/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2007

 * 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 A cycle-canceling algorithm for finding a minimum cost flow.

#include <vector>

#include <lemon/circulation.h>

#include <lemon/graph_adaptor.h>

/// \brief The used cycle-canceling method.

#define LIMITED_CYCLE_CANCELING

//#define MIN_MEAN_CYCLE_CANCELING

#ifdef LIMITED_CYCLE_CANCELING

  #include <lemon/bellman_ford.h>

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

  /// of the \ref lemon::BellmanFord "Bellman-Ford" algorithm.

  /// It should be at least 2.

  #define STARTING_LIMIT	2

  /// \brief The iteration limit for the

  /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by

  /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round.

  /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1.

  #define ALPHA_MUL		3

  /// \brief The iteration limit for the

  /// \ref lemon::BellmanFord "Bellman-Ford" algorithm is multiplied by

  /// <tt>ALPHA_MUL / ALPHA_DIV</tt> in every round.

  /// <tt>ALPHA_MUL / ALPHA_DIV</tt> must be greater than 1.

  #define ALPHA_DIV		2

//#define _ONLY_ONE_CYCLE_

//#define _NO_BACK_STEP_

//#define _DEBUG_ITER_

#endif

#ifdef MIN_MEAN_CYCLE_CANCELING

  #include <lemon/min_mean_cycle.h>

  #include <lemon/path.h>

#endif

namespace lemon {

  /// \addtogroup min_cost_flow

  /// @{

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

  /// a minimum cost flow.

  ///

  /// \ref lemon::CycleCanceling "CycleCanceling" implements a

  /// cycle-canceling algorithm for finding a minimum cost flow.

  ///

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

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

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

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

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

  ///

  /// \warning

  /// - Edge capacities and costs should be nonnegative integers.

  ///	However \c CostMap::Value should be signed type.

  /// - Supply values should be integers.

  /// - \c LowerMap::Value must be convertible to

  ///	\c CapacityMap::Value and \c CapacityMap::Value must be

  ///	convertible to \c SupplyMap::Value.

  ///

  /// \author Peter Kovacs

template < typename Graph,

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

	   typename CapacityMap = LowerMap,

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

	   typename SupplyMap = typename Graph::template NodeMap

				<typename CapacityMap::Value> >

  class CycleCanceling

  {

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::EdgeIt EdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename LowerMap::Value Lower;

    typedef typename CapacityMap::Value Capacity;

    typedef typename CostMap::Value Cost;

    typedef typename SupplyMap::Value Supply;

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

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

    typedef ResGraphAdaptor< const Graph, Capacity,

			     CapacityRefMap, CapacityRefMap > ResGraph;

    typedef typename ResGraph::Node ResNode;

    typedef typename ResGraph::NodeIt ResNodeIt;

    typedef typename ResGraph::Edge ResEdge;

    typedef typename ResGraph::EdgeIt ResEdgeIt;

  public:

    /// \brief The type of the flow map.

    typedef CapacityRefMap FlowMap;

  protected:

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

    class ResCostMap : public MapBase<ResEdge, Cost>

    {

    private:

      const CostMap &cost_map;

    public:

      typedef typename MapBase<ResEdge, Cost>::Value Value;

      typedef typename MapBase<ResEdge, Cost>::Key Key;

      ResCostMap(const CostMap &_cost) : cost_map(_cost) {}

      Value operator[](const Key &e) const {

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

      }

    }; //class ResCostMap

  protected:

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

    const Graph &graph;

    /// \brief The original lower bound map.

    const LowerMap *lower;

    /// \brief The modified capacity map.

    CapacityRefMap capacity;

    /// \brief The cost map.

    const CostMap &cost;

    /// \brief The modified supply map.

    SupplyRefMap supply;

    /// \brief The sum of supply values equals zero.

    bool valid_supply;

    /// \brief The current flow.

    FlowMap flow;

    /// \brief The residual graph.

    ResGraph res_graph;

    /// \brief The residual cost map.

    ResCostMap res_cost;

  public :

    /// \brief General constructor of the class (with lower bounds).

    ///

    /// General constructor of the class (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(_graph, 0),

      res_graph(_graph, capacity, flow), res_cost(cost)

    {

      // Removing nonzero 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 of the class (without lower bounds).

    ///

    /// General constructor of the class (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(_graph, 0),

      res_graph(_graph, capacity, flow), 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 of the class (with lower bounds).

