/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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.

 *

 */

#ifndef LEMON_CYCLE_CANCELING_H

#define LEMON_CYCLE_CANCELING_H

/// \ingroup min_cost_flow

///

/// \file

/// \brief Cycle-canceling algorithm for finding a minimum cost flow.

#include <vector>

#include <lemon/graph_adaptor.h>

#include <lemon/path.h>

#include <lemon/circulation.h>

#include <lemon/bellman_ford.h>

#include <lemon/min_mean_cycle.h>

namespace lemon {

  /// \addtogroup min_cost_flow

  /// @{

  /// \brief Implementation of a cycle-canceling algorithm for

  /// finding a minimum cost flow.

  ///

  /// \ref CycleCanceling implements a cycle-canceling algorithm for

  /// finding a minimum cost flow.

  ///

  /// \tparam Graph The directed graph type the algorithm runs on.

  /// \tparam LowerMap The type of the lower bound map.

  /// \tparam CapacityMap The type of the capacity (upper bound) map.

  /// \tparam CostMap The type of the cost (length) map.

  /// \tparam SupplyMap The type of the supply map.

  ///

  /// \warning

  /// - Edge capacities and costs should be \e non-negative \e integers.

  /// - Supply values should be \e signed \e integers.

  /// - The value types of the maps should be convertible to each other.

  /// - \c CostMap::Value must be signed type.

  ///

  /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is

  /// used for negative cycle detection with limited iteration number.

  /// However \ref CycleCanceling also provides the "Minimum Mean

  /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial,

  /// but rather slower in practice.

  /// To use this version of the algorithm, call \ref run() with \c true

  /// parameter.

  ///

  /// \author Peter Kovacs

  template < typename Graph,

             typename LowerMap = typename Graph::template EdgeMap<int>,

             typename CapacityMap = typename Graph::template EdgeMap<int>,

             typename CostMap = typename Graph::template EdgeMap<int>,

             typename SupplyMap = typename Graph::template NodeMap<int> >

  class CycleCanceling

  {

    GRAPH_TYPEDEFS(typename Graph);

    typedef typename CapacityMap::Value Capacity;

    typedef typename CostMap::Value Cost;

    typedef typename SupplyMap::Value Supply;

    typedef typename Graph::template EdgeMap<Capacity> CapacityEdgeMap;

    typedef typename Graph::template NodeMap<Supply> SupplyNodeMap;

    typedef ResGraphAdaptor< const Graph, Capacity,

                             CapacityEdgeMap, CapacityEdgeMap > ResGraph;

    typedef typename ResGraph::Node ResNode;

    typedef typename ResGraph::NodeIt ResNodeIt;

    typedef typename ResGraph::Edge ResEdge;

    typedef typename ResGraph::EdgeIt ResEdgeIt;

  public:

    /// The type of the flow map.

    typedef typename Graph::template EdgeMap<Capacity> FlowMap;

    /// The type of the potential map.

    typedef typename Graph::template NodeMap<Cost> PotentialMap;

  private:

    /// \brief Map adaptor class for handling residual edge costs.

    ///

    /// \ref ResidualCostMap is a map adaptor class for handling

    /// residual edge costs.

    class ResidualCostMap : public MapBase<ResEdge, Cost>

    {

    private:

      const CostMap &_cost_map;

    public:

      ///\e

      ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}

      ///\e

      Cost operator[](const ResEdge &e) const {

        return ResGraph::forward(e) ? _cost_map[e] : -_cost_map[e];

      }

    }; //class ResidualCostMap

  private:

    // The maximum number of iterations for the first execution of the

    // Bellman-Ford algorithm. It should be at least 2.

    static const int BF_FIRST_LIMIT = 2;

    // The iteration limit for the Bellman-Ford algorithm is multiplied

    // by BF_ALPHA in every round.

    static const double BF_ALPHA = 1.5;

  private:

    // The directed graph the algorithm runs on

    const Graph &_graph;

    // The original lower bound map

    const LowerMap *_lower;

    // The modified capacity map

    CapacityEdgeMap _capacity;

    // The original cost map

    const CostMap &_cost;

    // The modified supply map

    SupplyNodeMap _supply;

    bool _valid_supply;

    // Edge map of the current flow

    FlowMap *_flow;

    bool _local_flow;

    // Node map of the current potentials

    PotentialMap *_potential;

    bool _local_potential;

    // The residual graph

    ResGraph *_res_graph;

    // The residual cost map

    ResidualCostMap _res_cost;

  public:

    /// \brief General constructor (with lower bounds).

