RhodeCode

        _next_arc = last_arc + 1;

        // Make heap of the candidate list (approximating a partial sort)

        make_heap( _candidates.begin(), _candidates.begin() + _curr_length,

                   _sort_func );

        // Pop the first element of the heap

        _in_arc = _candidates[0];

        pop_heap( _candidates.begin(), _candidates.begin() + _curr_length,

                  _sort_func );

        _curr_length = std::min(_head_length, _curr_length - 1);

        return true;

      }

    }; //class AlteringListPivotRule

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

    /// \param graph The digraph the algorithm runs on.

    NetworkSimplex(const GR& graph) :

      _graph(graph),

      _plower(NULL), _pupper(NULL), _pcost(NULL),

      _psupply(NULL), _pstsup(false), _ptype(GEQ),

      _flow_map(NULL), _potential_map(NULL),

      _local_flow(false), _local_potential(false),

      _node_id(graph)

    {

      LEMON_ASSERT(std::numeric_limits<Flow>::is_integer &&

                   std::numeric_limits<Flow>::is_signed,

        "The flow type of NetworkSimplex must be signed integer");

      LEMON_ASSERT(std::numeric_limits<Cost>::is_integer &&

                   std::numeric_limits<Cost>::is_signed,

        "The cost type of NetworkSimplex must be signed integer");

    }

    /// Destructor.

    ~NetworkSimplex() {

      if (_local_flow) delete _flow_map;

      if (_local_potential) delete _potential_map;

    }

    /// \name Parameters

    /// The parameters of the algorithm can be specified using these

    /// functions.

    /// @{

    /// \brief Set the lower bounds on the arcs.

    ///

    /// This function sets the lower bounds on the arcs.

    /// If neither this function nor \ref boundMaps() is used before

    /// calling \ref run(), the lower bounds will be set to zero

    /// on all arcs.

    ///

    /// \param map An arc map storing the lower bounds.

    /// Its \c Value type must be convertible to the \c Flow type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template <typename LOWER>

    NetworkSimplex& lowerMap(const LOWER& map) {

      delete _plower;

      _plower = new FlowArcMap(_graph);

      for (ArcIt a(_graph); a != INVALID; ++a) {

        (*_plower)[a] = map[a];

      }

      return *this;

    }

    /// \brief Set the upper bounds (capacities) on the arcs.

    ///

    /// This function sets the upper bounds (capacities) on the arcs.

    /// If none of the functions \ref upperMap(), \ref capacityMap()

    /// and \ref boundMaps() is used before calling \ref run(),

    /// the upper bounds (capacities) will be set to

    /// \c std::numeric_limits<Flow>::max() on all arcs.

    ///

    /// \param map An arc map storing the upper bounds.

    /// Its \c Value type must be convertible to the \c Flow type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template<typename UPPER>

    NetworkSimplex& upperMap(const UPPER& map) {

      delete _pupper;

      _pupper = new FlowArcMap(_graph);

      for (ArcIt a(_graph); a != INVALID; ++a) {

        (*_pupper)[a] = map[a];

      }

      return *this;

    }

    /// \brief Set the upper bounds (capacities) on the arcs.

    ///

    /// This function sets the upper bounds (capacities) on the arcs.

    /// It is just an alias for \ref upperMap().

    ///

    /// \return <tt>(*this)</tt>

    template<typename CAP>

    NetworkSimplex& capacityMap(const CAP& map) {

      return upperMap(map);

    }

    /// \brief Set the lower and upper bounds on the arcs.

    ///

    /// This function sets the lower and upper bounds on the arcs.

    /// If neither this function nor \ref lowerMap() is used before

    /// calling \ref run(), the lower bounds will be set to zero

    /// on all arcs.

    /// If none of the functions \ref upperMap(), \ref capacityMap()

    /// and \ref boundMaps() is used before calling \ref run(),

    /// the upper bounds (capacities) will be set to

    /// \c std::numeric_limits<Flow>::max() on all arcs.

    ///

    /// \param lower An arc map storing the lower bounds.

    /// \param upper An arc map storing the upper bounds.

    ///

    /// The \c Value type of the maps must be convertible to the

    /// \c Flow type of the algorithm.

    ///

    /// \note This function is just a shortcut of calling \ref lowerMap()

    /// and \ref upperMap() separately.

