/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2006

  * 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_HAO_ORLIN_H

 #define LEMON_HAO_ORLIN_H

 #include <cassert>

 #include <vector>

 #include <queue>

 #include <list>

 #include <limits>

 #include <lemon/maps.h>

 #include <lemon/graph_utils.h>

 #include <lemon/graph_adaptor.h>

 #include <lemon/iterable_maps.h>

 /// \file

 /// \ingroup flowalgs

 /// \brief Implementation of the Hao-Orlin algorithm.

 ///

 /// Implementation of the HaoOrlin algorithms class for testing network 

 /// reliability.

 namespace lemon {

   /// \ingroup flowalgs

   ///

   /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs.

   ///

   /// Hao-Orlin calculates a minimum cut in a directed graph 

   /// \f$ D=(V,A) \f$. It takes a fixed node \f$ source \in V \f$ and consists

   /// of two phases: in the first phase it determines a minimum cut

   /// with \f$ source \f$ on the source-side (i.e. a set \f$ X\subsetneq V \f$

   /// with \f$ source \in X \f$ and minimal out-degree) and in the

   /// second phase it determines a minimum cut with \f$ source \f$ on the

   /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \notin X \f$

   /// and minimal out-degree). Obviously, the smaller of these two

   /// cuts will be a minimum cut of \f$ D \f$. The algorithm is a

   /// modified push-relabel preflow algorithm and our implementation

   /// calculates the minimum cut in \f$ O(n^3) \f$ time (we use the

   /// highest-label rule). The purpose of such an algorithm is testing

   /// network reliability. For an undirected graph with \f$ n \f$

   /// nodes and \f$ e \f$ edges you can use the algorithm of Nagamochi

   /// and Ibaraki which solves the undirected problem in 

   /// \f$ O(ne + n^2 \log(n)) \f$ time: it is implemented in the MinCut 

   /// algorithm

   /// class.

   ///

   /// \param _Graph is the graph type of the algorithm.

   /// \param _CapacityMap is an edge map of capacities which should

   /// be any numreric type. The default type is _Graph::EdgeMap<int>.

   /// \param _Tolerance is the handler of the inexact computation. The

   /// default type for this is Tolerance<typename CapacityMap::Value>.

   ///

   /// \author Attila Bernath and Balazs Dezso

 #ifdef DOXYGEN

   template <typename _Graph, typename _CapacityMap, typename _Tolerance>

 #else

   template <typename _Graph,

 	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,

             typename _Tolerance = Tolerance<typename _CapacityMap::Value> >

 #endif

   class HaoOrlin {

   protected:

     typedef _Graph Graph;

     typedef _CapacityMap CapacityMap;

     typedef _Tolerance Tolerance;

     typedef typename CapacityMap::Value Value;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::InEdgeIt InEdgeIt;

     const Graph* _graph;

     const CapacityMap* _capacity;

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

     FlowMap* _preflow;

     Node _source, _target;

     int _node_num;

     typedef ResGraphAdaptor<const Graph, Value, CapacityMap, 

                             FlowMap, Tolerance> OutResGraph;

     typedef typename OutResGraph::Edge OutResEdge;

     OutResGraph* _out_res_graph;

     typedef RevGraphAdaptor<const Graph> RevGraph;

     RevGraph* _rev_graph;

     typedef ResGraphAdaptor<const RevGraph, Value, CapacityMap, 

                             FlowMap, Tolerance> InResGraph;

     typedef typename InResGraph::Edge InResEdge;

     InResGraph* _in_res_graph;

     typedef IterableBoolMap<Graph, Node> WakeMap;

     WakeMap* _wake;

     typedef typename Graph::template NodeMap<int> DistMap;

     DistMap* _dist;  

     typedef typename Graph::template NodeMap<Value> ExcessMap;

     ExcessMap* _excess;

     typedef typename Graph::template NodeMap<bool> SourceSetMap;

     SourceSetMap* _source_set;

     std::vector<int> _level_size;

     int _highest_active;

     std::vector<std::list<Node> > _active_nodes;

     int _dormant_max;

     std::vector<std::list<Node> > _dormant;

     Value _min_cut;

     typedef typename Graph::template NodeMap<bool> MinCutMap;

     MinCutMap* _min_cut_map;

     Tolerance _tolerance;

   public: 

     /// \brief Constructor

     ///

     /// Constructor of the algorithm class. 