    ///

    /// General constructor (with lower bounds).

    ///

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

    /// \param lower The lower bounds of the edges.

    /// \param capacity The capacities (upper bounds) of the edges.

    /// \param cost The cost (length) values of the edges.

    /// \param supply The supply values of the nodes (signed).

    CycleCanceling( const Graph &graph,

                    const LowerMap &lower,

                    const CapacityMap &capacity,

                    const CostMap &cost,

                    const SupplyMap &supply ) :

      _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),

      _supply(graph), _flow(0), _local_flow(false),

      _potential(0), _local_potential(false), _res_cost(_cost)

    {

      // Removing non-zero lower bounds

      _capacity = subMap(capacity, lower);

      Supply sum = 0;

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

        Supply s = supply[n];

        for (InEdgeIt e(_graph, n); e != INVALID; ++e)

          s += lower[e];

        for (OutEdgeIt e(_graph, n); e != INVALID; ++e)

          s -= lower[e];

        sum += (_supply[n] = s);

      }

      _valid_supply = sum == 0;

    }

    /// \brief General constructor (without lower bounds).

    ///

    /// General constructor (without lower bounds).

    ///

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

    /// \param capacity The capacities (upper bounds) of the edges.

    /// \param cost The cost (length) values of the edges.

    /// \param supply The supply values of the nodes (signed).

    CycleCanceling( const Graph &graph,

                    const CapacityMap &capacity,

                    const CostMap &cost,

                    const SupplyMap &supply ) :

      _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),

      _supply(supply), _flow(0), _local_flow(false),

      _potential(0), _local_potential(false), _res_cost(_cost)

    {

      // Checking the sum of supply values

      Supply sum = 0;

      for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];

      _valid_supply = sum == 0;

    }

    /// \brief Simple constructor (with lower bounds).

    ///

    /// Simple constructor (with lower bounds).

    ///

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

    /// \param lower The lower bounds of the edges.

    /// \param capacity The capacities (upper bounds) of the edges.

    /// \param cost The cost (length) values of the edges.

    /// \param s The source node.

    /// \param t The target node.

    /// \param flow_value 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).

    CycleCanceling( const Graph &graph,

                    const LowerMap &lower,

                    const CapacityMap &capacity,

                    const CostMap &cost,

                    Node s, Node t,

                    Supply flow_value ) :

      _graph(graph), _lower(&lower), _capacity(graph), _cost(cost),

      _supply(graph), _flow(0), _local_flow(false),

      _potential(0), _local_potential(false), _res_cost(_cost)

    {

      // Removing non-zero lower bounds

      _capacity = subMap(capacity, lower);

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

        Supply sum = 0;

        if (n == s) sum =  flow_value;

        if (n == t) sum = -flow_value;

        for (InEdgeIt e(_graph, n); e != INVALID; ++e)

          sum += lower[e];

        for (OutEdgeIt e(_graph, n); e != INVALID; ++e)

          sum -= lower[e];

        _supply[n] = sum;

      }

      _valid_supply = true;

    }

    /// \brief Simple constructor (without lower bounds).

    ///

    /// Simple constructor (without lower bounds).

    ///

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

    /// \param capacity The capacities (upper bounds) of the edges.

    /// \param cost The cost (length) values of the edges.

    /// \param s The source node.

    /// \param t The target node.

    /// \param flow_value 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).

