deba@2211: /* -*- C++ -*-
deba@2211:  *
deba@2225:  * This file is a part of LEMON, a generic C++ optimization library
deba@2225:  *
alpar@2553:  * Copyright (C) 2003-2008
deba@2225:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@2211:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@2211:  *
deba@2211:  * Permission to use, modify and distribute this software is granted
deba@2211:  * provided that this copyright notice appears in all copies. For
deba@2211:  * precise terms see the accompanying LICENSE file.
deba@2211:  *
deba@2211:  * This software is provided "AS IS" with no warranty of any kind,
deba@2211:  * express or implied, and with no claim as to its suitability for any
deba@2211:  * purpose.
deba@2211:  *
deba@2211:  */
deba@2211: 
deba@2211: #ifndef LEMON_HAO_ORLIN_H
deba@2211: #define LEMON_HAO_ORLIN_H
deba@2211: 
deba@2211: #include <vector>
deba@2340: #include <list>
deba@2530: #include <ext/hash_set>
deba@2211: #include <limits>
deba@2211: 
deba@2211: #include <lemon/maps.h>
deba@2211: #include <lemon/graph_utils.h>
deba@2211: #include <lemon/graph_adaptor.h>
deba@2211: #include <lemon/iterable_maps.h>
deba@2211: 
deba@2211: /// \file
deba@2376: /// \ingroup min_cut
deba@2225: /// \brief Implementation of the Hao-Orlin algorithm.
deba@2225: ///
deba@2530: /// Implementation of the Hao-Orlin algorithm class for testing network 
deba@2211: /// reliability.
deba@2211: 
deba@2211: namespace lemon {
deba@2211: 
deba@2376:   /// \ingroup min_cut
deba@2225:   ///
athos@2228:   /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs.
deba@2211:   ///
deba@2530:   /// Hao-Orlin calculates a minimum cut in a directed graph
deba@2530:   /// \f$D=(V,A)\f$. It takes a fixed node \f$ source \in V \f$ and
deba@2530:   /// consists of two phases: in the first phase it determines a
deba@2530:   /// minimum cut with \f$ source \f$ on the source-side (i.e. a set
deba@2530:   /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal
deba@2530:   /// out-degree) and in the second phase it determines a minimum cut
deba@2530:   /// with \f$ source \f$ on the sink-side (i.e. a set 
deba@2530:   /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal
deba@2530:   /// out-degree). Obviously, the smaller of these two cuts will be a
deba@2530:   /// minimum cut of \f$ D \f$. The algorithm is a modified
deba@2530:   /// push-relabel preflow algorithm and our implementation calculates
deba@2530:   /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
deba@2530:   /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The
deba@2530:   /// purpose of such algorithm is testing network reliability. For an
deba@2530:   /// undirected graph you can run just the first phase of the
deba@2530:   /// algorithm or you can use the algorithm of Nagamochi and Ibaraki
deba@2530:   /// which solves the undirected problem in 
deba@2530:   /// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the
deba@2530:   /// NagamochiIbaraki algorithm class.
deba@2225:   ///
deba@2225:   /// \param _Graph is the graph type of the algorithm.
deba@2225:   /// \param _CapacityMap is an edge map of capacities which should
deba@2225:   /// be any numreric type. The default type is _Graph::EdgeMap<int>.
deba@2225:   /// \param _Tolerance is the handler of the inexact computation. The
athos@2228:   /// default type for this is Tolerance<typename CapacityMap::Value>.