     HaoOrlin(const Graph& graph, const CapacityMap& capacity, 

              const Tolerance& tolerance = Tolerance()) :

       _graph(&graph), _capacity(&capacity), 

       _preflow(0), _source(), _target(), 

       _out_res_graph(0), _rev_graph(0), _in_res_graph(0),

       _wake(0),_dist(0), _excess(0), _source_set(0), 

       _highest_active(), _active_nodes(), _dormant_max(), _dormant(), 

       _min_cut(), _min_cut_map(0), _tolerance(tolerance) {}

     ~HaoOrlin() {

       if (_min_cut_map) {

         delete _min_cut_map;

       } 

       if (_in_res_graph) {

         delete _in_res_graph;

       }

       if (_rev_graph) {

         delete _rev_graph;

       }

       if (_out_res_graph) {

         delete _out_res_graph;

       }

       if (_source_set) {

         delete _source_set;

       }

       if (_excess) {

         delete _excess;

       }

       if (_dist) {

         delete _dist;

       }

       if (_wake) {

         delete _wake;

       }

       if (_preflow) {

         delete _preflow;

       }

     }

   private:

     template <typename ResGraph>

     void findMinCut(const Node& target, bool out, ResGraph& res_graph) {

       typedef typename Graph::Node Node;

       typedef typename ResGraph::Edge ResEdge;

       typedef typename ResGraph::OutEdgeIt ResOutEdgeIt;

       for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) {

         (*_preflow)[it] = 0;      

       }

       for (NodeIt it(*_graph); it != INVALID; ++it) {

         (*_wake)[it] = true;

         (*_dist)[it] = 1;

         (*_excess)[it] = 0;

         (*_source_set)[it] = false;

       }

       _dormant[0].push_front(_source);

       (*_source_set)[_source] = true;

       _dormant_max = 0;

       (*_wake)[_source] = false;

       _level_size[0] = 1;

       _level_size[1] = _node_num - 1;

       _target = target;

       (*_dist)[target] = 0;

       for (ResOutEdgeIt it(res_graph, _source); it != INVALID; ++it) {

         Value delta = res_graph.rescap(it);

         (*_excess)[_source] -= delta;

         res_graph.augment(it, delta);

         Node a = res_graph.target(it);

         if ((*_excess)[a] == 0 && (*_wake)[a] && a != _target) {

           _active_nodes[(*_dist)[a]].push_front(a);

           if (_highest_active < (*_dist)[a]) {

             _highest_active = (*_dist)[a];

           }

         }

         (*_excess)[a] += delta;

       }

       do {

 	Node n;

 	while ((n = findActiveNode()) != INVALID) {

 	  for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e) {

             Node a = res_graph.target(e);

             if ((*_dist)[a] >= (*_dist)[n] || !(*_wake)[a]) continue;

 	    Value delta = res_graph.rescap(e);

 	    if (_tolerance.positive((*_excess)[n] - delta)) {

               (*_excess)[n] -= delta;

 	    } else {

 	      delta = (*_excess)[n];

               (*_excess)[n] = 0;

 	    }

 	    res_graph.augment(e, delta);

 	    if ((*_excess)[a] == 0 && a != _target) {

 	      _active_nodes[(*_dist)[a]].push_front(a);

 	    }

 	    (*_excess)[a] += delta;

             if ((*_excess)[n] == 0) break;

 	  }

 	  if ((*_excess)[n] != 0) {

 	    relabel(n, res_graph);

           }

 	}

 	Value current_value = cutValue(out);

  	if (_min_cut > current_value){

           if (out) {

             for (NodeIt it(*_graph); it != INVALID; ++it) {

               _min_cut_map->set(it, !(*_wake)[it]);

             } 

           } else {

             for (NodeIt it(*_graph); it != INVALID; ++it) {

               _min_cut_map->set(it, (*_wake)[it]);

             } 

           }

 	  _min_cut = current_value;

  	}

       } while (selectNewSink(res_graph));

     }

     template <typename ResGraph>

     void relabel(const Node& n, ResGraph& res_graph) {

       typedef typename ResGraph::OutEdgeIt ResOutEdgeIt;

       int k = (*_dist)[n];

       if (_level_size[k] == 1) {

 	++_dormant_max;

 	for (NodeIt it(*_graph); it != INVALID; ++it) {

 	  if ((*_wake)[it] && (*_dist)[it] >= k) {

 	    (*_wake)[it] = false;

 	    _dormant[_dormant_max].push_front(it);

 	    --_level_size[(*_dist)[it]];

 	  }

 	}

         --_highest_active;