    ///

    /// \return <tt>(*this)</tt>

    template <typename LOWER, typename UPPER>

    NetworkSimplex& boundMaps(const LOWER& lower, const UPPER& upper) {

      return lowerMap(lower).upperMap(upper);

    }

    /// \brief Set the costs of the arcs.

    ///

    /// This function sets the costs of the arcs.

    /// If it is not used before calling \ref run(), the costs

    /// will be set to \c 1 on all arcs.

    ///

    /// \param map An arc map storing the costs.

    /// Its \c Value type must be convertible to the \c Cost type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template<typename COST>

    NetworkSimplex& costMap(const COST& map) {

      delete _pcost;

      _pcost = new CostArcMap(_graph);

      for (ArcIt a(_graph); a != INVALID; ++a) {

        (*_pcost)[a] = map[a];

      }

      return *this;

    }

    /// \brief Set the supply values of the nodes.

    ///

    /// This function sets the supply values of the nodes.

    /// If neither this function nor \ref stSupply() is used before

    /// calling \ref run(), the supply of each node will be set to zero.

    /// (It makes sense only if non-zero lower bounds are given.)

    ///

    /// \param map A node map storing the supply values.

    /// Its \c Value type must be convertible to the \c Flow type

    /// of the algorithm.

    ///

    /// \return <tt>(*this)</tt>

    template<typename SUP>

    NetworkSimplex& supplyMap(const SUP& map) {

      delete _psupply;

      _pstsup = false;

      _psupply = new FlowNodeMap(_graph);

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

        (*_psupply)[n] = map[n];

      }

      return *this;

    }

    /// \brief Set single source and target nodes and a supply value.

    ///

    /// This function sets a single source node and a single target node

    /// and the required flow value.

    /// If neither this function nor \ref supplyMap() is used before

    /// calling \ref run(), the supply of each node will be set to zero.

    /// (It makes sense only if non-zero lower bounds are given.)

    ///

    /// \param s The source node.

    /// \param t The target node.

    /// \param k The required amount of flow from node \c s to node \c t

    /// (i.e. the supply of \c s and the demand of \c t).

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& stSupply(const Node& s, const Node& t, Flow k) {

      delete _psupply;

      _psupply = NULL;

      _pstsup = true;

      _psource = s;

      _ptarget = t;

      _pstflow = k;

      return *this;

    }

    /// \brief Set the problem type.

    ///

    /// This function sets the problem type for the algorithm.

    /// If it is not used before calling \ref run(), the \ref GEQ problem

    /// type will be used.

    ///

    /// For more information see \ref ProblemType.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& problemType(ProblemType problem_type) {

      _ptype = problem_type;

      return *this;

    }

    /// \brief Set the flow map.

    ///

    /// This function sets the flow map.

    /// If it is not used before calling \ref run(), an instance will

    /// be allocated automatically. The destructor deallocates this

    /// automatically allocated map, of course.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& flowMap(FlowMap& map) {

      if (_local_flow) {

        delete _flow_map;

        _local_flow = false;

      }

      _flow_map = ↦

      return *this;

    }

    /// \brief Set the potential map.

    ///

    /// This function sets the potential map, which is used for storing

    /// the dual solution.

    /// If it is not used before calling \ref run(), an instance will

    /// be allocated automatically. The destructor deallocates this

    /// automatically allocated map, of course.

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& potentialMap(PotentialMap& map) {

      if (_local_potential) {

        delete _potential_map;

        _local_potential = false;

      }

      _potential_map = ↦

      return *this;

    }

    /// @}

    /// \name Execution Control

    /// The algorithm can be executed using \ref run().

    /// @{

    /// \brief Run the algorithm.

    ///

    /// This function runs the algorithm.

    /// The paramters can be specified using functions \ref lowerMap(),

    /// \ref upperMap(), \ref capacityMap(), \ref boundMaps(),

    /// \ref costMap(), \ref supplyMap(), \ref stSupply(), 

    /// \ref problemType(), \ref flowMap() and \ref potentialMap().