deba@2211:   ///
deba@2211:   /// \author Attila Bernath and Balazs Dezso
deba@2225: #ifdef DOXYGEN
deba@2225:   template <typename _Graph, typename _CapacityMap, typename _Tolerance>
deba@2225: #else
deba@2211:   template <typename _Graph,
deba@2211: 	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,
deba@2211:             typename _Tolerance = Tolerance<typename _CapacityMap::Value> >
deba@2225: #endif
deba@2211:   class HaoOrlin {
deba@2530:   private:
deba@2211: 
deba@2211:     typedef _Graph Graph;
deba@2211:     typedef _CapacityMap CapacityMap;
deba@2211:     typedef _Tolerance Tolerance;
deba@2211: 
deba@2211:     typedef typename CapacityMap::Value Value;
deba@2211: 
deba@2530:     GRAPH_TYPEDEFS(typename Graph);
deba@2211:     
deba@2530:     const Graph& _graph;
deba@2211:     const CapacityMap* _capacity;
deba@2211: 
deba@2211:     typedef typename Graph::template EdgeMap<Value> FlowMap;
deba@2530:     FlowMap* _flow;
deba@2211: 
deba@2530:     Node _source;
deba@2211: 
deba@2211:     int _node_num;
deba@2211: 
deba@2530:     // Bucketing structure
deba@2530:     std::vector<Node> _first, _last;
deba@2530:     typename Graph::template NodeMap<Node>* _next;
deba@2530:     typename Graph::template NodeMap<Node>* _prev;    
deba@2530:     typename Graph::template NodeMap<bool>* _active;
deba@2530:     typename Graph::template NodeMap<int>* _bucket;
deba@2225:     
deba@2530:     std::vector<bool> _dormant;
deba@2211: 
deba@2530:     std::list<std::list<int> > _sets;
deba@2530:     std::list<int>::iterator _highest;
deba@2211:     
deba@2211:     typedef typename Graph::template NodeMap<Value> ExcessMap;
deba@2211:     ExcessMap* _excess;
deba@2211: 
deba@2211:     typedef typename Graph::template NodeMap<bool> SourceSetMap;
deba@2211:     SourceSetMap* _source_set;
deba@2211: 
deba@2211:     Value _min_cut;
deba@2211: 
deba@2211:     typedef typename Graph::template NodeMap<bool> MinCutMap;
deba@2211:     MinCutMap* _min_cut_map;
deba@2211: 
deba@2211:     Tolerance _tolerance;
deba@2211: 
deba@2211:   public: 
deba@2211: 
deba@2225:     /// \brief Constructor
deba@2225:     ///
deba@2225:     /// Constructor of the algorithm class. 
deba@2211:     HaoOrlin(const Graph& graph, const CapacityMap& capacity, 
deba@2211:              const Tolerance& tolerance = Tolerance()) :
deba@2530:       _graph(graph), _capacity(&capacity), _flow(0), _source(),
deba@2530:       _node_num(), _first(), _last(), _next(0), _prev(0), 
deba@2530:       _active(0), _bucket(0), _dormant(), _sets(), _highest(),
deba@2530:       _excess(0), _source_set(0), _min_cut(), _min_cut_map(0), 
deba@2530:       _tolerance(tolerance) {}
deba@2211: 
deba@2211:     ~HaoOrlin() {
deba@2211:       if (_min_cut_map) {
deba@2211:         delete _min_cut_map;
deba@2211:       } 
deba@2211:       if (_source_set) {
deba@2211:         delete _source_set;
deba@2211:       }
deba@2211:       if (_excess) {
deba@2211:         delete _excess;
deba@2211:       }
deba@2530:       if (_next) {
deba@2530: 	delete _next;
deba@2211:       }
deba@2530:       if (_prev) {
deba@2530: 	delete _prev;
deba@2211:       }
deba@2530:       if (_active) {
deba@2530: 	delete _active;
deba@2530:       }
deba@2530:       if (_bucket) {
deba@2530: 	delete _bucket;
deba@2530:       }
deba@2530:       if (_flow) {
deba@2530:         delete _flow;
deba@2211:       }
deba@2211:     }
deba@2211:     
deba@2211:   private:
deba@2530: 
deba@2530:     void activate(const Node& i) {
deba@2530:       _active->set(i, true);
deba@2530: 
deba@2530:       int bucket = (*_bucket)[i];
deba@2530: 