       } else {	

         int new_dist = _node_num;

         for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e) {

           Node t = res_graph.target(e);

           if ((*_wake)[t] && new_dist > (*_dist)[t]) {

             new_dist = (*_dist)[t];

           }

         }

         if (new_dist == _node_num) {

 	  ++_dormant_max;

 	  (*_wake)[n] = false;

 	  _dormant[_dormant_max].push_front(n);

 	  --_level_size[(*_dist)[n]];

 	} else {	    

 	  --_level_size[(*_dist)[n]];

 	  (*_dist)[n] = new_dist + 1;

 	  _highest_active = (*_dist)[n];

 	  _active_nodes[_highest_active].push_front(n);

 	  ++_level_size[(*_dist)[n]];

 	}

       }

     }

     template <typename ResGraph>

     bool selectNewSink(ResGraph& res_graph) {

       typedef typename ResGraph::OutEdgeIt ResOutEdgeIt;

       Node old_target = _target;

       (*_wake)[_target] = false;

       --_level_size[(*_dist)[_target]];

       _dormant[0].push_front(_target);

       (*_source_set)[_target] = true;

       if ((int)_dormant[0].size() == _node_num){

         _dormant[0].clear();

 	return false;

       }

       bool wake_was_empty = false;

       if(_wake->trueNum() == 0) {

 	while (!_dormant[_dormant_max].empty()){

 	  (*_wake)[_dormant[_dormant_max].front()] = true;

 	  ++_level_size[(*_dist)[_dormant[_dormant_max].front()]];

 	  _dormant[_dormant_max].pop_front();

 	}

 	--_dormant_max;

 	wake_was_empty = true;

       }

       int min_dist = std::numeric_limits<int>::max();

       for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

 	if (min_dist > (*_dist)[it]){

 	  _target = it;

 	  min_dist = (*_dist)[it];

 	}

       }

       if (wake_was_empty){

 	for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

           if ((*_excess)[it] != 0 && it != _target) {

             _active_nodes[(*_dist)[it]].push_front(it);

             if (_highest_active < (*_dist)[it]) {

               _highest_active = (*_dist)[it];		    

             }

 	  }

 	}

       }

       Node n = old_target;

       for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e){

         Node a = res_graph.target(e);

 	if (!(*_wake)[a]) continue;

         Value delta = res_graph.rescap(e);

         res_graph.augment(e, delta);

         (*_excess)[n] -= delta;

         if ((*_excess)[a] == 0 && (*_wake)[a] && a != _target) {

           _active_nodes[(*_dist)[a]].push_front(a);

           if (_highest_active < (*_dist)[a]) {

             _highest_active = (*_dist)[a];

           }

         }

         (*_excess)[a] += delta;

       }

       return true;

     }

     Node findActiveNode() {

       while (_highest_active > 0 && _active_nodes[_highest_active].empty()){ 

 	--_highest_active;

       }

       if( _highest_active > 0) {

        	Node n = _active_nodes[_highest_active].front();

 	_active_nodes[_highest_active].pop_front();

 	return n;

       } else {

 	return INVALID;

       }

     }

     Value cutValue(bool out) {

       Value value = 0;

       if (out) {

         for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

           for (InEdgeIt e(*_graph, it); e != INVALID; ++e) {

             if (!(*_wake)[_graph->source(e)]){

               value += (*_capacity)[e];

             }	

           }

         }

       } else {

         for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

           for (OutEdgeIt e(*_graph, it); e != INVALID; ++e) {

             if (!(*_wake)[_graph->target(e)]){

               value += (*_capacity)[e];

             }	

           }

         }

       }

       return value;

     }

   public:

     /// \name Execution control

     /// The simplest way to execute the algorithm is to use

     /// one of the member functions called \c run(...).

     /// \n

     /// If you need more control on the execution,

     /// first you must call \ref init(), then the \ref calculateIn() or

     /// \ref calculateIn() functions.

     /// @{

     /// \brief Initializes the internal data structures.

     ///

     /// Initializes the internal data structures. It creates

     /// the maps, residual graph adaptors and some bucket structures

     /// for the algorithm. 

     void init() {

       init(NodeIt(*_graph));

     }

     /// \brief Initializes the internal data structures.