    /// For example,

    /// \code

    ///   NetworkSimplex<ListDigraph> ns(graph);

    ///   ns.boundMaps(lower, upper).costMap(cost)

    ///     .supplyMap(sup).run();

    /// \endcode

    ///

    /// This function can be called more than once. All the parameters

    /// that have been given are kept for the next call, unless

    /// \ref reset() is called, thus only the modified parameters

    /// have to be set again. See \ref reset() for examples.

    ///

    /// \param pivot_rule The pivot rule that will be used during the

    /// algorithm. For more information see \ref PivotRule.

    ///

    /// \return \c true if a feasible flow can be found.

    bool run(PivotRule pivot_rule = BLOCK_SEARCH) {

      return init() && start(pivot_rule);

    }

    /// \brief Reset all the parameters that have been given before.

    ///

    /// This function resets all the paramaters that have been given

    /// before using functions \ref lowerMap(), \ref upperMap(),

    /// \ref capacityMap(), \ref boundMaps(), \ref costMap(),

    /// \ref supplyMap(), \ref stSupply(), \ref problemType(), 

    /// \ref flowMap() and \ref potentialMap().

    ///

    /// It is useful for multiple run() calls. If this function is not

    /// used, all the parameters given before are kept for the next

    /// \ref run() call.

    ///

    /// For example,

    /// \code

    ///   NetworkSimplex<ListDigraph> ns(graph);

    ///

    ///   // First run

    ///   ns.lowerMap(lower).capacityMap(cap).costMap(cost)

    ///     .supplyMap(sup).run();

    ///

    ///   // Run again with modified cost map (reset() is not called,

    ///   // so only the cost map have to be set again)

    ///   cost[e] += 100;

    ///   ns.costMap(cost).run();

    ///

    ///   // Run again from scratch using reset()

    ///   // (the lower bounds will be set to zero on all arcs)

    ///   ns.reset();

    ///   ns.capacityMap(cap).costMap(cost)

    ///     .supplyMap(sup).run();

    /// \endcode

    ///

    /// \return <tt>(*this)</tt>

    NetworkSimplex& reset() {

      delete _plower;

      delete _pupper;

      delete _pcost;

      delete _psupply;

      _plower = NULL;

      _pupper = NULL;

      _pcost = NULL;

      _psupply = NULL;

      _pstsup = false;

      _ptype = GEQ;

      if (_local_flow) delete _flow_map;

      if (_local_potential) delete _potential_map;

      _flow_map = NULL;

      _potential_map = NULL;

      _local_flow = false;

      _local_potential = false;

      return *this;

    }

    /// @}

    /// \name Query Functions

    /// The results of the algorithm can be obtained using these

    /// functions.\n

    /// The \ref run() function must be called before using them.

    /// @{

    /// \brief Return the total cost of the found flow.

    ///

    /// This function returns the total cost of the found flow.

    /// The complexity of the function is O(e).

    ///

    /// \note The return type of the function can be specified as a

    /// template parameter. For example,

    /// \code

    ///   ns.totalCost<double>();

    /// \endcode

    /// It is useful if the total cost cannot be stored in the \c Cost

    /// type of the algorithm, which is the default return type of the

    /// function.

    ///

    /// \pre \ref run() must be called before using this function.

    template <typename Num>

    Num totalCost() const {

      Num c = 0;

      if (_pcost) {

        for (ArcIt e(_graph); e != INVALID; ++e)

          c += (*_flow_map)[e] * (*_pcost)[e];

      } else {

        for (ArcIt e(_graph); e != INVALID; ++e)

          c += (*_flow_map)[e];

      }

      return c;

    }

#ifndef DOXYGEN

    Cost totalCost() const {

      return totalCost<Cost>();

    }

#endif

    /// \brief Return the flow on the given arc.

    ///

    /// This function returns the flow on the given arc.

    ///

    /// \pre \ref run() must be called before using this function.

    Flow flow(const Arc& a) const {

      return (*_flow_map)[a];

    }

    /// \brief Return a const reference to the flow map.

    ///

    /// This function returns a const reference to an arc map storing

    /// the found flow.

    ///

    /// \pre \ref run() must be called before using this function.

    const FlowMap& flowMap() const {

      return *_flow_map;

    }

    /// \brief Return the potential (dual value) of the given node.

    ///

    /// This function returns the potential (dual value) of the

    /// given node.

    ///

    /// \pre \ref run() must be called before using this function.