deba@2530:       if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;	    
deba@2530:       //unlace
deba@2530:       _next->set((*_prev)[i], (*_next)[i]);
deba@2530:       if ((*_next)[i] != INVALID) {
deba@2530: 	_prev->set((*_next)[i], (*_prev)[i]);
deba@2530:       } else {
deba@2530: 	_last[bucket] = (*_prev)[i];
deba@2530:       }
deba@2530:       //lace
deba@2530:       _next->set(i, _first[bucket]);
deba@2530:       _prev->set(_first[bucket], i);
deba@2530:       _prev->set(i, INVALID);
deba@2530:       _first[bucket] = i;
deba@2530:     }
deba@2530: 
deba@2530:     void deactivate(const Node& i) {
deba@2530:       _active->set(i, false);
deba@2530:       int bucket = (*_bucket)[i];
deba@2530: 
deba@2530:       if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;
deba@2530:       
deba@2530:       //unlace
deba@2530:       _prev->set((*_next)[i], (*_prev)[i]);
deba@2530:       if ((*_prev)[i] != INVALID) {
deba@2530: 	_next->set((*_prev)[i], (*_next)[i]);
deba@2530:       } else {
deba@2530: 	_first[bucket] = (*_next)[i];
deba@2530:       }
deba@2530:       //lace
deba@2530:       _prev->set(i, _last[bucket]);
deba@2530:       _next->set(_last[bucket], i);
deba@2530:       _next->set(i, INVALID);
deba@2530:       _last[bucket] = i;
deba@2530:     }
deba@2530: 
deba@2530:     void addItem(const Node& i, int bucket) {
deba@2530:       (*_bucket)[i] = bucket;
deba@2530:       if (_last[bucket] != INVALID) {
deba@2530: 	_prev->set(i, _last[bucket]);
deba@2530: 	_next->set(_last[bucket], i);
deba@2530: 	_next->set(i, INVALID);
deba@2530: 	_last[bucket] = i;
deba@2530:       } else {
deba@2530: 	_prev->set(i, INVALID);
deba@2530: 	_first[bucket] = i;
deba@2530: 	_next->set(i, INVALID);
deba@2530: 	_last[bucket] = i;
deba@2530:       }
deba@2530:     }
deba@2211:     
deba@2530:     void findMinCutOut() {
deba@2225: 
deba@2530:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2530: 	_excess->set(n, 0);
deba@2225:       }
deba@2225: 
deba@2530:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@2530: 	_flow->set(e, 0);
deba@2340:       }
deba@2340: 
deba@2530:       int bucket_num = 1;
deba@2530:       
deba@2530:       {
deba@2530: 	typename Graph::template NodeMap<bool> reached(_graph, false);
deba@2530: 	
deba@2530: 	reached.set(_source, true);
deba@2340: 
deba@2530: 	bool first_set = true;
deba@2530: 
deba@2530: 	for (NodeIt t(_graph); t != INVALID; ++t) {
deba@2530: 	  if (reached[t]) continue;
deba@2530: 	  _sets.push_front(std::list<int>());
deba@2530: 	  _sets.front().push_front(bucket_num);
deba@2530: 	  _dormant[bucket_num] = !first_set;
deba@2530: 
deba@2530: 	  _bucket->set(t, bucket_num);
deba@2530: 	  _first[bucket_num] = _last[bucket_num] = t;
deba@2530: 	  _next->set(t, INVALID);
deba@2530: 	  _prev->set(t, INVALID);
deba@2530: 
deba@2530: 	  ++bucket_num;
deba@2530: 	  
deba@2530: 	  std::vector<Node> queue;
deba@2530: 	  queue.push_back(t);
deba@2530: 	  reached.set(t, true);
deba@2530: 	  
deba@2530: 	  while (!queue.empty()) {
deba@2530: 	    _sets.front().push_front(bucket_num);
deba@2530: 	    _dormant[bucket_num] = !first_set;
deba@2530: 	    _first[bucket_num] = _last[bucket_num] = INVALID;
deba@2530: 	    
deba@2530: 	    std::vector<Node> nqueue;
deba@2530: 	    for (int i = 0; i < int(queue.size()); ++i) {
deba@2530: 	      Node n = queue[i];
deba@2530: 	      for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2530: 		Node u = _graph.source(e);
deba@2530: 		if (!reached[u] && _tolerance.positive((*_capacity)[e])) {
deba@2530: 		  reached.set(u, true);
deba@2530: 		  addItem(u, bucket_num);
deba@2530: 		  nqueue.push_back(u);