    ///

    /// Simple constructor of the class (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(_graph, 0),

      res_graph(_graph, capacity, flow), res_cost(cost)

    {

      // Removing nonzero lower bounds

      capacity = subMap(_capacity, _lower);

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

	Supply s = 0;

	if (n == _s) s =  _flow_value;

	if (n == _t) s = -_flow_value;

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

	  s += _lower[e];

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

	  s -= _lower[e];

	supply[n] = s;

      }

      valid_supply = true;

    }

    /// \brief Simple constructor of the class (without lower bounds).

    ///

    /// Simple constructor of the class (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(_graph, 0),

      res_graph(_graph, capacity, flow), res_cost(cost)

    {

      supply[_s] =  _flow_value;

      supply[_t] = -_flow_value;

      valid_supply = true;

    }

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

    ///

    /// Returns a const reference to the flow map.

    ///

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

    const FlowMap& flowMap() const {

      return flow;

    }

    /// \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;

    }

    /// \brief Runs the algorithm.

    ///

    /// Runs the algorithm.

    ///

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

    bool run() {

      return init() && start();

    }

  protected:

    /// \brief Initializes the algorithm.

    bool init() {

      // Checking the sum of supply values

      Supply sum = 0;

      for (NodeIt n(graph); n != INVALID; ++n) sum += supply[n];

      if (sum != 0) return false;

      // Finding a feasible flow

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

		   CapacityRefMap, SupplyMap >

	circulation( graph, constMap<Edge>((Capacity)0),

		     capacity, supply, flow );

      return circulation.run() == -1;

    }

#ifdef LIMITED_CYCLE_CANCELING

    /// \brief Executes a cycle-canceling algorithm using

    /// \ref lemon::BellmanFord "Bellman-Ford" algorithm with limited

    /// iteration count.

    bool start() {

      typename BellmanFord<ResGraph, ResCostMap>::PredMap pred(res_graph);

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

      std::vector<ResEdge> cycle;

      int node_num = countNodes(graph);

#ifdef _DEBUG_ITER_

      int cycle_num = 0;

#endif

      int length_bound = STARTING_LIMIT;

      bool optimal = false;

      while (!optimal) {

	BellmanFord<ResGraph, ResCostMap> bf(res_graph, res_cost);

	bf.predMap(pred);

	bf.init(0);

	int iter_num = 0;

	bool cycle_found = false;

	while (!cycle_found) {

#ifdef _NO_BACK_STEP_

	  int curr_iter_num = length_bound <= node_num ?

			      length_bound - iter_num : node_num - iter_num;

#else

	  int curr_iter_num = iter_num + length_bound <= node_num ?

			      length_bound : node_num - iter_num;

#endif

	  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 = true;

	    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);

		}

#ifdef _DEBUG_ITER_

		++cycle_num;

#endif

		// Augmenting along the cycle

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

		  res_graph.augment(cycle[i], d);

#ifdef _ONLY_ONE_CYCLE_

		break;

#endif

	      }

	    }

	  }

	  if (!cycle_found)

	    length_bound = length_bound * ALPHA_MUL / ALPHA_DIV;

	}

      }

#ifdef _DEBUG_ITER_

      std::cout << "Limited cycle-canceling algorithm finished. "

		<< "Found " << cycle_num << " negative cycles."

		<< std::endl;

#endif

      // Handling nonzero lower bounds

      if (lower) {

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

	  flow[e] += (*lower)[e];

      }

      return true;

    }

#endif

#ifdef MIN_MEAN_CYCLE_CANCELING

    /// \brief Executes the minimum mean cycle-canceling algorithm

    /// using \ref lemon::MinMeanCycle "MinMeanCycle" class.

    bool start() {

      typedef Path<ResGraph> ResPath;

      MinMeanCycle<ResGraph, ResCostMap> mmc(res_graph, res_cost);

      ResPath cycle;

#ifdef _DEBUG_ITER_

      int cycle_num = 0;

#endif

      mmc.cyclePath(cycle).init();

      if (mmc.findMinMean()) {

	while (mmc.cycleLength() < 0) {

#ifdef _DEBUG_ITER_

	  ++iter;

#endif

	  // 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;

	}

      }

#ifdef _DEBUG_ITER_

      std::cout << "Minimum mean cycle-canceling algorithm finished. "

		<< "Found " << cycle_num << " negative cycles."

		<< std::endl;

#endif

      // Handling nonzero lower bounds

      if (lower) {

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

	  flow[e] += (*lower)[e];

      }

      return true;

    }

#endif

  }; //class CycleCanceling

  ///@}

} //namespace lemon

#endif //LEMON_CYCLE_CANCELING_H