    Cost potential(const Node& n) const {

      return (*_potential_map)[n];

    }

    /// \brief Return a const reference to the potential map

    /// (the dual solution).

    ///

    /// This function returns a const reference to a node map storing

    /// the found potentials, which form the dual solution of the

    /// \ref min_cost_flow "minimum cost flow" problem.

    ///

    /// \pre \ref run() must be called before using this function.

    const PotentialMap& potentialMap() const {

      return *_potential_map;

    }

    /// @}

  private:

    // Initialize internal data structures

    bool init() {

      // Initialize result maps

      if (!_flow_map) {

        _flow_map = new FlowMap(_graph);

        _local_flow = true;

      }

      if (!_potential_map) {

        _potential_map = new PotentialMap(_graph);

        _local_potential = true;

      }

      // Initialize vectors

      _node_num = countNodes(_graph);

      _arc_num = countArcs(_graph);

      int all_node_num = _node_num + 1;

      int all_arc_num = _arc_num + _node_num;

      if (_node_num == 0) return false;

      _arc_ref.resize(_arc_num);

      _source.resize(all_arc_num);

      _target.resize(all_arc_num);

      _cap.resize(all_arc_num);

      _cost.resize(all_arc_num);

      _supply.resize(all_node_num);

      _flow.resize(all_arc_num);

      _pi.resize(all_node_num);

      _parent.resize(all_node_num);

      _pred.resize(all_node_num);

      _forward.resize(all_node_num);

      _thread.resize(all_node_num);

      _rev_thread.resize(all_node_num);

      _succ_num.resize(all_node_num);

      _last_succ.resize(all_node_num);

      _state.resize(all_arc_num);

      // Initialize node related data

      bool valid_supply = true;

      Flow sum_supply = 0;

      if (!_pstsup && !_psupply) {

        _pstsup = true;

        _psource = _ptarget = NodeIt(_graph);

        _pstflow = 0;

      }

      if (_psupply) {

        int i = 0;

        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {

          _node_id[n] = i;

          _supply[i] = (*_psupply)[n];

          sum_supply += _supply[i];

        }

        valid_supply = (_ptype == GEQ && sum_supply <= 0) ||

                       (_ptype == LEQ && sum_supply >= 0);

      } else {

        int i = 0;

        for (NodeIt n(_graph); n != INVALID; ++n, ++i) {

          _node_id[n] = i;

          _supply[i] = 0;

        }

        _supply[_node_id[_psource]] =  _pstflow;

        _supply[_node_id[_ptarget]] = -_pstflow;

      }

      if (!valid_supply) return false;

      // Infinite capacity value

      Flow inf_cap =

        std::numeric_limits<Flow>::has_infinity ?

        std::numeric_limits<Flow>::infinity() :

        std::numeric_limits<Flow>::max();

      // Initialize artifical cost

      Cost art_cost;

      if (std::numeric_limits<Cost>::is_exact) {

        art_cost = std::numeric_limits<Cost>::max() / 4 + 1;

      } else {

        art_cost = std::numeric_limits<Cost>::min();

        for (int i = 0; i != _arc_num; ++i) {

          if (_cost[i] > art_cost) art_cost = _cost[i];

        }

        art_cost = (art_cost + 1) * _node_num;

      }

      // Run Circulation to check if a feasible solution exists

      typedef ConstMap<Arc, Flow> ConstArcMap;

      FlowNodeMap *csup = NULL;

      bool local_csup = false;

      if (_psupply) {

        csup = _psupply;

      } else {

        csup = new FlowNodeMap(_graph, 0);

        (*csup)[_psource] =  _pstflow;

        (*csup)[_ptarget] = -_pstflow;

        local_csup = true;

      }

      bool circ_result = false;

      if (_ptype == GEQ || (_ptype == LEQ && sum_supply == 0)) {

        // GEQ problem type

        if (_plower) {

          if (_pupper) {

            Circulation<GR, FlowArcMap, FlowArcMap, FlowNodeMap>

              circ(_graph, *_plower, *_pupper, *csup);

            circ_result = circ.run();

          } else {

            Circulation<GR, FlowArcMap, ConstArcMap, FlowNodeMap>

            circ_result = circ.run();

          }

        } else {

          if (_pupper) {

            Circulation<GR, ConstArcMap, FlowArcMap, FlowNodeMap>

            circ_result = circ.run();

