upperMap().
- Value is renamed to Flow.

Preflow:
- Value is renamed to Flow.
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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 <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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  /// In fact, this implementation is the specialization of the
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  /// \ref CapacityScaling "successive shortest path" algorithm.
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  ///
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  /// \tparam Digraph The digraph type the algorithm runs on.
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  /// The default value is \c ListDigraph.
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  /// \tparam LengthMap The type of the length (cost) map.
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  /// The default value is <tt>Digraph::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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  /// with \ref SplitNodes.
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#ifdef DOXYGEN
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  template <typename Digraph, typename LengthMap>
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#else
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  template < typename Digraph = ListDigraph,
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             typename LengthMap = typename Digraph::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(Digraph);
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    typedef typename LengthMap::Value Length;
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    typedef ConstMap<Arc, int> ConstArcMap;
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    typedef typename Digraph::template NodeMap<Arc> PredMap;
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  public:
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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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    /// The type of the path structures.
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    typedef SimplePath<Digraph> Path;
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  private:
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    /// \brief Special implementation of the Dijkstra algorithm
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    /// for finding shortest paths in the residual network.
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    ///
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    /// \ref ResidualDijkstra is a special implementation of the
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    /// \ref Dijkstra algorithm for finding shortest paths in the
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    /// residual network of the digraph with respect to the reduced arc
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    /// lengths 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 &digraph,
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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(digraph), _flow(flow), _length(length), _potential(potential),
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        _dist(digraph), _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 digraph The digraph the algorithm runs on.
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    /// \param length The length (cost) values of the arcs.
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    /// \param s The source node.
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    /// \param t The target node.
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    Suurballe( const Digraph &digraph,
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               const LengthMap &length,
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               Node s, Node t ) :
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      _graph(digraph), _length(length), _flow(0), _local_flow(false),
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      _potential(0), _local_potential(false), _source(s), _target(t),
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      _pred(digraph) {}
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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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    ///
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    /// The found flow contains only 0 and 1 values. It is the union of
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    /// the found arc-disjoint paths.
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    ///
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    /// \return \c (*this)
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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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    ///
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    /// The potentials provide the dual solution of the underlying
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    /// minimum cost flow problem.
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    ///
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    /// \return \c (*this)
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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 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(k)</tt> is just a
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    /// shortcut of the following code.
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    /// \code
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    ///   s.init();
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    ///   s.findFlow(k);
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    ///   s.findPaths();
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    /// \endcode
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    int run(int k = 2) {
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      init();
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      findFlow(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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    void init() {
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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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      _dijkstra = new ResidualDijkstra( _graph, *_flow, _length,
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                                        *_potential, _pred,
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                                        _source, _target );
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    }
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    /// \brief Execute the successive shortest path algorithm to find
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    /// 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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    /// \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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    /// \pre \ref init() must be called before using this function.
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    int findFlow(int k = 2) {
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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 flow.
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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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    void findPaths() {
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      // Create the residual flow map (the union of the paths not found
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      // so far)
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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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      paths.clear();
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      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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        while (n != _target) {
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          OutArcIt e(_graph, n);
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          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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        }
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      }
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    }
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    /// @}
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    /// \name Query Functions
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    /// 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.
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    /// @{
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    /// \brief Return a const reference to the arc map storing the
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    /// found flow.
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    ///
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    /// This function returns a const reference to the arc map storing
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    /// the flow that is the union of the found arc-disjoint paths.
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    ///
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    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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    const FlowMap& flowMap() const {
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      return *_flow;
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    }
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    /// \brief Return a const reference to the node map storing the
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    /// found potentials (the dual solution).
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    ///
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    /// This function returns a const reference to the node map storing
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    /// the found potentials that provide the dual solution of the
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    /// underlying minimum cost flow problem.
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    ///
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    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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    const PotentialMap& potentialMap() const {
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      return *_potential;
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    }
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    /// \brief Return the flow on the given arc.
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    ///
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    /// This function returns the flow on the given arc.
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    /// It is \c 1 if the arc is involved in one of the found paths,
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    /// otherwise it is \c 0.
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    ///
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    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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    int flow(const Arc& arc) const {
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      return (*_flow)[arc];
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    }
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    /// \brief Return the potential of the given node.
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    ///
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    /// This function returns the potential of the given node.
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    ///
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    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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    Length potential(const Node& node) const {
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      return (*_potential)[node];
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    }
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    /// \brief Return the total length (cost) of the found paths (flow).
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    ///
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    /// This function returns the total length (cost) of the found paths
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    /// (flow). The complexity of the function is \f$ O(e) \f$.
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    ///
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    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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    Length totalLength() const {
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      Length c = 0;
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      for (ArcIt e(_graph); e != INVALID; ++e)
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        c += (*_flow)[e] * _length[e];
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      return c;
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    }
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    /// \brief Return the number of the found paths.
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    ///
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    /// This function returns the number of the found paths.
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    ///
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    /// \pre \ref run() or \ref findFlow() must be called before using
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    /// this function.
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    int pathNum() const {
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      return _path_num;
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    }
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    /// \brief Return a const reference to the specified path.
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    ///
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    /// This function returns a const reference to the specified path.
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    ///
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    /// \param i The function returns the \c i-th path.
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    /// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
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    ///
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    /// \pre \ref run() or \ref findPaths() must be called before using
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    /// this function.
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    Path path(int i) const {
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      return paths[i];
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    }
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    /// @}
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  }; //class Suurballe
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  ///@}
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} //namespace lemon
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#endif //LEMON_SUURBALLE_H