    CycleCanceling( const Graph &graph,

                    const CapacityMap &capacity,

                    const CostMap &cost,

                    Node s, Node t,

                    Supply flow_value ) :

      _graph(graph), _lower(NULL), _capacity(capacity), _cost(cost),

      _supply(graph, 0), _flow(0), _local_flow(false),

      _potential(0), _local_potential(false), _res_cost(_cost)

    {

      _supply[s] =  flow_value;

      _supply[t] = -flow_value;

      _valid_supply = true;

    }

    /// Destructor.

    ~CycleCanceling() {

      if (_local_flow) delete _flow;

      if (_local_potential) delete _potential;

      delete _res_graph;

    }

    /// \brief Sets the flow map.

    ///

    /// Sets the flow map.

    ///

    /// \return \c (*this)

    CycleCanceling& flowMap(FlowMap &map) {

      if (_local_flow) {

        delete _flow;

        _local_flow = false;

      }

      _flow = ↦

      return *this;

    }

    /// \brief Sets the potential map.

    ///

    /// Sets the potential map.

    ///

    /// \return \c (*this)

    CycleCanceling& potentialMap(PotentialMap &map) {

      if (_local_potential) {

        delete _potential;

        _local_potential = false;

      }

      _potential = ↦

      return *this;

    }

    /// \name Execution control

    /// The only way to execute the algorithm is to call the run()

    /// function.

    /// @{

    /// \brief Runs the algorithm.

    ///

    /// Runs the algorithm.

    ///

    /// \param min_mean_cc Set this parameter to \c true to run the

    /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly

    /// polynomial, but rather slower in practice.

    ///

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

    bool run(bool min_mean_cc = false) {

      return init() && start(min_mean_cc);

    }

    /// @}

    /// \name Query Functions

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

    /// functions.

    /// \n run() must be called before using them.

    /// @{

    /// \brief Returns a const reference to the edge map storing the

    /// found flow.

    ///

    /// Returns a const reference to the edge map storing the found flow.

    ///

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

    const FlowMap& flowMap() const {

      return *_flow;

    }

    /// \brief Returns a const reference to the node map storing the

    /// found potentials (the dual solution).

    ///

    /// Returns a const reference to the node map storing the found

    /// potentials (the dual solution).

    ///

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

    const PotentialMap& potentialMap() const {

      return *_potential;

    }

    /// \brief Returns the flow on the edge.

    ///

    /// Returns the flow on the edge.

    ///

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

    Capacity flow(const Edge& edge) const {

      return (*_flow)[edge];

    }

    /// \brief Returns the potential of the node.

    ///

    /// Returns the potential of the node.

    ///

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

    Cost potential(const Node& node) const {

      return (*_potential)[node];

    }

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

    ///

    /// Returns the total cost of the found flow. The complexity of the

    /// function is \f$ O(e) \f$.

    ///

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

    Cost totalCost() const {

      Cost c = 0;

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

        c += (*_flow)[e] * _cost[e];

      return c;

    }

    /// @}

  private:

    /// Initializes the algorithm.

    bool init() {

      if (!_valid_supply) return false;

      // Initializing flow and potential maps

      if (!_flow) {

        _flow = new FlowMap(_graph);

        _local_flow = true;

      }

      if (!_potential) {

        _potential = new PotentialMap(_graph);

        _local_potential = true;

      }

      _res_graph = new ResGraph(_graph, _capacity, *_flow);

      // Finding a feasible flow using Circulation

      Circulation< Graph, ConstMap<Edge, Capacity>, CapacityEdgeMap,

                   SupplyMap >

        circulation( _graph, constMap<Edge>(Capacity(0)), _capacity,

                     _supply );

      return circulation.flowMap(*_flow).run();

    }

    bool start(bool min_mean_cc) {

      if (min_mean_cc)

        startMinMean();

      else

        start();

      // Handling non-zero lower bounds

      if (_lower) {

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

          (*_flow)[e] += (*_lower)[e];

      }

      return true;

    }

    /// \brief Executes the algorithm using \ref BellmanFord.