          } else {

            Circulation<GR, ConstArcMap, ConstArcMap, FlowNodeMap>

            circ_result = circ.run();

          }

        }

      } else {

        // LEQ problem type

        typedef ReverseDigraph<const GR> RevGraph;

        typedef NegMap<FlowNodeMap> NegNodeMap;

        RevGraph rgraph(_graph);

        NegNodeMap neg_csup(*csup);

        if (_plower) {

          if (_pupper) {

            Circulation<RevGraph, FlowArcMap, FlowArcMap, NegNodeMap>

              circ(rgraph, *_plower, *_pupper, neg_csup);

            circ_result = circ.run();

          } else {

            Circulation<RevGraph, FlowArcMap, ConstArcMap, NegNodeMap>

            circ_result = circ.run();

          }

        } else {

          if (_pupper) {

            Circulation<RevGraph, ConstArcMap, FlowArcMap, NegNodeMap>

            circ_result = circ.run();

          } else {

            Circulation<RevGraph, ConstArcMap, ConstArcMap, NegNodeMap>

            circ_result = circ.run();

          }

        }

      }

      if (local_csup) delete csup;

      if (!circ_result) return false;

      // Set data for the artificial root node

      _root = _node_num;

      _parent[_root] = -1;

      _pred[_root] = -1;

      _thread[_root] = 0;

      _rev_thread[0] = _root;

      _succ_num[_root] = all_node_num;

      _last_succ[_root] = _root - 1;

      _supply[_root] = -sum_supply;

      if (sum_supply < 0) {

        _pi[_root] = -art_cost;

      } else {

        _pi[_root] = art_cost;

      }

      // Store the arcs in a mixed order

      int k = std::max(int(std::sqrt(double(_arc_num))), 10);

      int i = 0;

      for (ArcIt e(_graph); e != INVALID; ++e) {

        _arc_ref[i] = e;

        if ((i += k) >= _arc_num) i = (i % k) + 1;

      }

      // Initialize arc maps

      if (_pupper && _pcost) {

        for (int i = 0; i != _arc_num; ++i) {

          Arc e = _arc_ref[i];

          _source[i] = _node_id[_graph.source(e)];

          _target[i] = _node_id[_graph.target(e)];

          _cap[i] = (*_pupper)[e];

          _cost[i] = (*_pcost)[e];

          _flow[i] = 0;

          _state[i] = STATE_LOWER;

        }

      } else {

        for (int i = 0; i != _arc_num; ++i) {

          Arc e = _arc_ref[i];

          _source[i] = _node_id[_graph.source(e)];

          _target[i] = _node_id[_graph.target(e)];

          _flow[i] = 0;

          _state[i] = STATE_LOWER;

        }

        if (_pupper) {

          for (int i = 0; i != _arc_num; ++i)

            _cap[i] = (*_pupper)[_arc_ref[i]];

        } else {

          for (int i = 0; i != _arc_num; ++i)

            _cap[i] = inf_cap;

        }

        if (_pcost) {

          for (int i = 0; i != _arc_num; ++i)

            _cost[i] = (*_pcost)[_arc_ref[i]];

        } else {

          for (int i = 0; i != _arc_num; ++i)

            _cost[i] = 1;

        }

      }

      // Remove non-zero lower bounds

      if (_plower) {

        for (int i = 0; i != _arc_num; ++i) {

          Flow c = (*_plower)[_arc_ref[i]];

          if (c != 0) {

            _cap[i] -= c;

            _supply[_source[i]] -= c;

            _supply[_target[i]] += c;

          }

        }

      }

      // Add artificial arcs and initialize the spanning tree data structure

      for (int u = 0, e = _arc_num; u != _node_num; ++u, ++e) {

        _thread[u] = u + 1;

        _rev_thread[u + 1] = u;

        _succ_num[u] = 1;

        _last_succ[u] = u;

        _parent[u] = _root;

        _pred[u] = e;

        _cost[e] = art_cost;

        _cap[e] = inf_cap;

        _state[e] = STATE_TREE;

        if (_supply[u] > 0 || (_supply[u] == 0 && sum_supply <= 0)) {

          _flow[e] = _supply[u];

          _forward[u] = true;

          _pi[u] = -art_cost + _pi[_root];