deba@2530: 		}
deba@2530: 	      }
deba@2225: 	    }
deba@2530: 	    queue.swap(nqueue);
deba@2530: 	    ++bucket_num;
deba@2225: 	  }
deba@2530: 	  _sets.front().pop_front();
deba@2530: 	  --bucket_num;
deba@2530: 	  first_set = false;
deba@2225: 	}
deba@2225: 
deba@2530: 	_bucket->set(_source, 0);
deba@2530: 	_dormant[0] = true;
deba@2530:       }
deba@2530:       _source_set->set(_source, true);	  
deba@2530: 	  
deba@2530:       Node target = _last[_sets.back().back()];
deba@2530:       {
deba@2530: 	for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) {
deba@2530: 	  if (_tolerance.positive((*_capacity)[e])) {
deba@2530: 	    Node u = _graph.target(e);
deba@2530: 	    _flow->set(e, (*_capacity)[e]);
deba@2530: 	    _excess->set(u, (*_excess)[u] + (*_capacity)[e]);
deba@2530: 	    if (!(*_active)[u] && u != _source) {
deba@2530: 	      activate(u);
deba@2530: 	    }
deba@2211: 	  }
deba@2211: 	}
deba@2530: 	if ((*_active)[target]) {
deba@2530: 	  deactivate(target);
deba@2530: 	}
deba@2530: 	
deba@2530: 	_highest = _sets.back().begin();
deba@2530: 	while (_highest != _sets.back().end() && 
deba@2530: 	       !(*_active)[_first[*_highest]]) {
deba@2530: 	  ++_highest;
deba@2530: 	}
deba@2530:       }
deba@2530: 
deba@2530: 
deba@2530:       while (true) {
deba@2530: 	while (_highest != _sets.back().end()) {
deba@2530: 	  Node n = _first[*_highest];
deba@2530: 	  Value excess = (*_excess)[n];
deba@2530: 	  int next_bucket = _node_num;
deba@2530: 
deba@2530: 	  int under_bucket;
deba@2530: 	  if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
deba@2530: 	    under_bucket = -1;
deba@2530: 	  } else {
deba@2530: 	    under_bucket = *(++std::list<int>::iterator(_highest));
deba@2530: 	  }
deba@2530: 
deba@2530: 	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2530: 	    Node v = _graph.target(e);
deba@2530: 	    if (_dormant[(*_bucket)[v]]) continue;
deba@2530: 	    Value rem = (*_capacity)[e] - (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    if ((*_bucket)[v] == under_bucket) {
deba@2530: 	      if (!(*_active)[v] && v != target) {
deba@2530: 		activate(v);
deba@2530: 	      }
deba@2530: 	      if (!_tolerance.less(rem, excess)) {
deba@2530: 		_flow->set(e, (*_flow)[e] + excess);
deba@2530: 		_excess->set(v, (*_excess)[v] + excess);
deba@2530: 		excess = 0;
deba@2530: 		goto no_more_push;
deba@2530: 	      } else {
deba@2530: 		excess -= rem;
deba@2530: 		_excess->set(v, (*_excess)[v] + rem);
deba@2530: 		_flow->set(e, (*_capacity)[e]);
deba@2530: 	      }
deba@2530: 	    } else if (next_bucket > (*_bucket)[v]) {
deba@2530: 	      next_bucket = (*_bucket)[v];
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 
deba@2530: 	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2530: 	    Node v = _graph.source(e);
deba@2530: 	    if (_dormant[(*_bucket)[v]]) continue;
deba@2530: 	    Value rem = (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    if ((*_bucket)[v] == under_bucket) {
deba@2530: 	      if (!(*_active)[v] && v != target) {
deba@2530: 		activate(v);
deba@2530: 	      }
deba@2530: 	      if (!_tolerance.less(rem, excess)) {
deba@2530: 		_flow->set(e, (*_flow)[e] - excess);
deba@2530: 		_excess->set(v, (*_excess)[v] + excess);
deba@2530: 		excess = 0;
deba@2530: 		goto no_more_push;
deba@2530: 	      } else {
deba@2530: 		excess -= rem;
deba@2530: 		_excess->set(v, (*_excess)[v] + rem);
deba@2530: 		_flow->set(e, 0);
deba@2530: 	      }
deba@2530: 	    } else if (next_bucket > (*_bucket)[v]) {
deba@2530: 	      next_bucket = (*_bucket)[v];
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	  
