RhodeCode

    /// @}

    /// \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.

    /// Its complexity is O(e).

    ///

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

    /// template parameter. For example,

    /// \code

    ///   cs.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 Number>

    Number totalCost() const {

      Number c = 0;

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

        int i = _arc_idb[a];

        c += static_cast<Number>(_res_cap[i]) *

             (-static_cast<Number>(_cost[i]));

      }

      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.

    Value flow(const Arc& a) const {

      return _res_cap[_arc_idb[a]];

    }

    /// \brief Return the flow map (the primal solution).

    ///

    /// This function copies the flow value on each arc into the given

    /// map. The \c Value type of the algorithm must be convertible to

    /// the \c Value type of the map.

    ///

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

    template <typename FlowMap>

    void flowMap(FlowMap &map) const {

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

        map.set(a, _res_cap[_arc_idb[a]]);

      }

    }

    /// \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 _pi[_node_id[n]];

    }

    /// \brief Return the potential map (the dual solution).

    ///

    /// This function copies the potential (dual value) of each node

    /// into the given map.

    /// The \c Cost type of the algorithm must be convertible to the

    /// \c Value type of the map.

    ///

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

    template <typename PotentialMap>

    void potentialMap(PotentialMap &map) const {

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

        map.set(n, _pi[_node_id[n]]);

      }

    }

    /// @}

  private:

    // Initialize the algorithm

    ProblemType init() {

      // Check the sum of supply values

      _sum_supply = 0;

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

        _sum_supply += _supply[i];

      }

      if (_sum_supply > 0) return INFEASIBLE;

      // Initialize vectors

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

        _pi[i] = 0;

        _excess[i] = _supply[i];

      }

      // Remove non-zero lower bounds

      const Value MAX = std::numeric_limits<Value>::max();

      int last_out;

      if (_have_lower) {

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

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j]) {

              Value c = _lower[j];

              if (c >= 0) {

                _res_cap[j] = _upper[j] < MAX ? _upper[j] - c : INF;

              } else {

                _res_cap[j] = _upper[j] < MAX + c ? _upper[j] - c : INF;

              }

              _excess[i] -= c;

              _excess[_target[j]] += c;

            } else {

              _res_cap[j] = 0;

            }

          }

        }

      } else {

        for (int j = 0; j != _res_arc_num; ++j) {

          _res_cap[j] = _forward[j] ? _upper[j] : 0;

        }

      }

      // Handle negative costs

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

        last_out = _first_out[i+1] - 1;

        for (int j = _first_out[i]; j != last_out; ++j) {

          Value rc = _res_cap[j];

          if (_cost[j] < 0 && rc > 0) {

            if (rc >= MAX) return UNBOUNDED;

            _excess[i] -= rc;

            _excess[_target[j]] += rc;

            _res_cap[j] = 0;

            _res_cap[_reverse[j]] += rc;

          }

        }

      }

      // Handle GEQ supply type

      if (_sum_supply < 0) {

        _pi[_root] = 0;

        _excess[_root] = -_sum_supply;

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = -_sum_supply + 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      } else {

        _pi[_root] = 0;

        _excess[_root] = 0;

        for (int a = _first_out[_root]; a != _res_arc_num; ++a) {

          int ra = _reverse[a];

          _res_cap[a] = 1;

          _res_cap[ra] = 0;

          _cost[a] = 0;

          _cost[ra] = 0;

        }

      }

      // Initialize delta value

      if (_factor > 1) {

        // With scaling

        Value max_sup = 0, max_dem = 0;

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

          Value ex = _excess[i];

          if ( ex > max_sup) max_sup =  ex;

          if (-ex > max_dem) max_dem = -ex;

        }

        Value max_cap = 0;

        for (int j = 0; j != _res_arc_num; ++j) {

          if (_res_cap[j] > max_cap) max_cap = _res_cap[j];

        }

        max_sup = std::min(std::min(max_sup, max_dem), max_cap);

        for (_delta = 1; 2 * _delta <= max_sup; _delta *= 2) ;

      } else {

        // Without scaling

    /// @}

    /// \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.

    /// Its complexity is O(e).