        } else {

          _flow[e] = -_supply[u];

          _forward[u] = false;

          _pi[u] = art_cost + _pi[_root];

        }

      }

      return true;

    }

    // Find the join node

    void findJoinNode() {

      int u = _source[in_arc];

      int v = _target[in_arc];

      while (u != v) {

        if (_succ_num[u] < _succ_num[v]) {

          u = _parent[u];

        } else {

          v = _parent[v];

        }

      }

      join = u;

    }

    // Find the leaving arc of the cycle and returns true if the

    // leaving arc is not the same as the entering arc

    bool findLeavingArc() {

      // Initialize first and second nodes according to the direction

      // of the cycle

      if (_state[in_arc] == STATE_LOWER) {

        first  = _source[in_arc];

        second = _target[in_arc];

      } else {

        first  = _target[in_arc];

        second = _source[in_arc];

      }

      delta = _cap[in_arc];

      int result = 0;

      Flow d;

      int e;

      // Search the cycle along the path form the first node to the root

      for (int u = first; u != join; u = _parent[u]) {

        e = _pred[u];

        d = _forward[u] ? _flow[e] : _cap[e] - _flow[e];

        if (d < delta) {

          delta = d;

          u_out = u;

          result = 1;

        }

      }

      // Search the cycle along the path form the second node to the root

      for (int u = second; u != join; u = _parent[u]) {

        e = _pred[u];

        d = _forward[u] ? _cap[e] - _flow[e] : _flow[e];

        if (d <= delta) {

          delta = d;

          u_out = u;

          result = 2;

        }

      }

      if (result == 1) {

        u_in = first;

        v_in = second;

      } else {

        u_in = second;

        v_in = first;

      }

      return result != 0;

    }

    // Change _flow and _state vectors

    void changeFlow(bool change) {

      // Augment along the cycle

      if (delta > 0) {

        Flow val = _state[in_arc] * delta;

        _flow[in_arc] += val;

        for (int u = _source[in_arc]; u != join; u = _parent[u]) {

          _flow[_pred[u]] += _forward[u] ? -val : val;

        }

        for (int u = _target[in_arc]; u != join; u = _parent[u]) {

          _flow[_pred[u]] += _forward[u] ? val : -val;

        }

      }

      // Update the state of the entering and leaving arcs

      if (change) {

        _state[in_arc] = STATE_TREE;

        _state[_pred[u_out]] =

          (_flow[_pred[u_out]] == 0) ? STATE_LOWER : STATE_UPPER;

      } else {

        _state[in_arc] = -_state[in_arc];

      }

    }

    // Update the tree structure

    void updateTreeStructure() {

      int u, w;

      int old_rev_thread = _rev_thread[u_out];

      int old_succ_num = _succ_num[u_out];

      int old_last_succ = _last_succ[u_out];

      v_out = _parent[u_out];

      u = _last_succ[u_in];  // the last successor of u_in

      right = _thread[u];    // the node after it

      // Handle the case when old_rev_thread equals to v_in

      // (it also means that join and v_out coincide)

      if (old_rev_thread == v_in) {

        last = _thread[_last_succ[u_out]];

      } else {

        last = _thread[v_in];

      }

      // Update _thread and _parent along the stem nodes (i.e. the nodes

      // between u_in and u_out, whose parent have to be changed)

      _thread[v_in] = stem = u_in;

      _dirty_revs.clear();

      _dirty_revs.push_back(v_in);

      par_stem = v_in;

      while (stem != u_out) {

        // Insert the next stem node into the thread list

        new_stem = _parent[stem];

        _thread[u] = new_stem;

        _dirty_revs.push_back(u);

        // Remove the subtree of stem from the thread list

        w = _rev_thread[stem];

        _thread[w] = right;

        _rev_thread[right] = w;

        // Change the parent node and shift stem nodes

        _parent[stem] = par_stem;

        par_stem = stem;

        stem = new_stem;

        // Update u and right

        u = _last_succ[stem] == _last_succ[par_stem] ?