     ///

     /// Initializes the internal data structures. It creates

     /// the maps, residual graph adaptor and some bucket structures

     /// for the algorithm. Node \c source  is used as the push-relabel

     /// algorithm's source.

     void init(const Node& source) {

       _source = source;

       _node_num = countNodes(*_graph);

       _dormant.resize(_node_num);

       _level_size.resize(_node_num, 0);

       _active_nodes.resize(_node_num);

       if (!_preflow) {

         _preflow = new FlowMap(*_graph);

       }

       if (!_wake) {

         _wake = new WakeMap(*_graph);

       }

       if (!_dist) {

         _dist = new DistMap(*_graph);

       }

       if (!_excess) {

         _excess = new ExcessMap(*_graph);

       }

       if (!_source_set) {

         _source_set = new SourceSetMap(*_graph);

       }

       if (!_out_res_graph) {

         _out_res_graph = new OutResGraph(*_graph, *_capacity, *_preflow);

       }

       if (!_rev_graph) {

         _rev_graph = new RevGraph(*_graph);

       }

       if (!_in_res_graph) {

         _in_res_graph = new InResGraph(*_rev_graph, *_capacity, *_preflow);

       }

       if (!_min_cut_map) {

         _min_cut_map = new MinCutMap(*_graph);

       }

       _min_cut = std::numeric_limits<Value>::max();

     }

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// source-side.

     ///

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X \f$

     ///  and minimal out-degree).

     void calculateOut() {

       for (NodeIt it(*_graph); it != INVALID; ++it) {

         if (it != _source) {

           calculateOut(it);

           return;

         }

       }

     }

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// source-side.

     ///

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source \in X \f$

     ///  and minimal out-degree). The \c target is the initial target

     /// for the push-relabel algorithm.

     void calculateOut(const Node& target) {

       findMinCut(target, true, *_out_res_graph);

     }

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// sink-side.

     ///

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with 

     /// \f$ source \notin X \f$

     /// and minimal out-degree).

     void calculateIn() {

       for (NodeIt it(*_graph); it != INVALID; ++it) {

         if (it != _source) {

           calculateIn(it);

           return;

         }

       }

     }

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// sink-side.

     ///

     /// \brief Calculates a minimum cut with \f$ source \f$ on the

     /// sink-side (i.e. a set \f$ X\subsetneq V 

     /// \f$ with \f$ source \notin X \f$ and minimal out-degree).  

     /// The \c target is the initial

     /// target for the push-relabel algorithm.

     void calculateIn(const Node& target) {

       findMinCut(target, false, *_in_res_graph);

     }

     /// \brief Runs the algorithm.

     ///

     /// Runs the algorithm. It finds nodes \c source and \c target

     /// arbitrarily and then calls \ref init(), \ref calculateOut()

     /// and \ref calculateIn().

     void run() {

       init();

       for (NodeIt it(*_graph); it != INVALID; ++it) {

         if (it != _source) {

           calculateOut(it);

           calculateIn(it);

           return;

         }

       }

     }

     /// \brief Runs the algorithm.

     ///

     /// Runs the algorithm. It uses the given \c source node, finds a

     /// proper \c target and then calls the \ref init(), \ref

     /// calculateOut() and \ref calculateIn().

     void run(const Node& s) {

       init(s);

       for (NodeIt it(*_graph); it != INVALID; ++it) {

         if (it != _source) {

           calculateOut(it);

           calculateIn(it);

           return;

         }

       }

     }

     /// \brief Runs the algorithm.

     ///

     /// Runs the algorithm. It just calls the \ref init() and then

     /// \ref calculateOut() and \ref calculateIn().

     void run(const Node& s, const Node& t) {

       init(s); 

       calculateOut(t);

       calculateIn(t);

     }

     /// @}

     /// \name Query Functions 

     /// The result of the %HaoOrlin algorithm

     /// can be obtained using these functions.

     /// \n

     /// Before using these functions, either \ref run(), \ref

     /// calculateOut() or \ref calculateIn() must be called.

     /// @{

     /// \brief Returns the value of the minimum value cut.

     /// 

     /// Returns the value of the minimum value cut.

     Value minCut() const {

       return _min_cut;

     }

     /// \brief Returns a minimum cut.

     ///

     /// Sets \c nodeMap to the characteristic vector of a minimum

     /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$

     /// with minimal out-degree (i.e. \c nodeMap will be true exactly

     /// for the nodes of \f$ X \f$).  \pre nodeMap should be a

     /// bool-valued node-map.

     template <typename NodeMap>

     Value minCut(NodeMap& nodeMap) const {

       for (NodeIt it(*_graph); it != INVALID; ++it) {

 	nodeMap.set(it, (*_min_cut_map)[it]);

       }

       return minCut();

     }

     /// @}

   }; //class HaoOrlin 

 } //namespace lemon

 #endif //LEMON_HAO_ORLIN_H