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

    ///   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 Number>

    Number totalCost() const {

      Number c = 0;

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

        int i = _arc_id[a];

        c += Number(_flow[i]) * 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 _flow[_arc_id[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, _flow[_arc_id[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 internal data structures

    bool init() {

      if (_node_num == 0) return false;

      // Check the sum of supply values

      _sum_supply = 0;

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

        _sum_supply += _supply[i];

      }

      if ( !((_stype == GEQ && _sum_supply <= 0) ||

             (_stype == LEQ && _sum_supply >= 0)) ) return false;

      // Remove non-zero lower bounds

      if (_have_lower) {

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

          Value c = _lower[i];

          if (c >= 0) {

            _cap[i] = _upper[i] < INF ? _upper[i] - c : INF;

          } else {

            _cap[i] = _upper[i] < INF + c ? _upper[i] - c : INF;

          }

          _supply[_source[i]] -= c;

          _supply[_target[i]] += c;

        }

      } else {

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

          _cap[i] = _upper[i];

        }

      }

      // Initialize artifical cost

      Cost ART_COST;

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

        ART_COST = std::numeric_limits<Cost>::max() / 2 + 1;

      } else {

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

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

        }

        ART_COST = (ART_COST + 1) * _node_num;

      }

      // Initialize arc maps

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

        _flow[i] = 0;

        _state[i] = STATE_LOWER;

      }

      // 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] = _node_num + 1;

      _last_succ[_root] = _root - 1;

      _supply[_root] = -_sum_supply;

      _pi[_root] = 0;

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

      if (_sum_supply == 0) {

        // EQ supply constraints

        _search_arc_num = _arc_num;

        _all_arc_num = _arc_num + _node_num;

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

          _parent[u] = _root;

          _pred[u] = e;

          _thread[u] = u + 1;

          _rev_thread[u + 1] = u;

          _succ_num[u] = 1;

          _last_succ[u] = u;

          _cap[e] = INF;

          _state[e] = STATE_TREE;

          if (_supply[u] >= 0) {

            _forward[u] = true;

            _pi[u] = 0;

            _source[e] = u;

            _target[e] = _root;

            _flow[e] = _supply[u];

            _cost[e] = 0;

          } else {

            _forward[u] = false;

            _pi[u] = ART_COST;

            _source[e] = _root;

            _target[e] = u;

            _flow[e] = -_supply[u];

            _cost[e] = ART_COST;

          }

        }

      }

      else if (_sum_supply > 0) {

        // LEQ supply constraints

        _search_arc_num = _arc_num + _node_num;

        int f = _arc_num + _node_num;

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

          _parent[u] = _root;

          _thread[u] = u + 1;

          _rev_thread[u + 1] = u;

          _succ_num[u] = 1;

          _last_succ[u] = u;

          if (_supply[u] >= 0) {

            _forward[u] = true;

            _pi[u] = 0;

            _pred[u] = e;

            _source[e] = u;

            _target[e] = _root;

            _cap[e] = INF;

            _flow[e] = _supply[u];

            _cost[e] = 0;

            _state[e] = STATE_TREE;

          } else {

            _forward[u] = false;

            _pi[u] = ART_COST;

            _pred[u] = f;

            _source[f] = _root;

            _target[f] = u;

            _cap[f] = INF;

            _flow[f] = -_supply[u];

            _cost[f] = ART_COST;

            _state[f] = STATE_TREE;

            _source[e] = u;

            _target[e] = _root;

            _cap[e] = INF;

            _flow[e] = 0;

            _cost[e] = 0;

            _state[e] = STATE_LOWER;

            ++f;

          }

        }

        _all_arc_num = f;

      }

      else {

        // GEQ supply constraints

        _search_arc_num = _arc_num + _node_num;

        int f = _arc_num + _node_num;

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

          _parent[u] = _root;

          _thread[u] = u + 1;

          _rev_thread[u + 1] = u;

          _succ_num[u] = 1;

          _last_succ[u] = u;

          if (_supply[u] <= 0) {

            _forward[u] = false;

            _pi[u] = 0;

            _pred[u] = e;

            _source[e] = _root;

            _target[e] = u;

            _cap[e] = INF;

            _flow[e] = -_supply[u];

            _cost[e] = 0;

            _state[e] = STATE_TREE;

          } else {

            _forward[u] = true;

            _pi[u] = -ART_COST;

            _pred[u] = f;

            _source[f] = u;

            _target[f] = _root;

            _cap[f] = INF;

            _flow[f] = _supply[u];

            _state[f] = STATE_TREE;

            _cost[f] = ART_COST;

            _source[e] = _root;

            _target[e] = u;

            _cap[e] = INF;

      // 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

    ProblemType 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 INFEASIBLE; // avoid warning

    }

    template <typename PivotRuleImpl>

    ProblemType start() {

      PivotRuleImpl pivot(*this);

      // Execute the Network Simplex algorithm

      while (pivot.findEnteringArc()) {

        findJoinNode();

        bool change = findLeavingArc();

        if (delta >= INF) return UNBOUNDED;

        changeFlow(change);

        if (change) {

          updateTreeStructure();

          updatePotential();

        }

      }

      // Check feasibility

      for (int e = _search_arc_num; e != _all_arc_num; ++e) {

        if (_flow[e] != 0) return INFEASIBLE;

      }

      // Transform the solution and the supply map to the original form

      if (_have_lower) {

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

          Value c = _lower[i];

          if (c != 0) {

            _flow[i] += c;

            _supply[_source[i]] += c;

            _supply[_target[i]] -= c;

          }

        }

      }

      // Shift potentials to meet the requirements of the GEQ/LEQ type

      // optimality conditions

      if (_sum_supply == 0) {

        if (_stype == GEQ) {

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

            if (_pi[i] > max_pot) max_pot = _pi[i];

          }

          if (max_pot > 0) {

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

              _pi[i] -= max_pot;

          }

        } else {

          Cost min_pot = std::numeric_limits<Cost>::max();

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

            if (_pi[i] < min_pot) min_pot = _pi[i];

          }

          if (min_pot < 0) {

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

              _pi[i] -= min_pot;

          }

        }

      }

      return OPTIMAL;

    }

  }; //class NetworkSimplex

  ///@}

} //namespace lemon

#endif //LEMON_NETWORK_SIMPLEX_H