    ///

    /// Executes the algorithm using the \ref BellmanFord

    /// "Bellman-Ford" algorithm for negative cycle detection with

    /// successively larger limit for the number of iterations.

    void start() {

      typename BellmanFord<ResGraph, ResidualCostMap>::PredMap pred(*_res_graph);

      typename ResGraph::template NodeMap<int> visited(*_res_graph);

      std::vector<ResEdge> cycle;

      int node_num = countNodes(_graph);

      int length_bound = BF_FIRST_LIMIT;

      bool optimal = false;

      while (!optimal) {

        BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost);

        bf.predMap(pred);

        bf.init(0);

        int iter_num = 0;

        bool cycle_found = false;

        while (!cycle_found) {

          int curr_iter_num = iter_num + length_bound <= node_num ?

                              length_bound : node_num - iter_num;

          iter_num += curr_iter_num;

          int real_iter_num = curr_iter_num;

          for (int i = 0; i < curr_iter_num; ++i) {

            if (bf.processNextWeakRound()) {

              real_iter_num = i;

              break;

            }

          }

          if (real_iter_num < curr_iter_num) {

            // Optimal flow is found

            optimal = true;

            // Setting node potentials

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

              (*_potential)[n] = bf.dist(n);

            break;

          } else {

            // Searching for node disjoint negative cycles

            for (ResNodeIt n(*_res_graph); n != INVALID; ++n)

              visited[n] = 0;

            int id = 0;

            for (ResNodeIt n(*_res_graph); n != INVALID; ++n) {

              if (visited[n] > 0) continue;

              visited[n] = ++id;

              ResNode u = pred[n] == INVALID ?

                          INVALID : _res_graph->source(pred[n]);

              while (u != INVALID && visited[u] == 0) {

                visited[u] = id;

                u = pred[u] == INVALID ?

                    INVALID : _res_graph->source(pred[u]);

              }

              if (u != INVALID && visited[u] == id) {

                // Finding the negative cycle

                cycle_found = true;

                cycle.clear();

                ResEdge e = pred[u];

                cycle.push_back(e);

                Capacity d = _res_graph->rescap(e);

                while (_res_graph->source(e) != u) {

                  cycle.push_back(e = pred[_res_graph->source(e)]);

                  if (_res_graph->rescap(e) < d)

                    d = _res_graph->rescap(e);

                }

                // Augmenting along the cycle

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

                  _res_graph->augment(cycle[i], d);

              }

            }

          }

          if (!cycle_found)

            length_bound = int(length_bound * BF_ALPHA);

        }

      }

    }

    /// \brief Executes the algorithm using \ref MinMeanCycle.

    ///

    /// Executes the algorithm using \ref MinMeanCycle for negative

    /// cycle detection.

    void startMinMean() {

      typedef Path<ResGraph> ResPath;

      MinMeanCycle<ResGraph, ResidualCostMap> mmc(*_res_graph, _res_cost);

      ResPath cycle;

      mmc.cyclePath(cycle).init();

      if (mmc.findMinMean()) {

        while (mmc.cycleLength() < 0) {

          // Finding the cycle

          mmc.findCycle();

          // Finding the largest flow amount that can be augmented

          // along the cycle

          Capacity delta = 0;

          for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e) {

            if (delta == 0 || _res_graph->rescap(e) < delta)

              delta = _res_graph->rescap(e);

          }

          // Augmenting along the cycle

          for (typename ResPath::EdgeIt e(cycle); e != INVALID; ++e)

            _res_graph->augment(e, delta);

          // Finding the minimum cycle mean for the modified residual

          // graph

          mmc.reset();

          if (!mmc.findMinMean()) break;

        }

      }

      // Computing node potentials

      BellmanFord<ResGraph, ResidualCostMap> bf(*_res_graph, _res_cost);

      bf.init(0); bf.start();

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

        (*_potential)[n] = bf.dist(n);

    }

  }; //class CycleCanceling

  ///@}

} //namespace lemon

#endif //LEMON_CYCLE_CANCELING_H