          _rev_thread[par_stem] : _last_succ[stem];

        right = _thread[u];

      }

      _parent[u_out] = par_stem;

      _thread[u] = last;

      _rev_thread[last] = u;

      _last_succ[u_out] = u;

      // Remove the subtree of u_out from the thread list except for

      // the case when old_rev_thread equals to v_in

      // (it also means that join and v_out coincide)

      if (old_rev_thread != v_in) {

        _thread[old_rev_thread] = right;

        _rev_thread[right] = old_rev_thread;

      }

      // Update _rev_thread using the new _thread values

      for (int i = 0; i < int(_dirty_revs.size()); ++i) {

        u = _dirty_revs[i];

        _rev_thread[_thread[u]] = u;

      }

      // Update _pred, _forward, _last_succ and _succ_num for the

      // stem nodes from u_out to u_in

      int tmp_sc = 0, tmp_ls = _last_succ[u_out];

      u = u_out;

      while (u != u_in) {

        w = _parent[u];

        _pred[u] = _pred[w];

        _forward[u] = !_forward[w];

        tmp_sc += _succ_num[u] - _succ_num[w];

        _succ_num[u] = tmp_sc;

        _last_succ[w] = tmp_ls;

        u = w;

      }

      _pred[u_in] = in_arc;

      _forward[u_in] = (u_in == _source[in_arc]);

      _succ_num[u_in] = old_succ_num;

      // Set limits for updating _last_succ form v_in and v_out

      // towards the root

      int up_limit_in = -1;

      int up_limit_out = -1;

      if (_last_succ[join] == v_in) {

        up_limit_out = join;

      } else {

        up_limit_in = join;

      }

      // Update _last_succ from v_in towards the root

      for (u = v_in; u != up_limit_in && _last_succ[u] == v_in;

           u = _parent[u]) {

        _last_succ[u] = _last_succ[u_out];

      }

      // Update _last_succ from v_out towards the root

      if (join != old_rev_thread && v_in != old_rev_thread) {

        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;

             u = _parent[u]) {

          _last_succ[u] = old_rev_thread;

        }

      } else {

        for (u = v_out; u != up_limit_out && _last_succ[u] == old_last_succ;

             u = _parent[u]) {

          _last_succ[u] = _last_succ[u_out];

        }

      }

      // Update _succ_num from v_in to join

      for (u = v_in; u != join; u = _parent[u]) {

        _succ_num[u] += old_succ_num;

      }

      // Update _succ_num from v_out to join

      for (u = v_out; u != join; u = _parent[u]) {

        _succ_num[u] -= old_succ_num;

      }

    }

    // Update potentials

    void updatePotential() {

      Cost sigma = _forward[u_in] ?

        _pi[v_in] - _pi[u_in] - _cost[_pred[u_in]] :

        _pi[v_in] - _pi[u_in] + _cost[_pred[u_in]];

      // Update potentials in the subtree, which has been moved

      int end = _thread[_last_succ[u_in]];

      for (int u = u_in; u != end; u = _thread[u]) {

        _pi[u] += sigma;

      }

    }

    // Execute the algorithm

    bool start(PivotRule pivot_rule) {

      // Select the pivot rule implementation

      switch (pivot_rule) {

        case FIRST_ELIGIBLE:

          return start<FirstEligiblePivotRule>();

        case BEST_ELIGIBLE:

          return start<BestEligiblePivotRule>();

        case BLOCK_SEARCH:

          return start<BlockSearchPivotRule>();

        case CANDIDATE_LIST:

          return start<CandidateListPivotRule>();

        case ALTERING_LIST:

          return start<AlteringListPivotRule>();

      }

      return false;

    }

    template <typename PivotRuleImpl>

    bool start() {

      PivotRuleImpl pivot(*this);

      // Execute the Network Simplex algorithm

      while (pivot.findEnteringArc()) {

        findJoinNode();

        bool change = findLeavingArc();

        changeFlow(change);

        if (change) {

          updateTreeStructure();

          updatePotential();

        }

      }

      // Copy flow values to _flow_map

      if (_plower) {

        for (int i = 0; i != _arc_num; ++i) {

          Arc e = _arc_ref[i];

          _flow_map->set(e, (*_plower)[e] + _flow[i]);

        }

      } else {

        for (int i = 0; i != _arc_num; ++i) {

          _flow_map->set(_arc_ref[i], _flow[i]);

        }

      }

      // Copy potential values to _potential_map

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

        _potential_map->set(n, _pi[_node_id[n]]);

