/* -*- 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/graph_adaptor.h>
#include <lemon/circulation.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 signed 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:

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

      Cost operator[](const ResEdge &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