    ///

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

    /// template parameter. For example,

    /// \code

    ///   cs.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 Number>

    Number totalCost() const {

      Number c = 0;

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

        int i = _arc_idb[a];

        c += static_cast<Number>(_res_cap[i]) *

             (-static_cast<Number>(_scost[i]));

      }

      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.

    Value flow(const Arc& a) const {

      return _res_cap[_arc_idb[a]];

    }

    /// \brief Return the flow map (the primal solution).

    ///

    /// This function copies the flow value on each arc into the given

    /// map. The \c Value type of the algorithm must be convertible to

    /// the \c Value type of the map.

    ///

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

    template <typename FlowMap>

    void flowMap(FlowMap &map) const {

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

        map.set(a, _res_cap[_arc_idb[a]]);

      }

    }

    /// \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 static_cast<Cost>(_pi[_node_id[n]]);

    }

    /// \brief Return the potential map (the dual solution).

    ///

    /// This function copies the potential (dual value) of each node

    /// into the given map.

    /// The \c Cost type of the algorithm must be convertible to the

    /// \c Value type of the map.

    ///

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

    template <typename PotentialMap>

    void potentialMap(PotentialMap &map) const {

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

        map.set(n, static_cast<Cost>(_pi[_node_id[n]]));

      }

    }

    /// @}

  private:

    // Initialize the algorithm

    ProblemType init() {

      // Check the sum of supply values

      _sum_supply = 0;

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

        _sum_supply += _supply[i];

      }

      if (_sum_supply > 0) return INFEASIBLE;

      // Initialize vectors

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

        _pi[i] = 0;

        _excess[i] = _supply[i];

      }

      // Remove infinite upper bounds and check negative arcs

      const Value MAX = std::numeric_limits<Value>::max();

      int last_out;

      if (_have_lower) {

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

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j]) {

              Value c = _scost[j] < 0 ? _upper[j] : _lower[j];

              if (c >= MAX) return UNBOUNDED;

              _excess[i] -= c;

              _excess[_target[j]] += c;

            }

          }

        }

      } else {

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

          last_out = _first_out[i+1];

          for (int j = _first_out[i]; j != last_out; ++j) {

            if (_forward[j] && _scost[j] < 0) {

              Value c = _upper[j];

              if (c >= MAX) return UNBOUNDED;

              _excess[i] -= c;

              _excess[_target[j]] += c;

            }

          }

        }

      }

      Value ex, max_cap = 0;

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

        ex = _excess[i];

        _excess[i] = 0;

        if (ex < 0) max_cap -= ex;

      }

      for (int j = 0; j != _res_arc_num; ++j) {

        if (_upper[j] >= MAX) _upper[j] = max_cap;

      }

      // Initialize the large cost vector and the epsilon parameter

      _epsilon = 0;

      LargeCost lc;

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

        last_out = _first_out[i+1];

        for (int j = _first_out[i]; j != last_out; ++j) {

          lc = static_cast<LargeCost>(_scost[j]) * _res_node_num * _alpha;

          _cost[j] = lc;

          if (lc > _epsilon) _epsilon = lc;

        }

      }

      _epsilon /= _alpha;

      // Initialize maps for Circulation and remove non-zero lower bounds

      ConstMap<Arc, Value> low(0);

      typedef typename Digraph::template ArcMap<Value> ValueArcMap;

      typedef typename Digraph::template NodeMap<Value> ValueNodeMap;

      ValueArcMap cap(_graph), flow(_graph);

      ValueNodeMap sup(_graph);

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

        sup[n] = _supply[_node_id[n]];

      }

      if (_have_lower) {

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

          int j = _arc_idf[a];

          Value c = _lower[j];

          cap[a] = _upper[j] - c;

          sup[_graph.source(a)] -= c;

          sup[_graph.target(a)] += c;

        }

      } else {

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

          cap[a] = _upper[_arc_idf[a]];

        }

      }

      // Find a feasible flow using Circulation

      Circulation<Digraph, ConstMap<Arc, Value>, ValueArcMap, ValueNodeMap>

        circ(_graph, low, cap, sup);

      if (!circ.flowMap(flow).run()) return INFEASIBLE;

      // Set residual capacities and handle GEQ supply type

      if (_sum_supply < 0) {