      }

      return true;

    }

  }; //class NetworkSimplex

  ///@}

} //namespace lemon

#endif //LEMON_NETWORK_SIMPLEX_H

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * Copyright (C) 2003-2009

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#include <iostream>

#include <fstream>

#include <lemon/list_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/network_simplex.h>

#include <lemon/concepts/digraph.h>

#include <lemon/concept_check.h>

#include "test_tools.h"

using namespace lemon;

char test_lgf[] =

  "@nodes\n"

  "label  sup1 sup2 sup3 sup4 sup5\n"

  "    1    20   27    0   20   30\n"

  "    2    -4    0    0   -8   -3\n"

  "    3     0    0    0    0    0\n"

  "    4     0    0    0    0    0\n"

  "    5     9    0    0    6   11\n"

  "    6    -6    0    0   -5   -6\n"

  "    7     0    0    0    0    0\n"

  "    8     0    0    0    0    3\n"

  "    9     3    0    0    0    0\n"

  "   10    -2    0    0   -7   -2\n"

  "   11     0    0    0  -10    0\n"

  "   12   -20  -27    0  -30  -20\n"

  "\n"

  "@arcs\n"

  "       cost  cap low1 low2\n"

  " 1  2    70   11    0    8\n"

  " 1  3   150    3    0    1\n"

  " 1  4    80   15    0    2\n"

  " 2  8    80   12    0    0\n"

  " 3  5   140    5    0    3\n"

  " 4  6    60   10    0    1\n"

  " 4  7    80    2    0    0\n"

  " 4  8   110    3    0    0\n"

  " 5  7    60   14    0    0\n"

  " 5 11   120   12    0    0\n"

  " 6  3     0    3    0    0\n"

  " 6  9   140    4    0    0\n"

  " 6 10    90    8    0    0\n"

  " 7  1    30    5    0    0\n"

  " 8 12    60   16    0    4\n"

  " 9 12    50    6    0    0\n"

  "10 12    70   13    0    5\n"

  "10  2   100    7    0    0\n"

  "10  7    60   10    0    0\n"

  "11 10    20   14    0    6\n"

  "12 11    30   10    0    0\n"

  "\n"

  "@attributes\n"

  "source 1\n"

  "target 12\n";

enum ProblemType {

  EQ,

  GEQ,

  LEQ

};

// Check the interface of an MCF algorithm

template <typename GR, typename Flow, typename Cost>

class McfClassConcept

{

public:

  template <typename MCF>

  struct Constraints {

    void constraints() {

      checkConcept<concepts::Digraph, GR>();

      MCF mcf(g);

      b = mcf.reset()

             .lowerMap(lower)

             .upperMap(upper)

             .capacityMap(upper)

             .boundMaps(lower, upper)

             .costMap(cost)

             .supplyMap(sup)

             .stSupply(n, n, k)

             .flowMap(flow)

             .potentialMap(pot)

             .run();

      const MCF& const_mcf = mcf;

      const typename MCF::FlowMap &fm = const_mcf.flowMap();

      const typename MCF::PotentialMap &pm = const_mcf.potentialMap();

      v = const_mcf.totalCost();

      double x = const_mcf.template totalCost<double>();

      v = const_mcf.flow(a);

      v = const_mcf.potential(n);

      ignore_unused_variable_warning(fm);

      ignore_unused_variable_warning(pm);

      ignore_unused_variable_warning(x);

    }

    typedef typename GR::Node Node;

    typedef typename GR::Arc Arc;

    typedef concepts::ReadMap<Node, Flow> NM;

    typedef concepts::ReadMap<Arc, Flow> FAM;

    typedef concepts::ReadMap<Arc, Cost> CAM;

    const GR &g;

    const FAM &lower;

    const FAM &upper;

    const CAM &cost;

    const NM ⊃

    const Node &n;

    const Arc &a;

    const Flow &k;

    Flow v;

    bool b;

    typename MCF::FlowMap &flow;

    typename MCF::PotentialMap &pot;

  };

};

// Check the feasibility of the given flow (primal soluiton)

template < typename GR, typename LM, typename UM,

           typename SM, typename FM >

bool checkFlow( const GR& gr, const LM& lower, const UM& upper,

                const SM& supply, const FM& flow,

                ProblemType type = EQ )