deba@2530: 	no_more_push:
deba@2530: 	  
deba@2530: 	  _excess->set(n, excess);
deba@2530: 	  
deba@2530: 	  if (excess != 0) {
deba@2530: 	    if ((*_next)[n] == INVALID) {
deba@2530: 	      typename std::list<std::list<int> >::iterator new_set = 
deba@2530: 		_sets.insert(--_sets.end(), std::list<int>());
deba@2530: 	      new_set->splice(new_set->end(), _sets.back(), 
deba@2530: 			      _sets.back().begin(), ++_highest);
deba@2530: 	      for (std::list<int>::iterator it = new_set->begin();
deba@2530: 		   it != new_set->end(); ++it) {
deba@2530: 		_dormant[*it] = true;
deba@2530: 	      }
deba@2530: 	      while (_highest != _sets.back().end() && 
deba@2530: 		     !(*_active)[_first[*_highest]]) {
deba@2530: 		++_highest;
deba@2530: 	      }
deba@2530: 	    } else if (next_bucket == _node_num) {
deba@2530: 	      _first[(*_bucket)[n]] = (*_next)[n];
deba@2530: 	      _prev->set((*_next)[n], INVALID);
deba@2530: 	      
deba@2530: 	      std::list<std::list<int> >::iterator new_set = 
deba@2530: 		_sets.insert(--_sets.end(), std::list<int>());
deba@2530: 	      
deba@2530: 	      new_set->push_front(bucket_num);
deba@2530: 	      _bucket->set(n, bucket_num);
deba@2530: 	      _first[bucket_num] = _last[bucket_num] = n;
deba@2530: 	      _next->set(n, INVALID);
deba@2530: 	      _prev->set(n, INVALID);
deba@2530: 	      _dormant[bucket_num] = true;
deba@2530: 	      ++bucket_num;
deba@2530: 
deba@2530: 	      while (_highest != _sets.back().end() && 
deba@2530: 		     !(*_active)[_first[*_highest]]) {
deba@2530: 		++_highest;
deba@2530: 	      }
deba@2530: 	    } else {
deba@2530: 	      _first[*_highest] = (*_next)[n];
deba@2530: 	      _prev->set((*_next)[n], INVALID);
deba@2530: 	      
deba@2530: 	      while (next_bucket != *_highest) {
deba@2530: 		--_highest;
deba@2530: 	      }
deba@2530: 
deba@2530: 	      if (_highest == _sets.back().begin()) {
deba@2530: 		_sets.back().push_front(bucket_num);
deba@2530: 		_dormant[bucket_num] = false;
deba@2530: 		_first[bucket_num] = _last[bucket_num] = INVALID;
deba@2530: 		++bucket_num;
deba@2530: 	      }
deba@2530: 	      --_highest;
deba@2530: 
deba@2530: 	      _bucket->set(n, *_highest);
deba@2530: 	      _next->set(n, _first[*_highest]);
deba@2530: 	      if (_first[*_highest] != INVALID) {
deba@2530: 		_prev->set(_first[*_highest], n);
deba@2530: 	      } else {
deba@2530: 		_last[*_highest] = n;
deba@2530: 	      }
deba@2530: 	      _first[*_highest] = n;	      
deba@2530: 	    }
deba@2530: 	  } else {
deba@2530: 
deba@2530: 	    deactivate(n);
deba@2530: 	    if (!(*_active)[_first[*_highest]]) {
deba@2530: 	      ++_highest;
deba@2530: 	      if (_highest != _sets.back().end() && 
deba@2530: 		  !(*_active)[_first[*_highest]]) {
deba@2530: 		_highest = _sets.back().end();
deba@2530: 	      }
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	}
deba@2530: 
deba@2530: 	if ((*_excess)[target] < _min_cut) {
deba@2530: 	  _min_cut = (*_excess)[target];
deba@2530: 	  for (NodeIt i(_graph); i != INVALID; ++i) {
deba@2530: 	    _min_cut_map->set(i, true);
deba@2530: 	  }
deba@2530: 	  for (std::list<int>::iterator it = _sets.back().begin();
deba@2530: 	       it != _sets.back().end(); ++it) {
deba@2530: 	    Node n = _first[*it];
deba@2530: 	    while (n != INVALID) {
deba@2530: 	      _min_cut_map->set(n, false);
deba@2530: 	      n = (*_next)[n];
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	}
deba@2530: 
deba@2530: 	{
deba@2530: 	  Node new_target;
deba@2530: 	  if ((*_prev)[target] != INVALID) {
deba@2530: 	    _last[(*_bucket)[target]] = (*_prev)[target];
deba@2530: 	    _next->set((*_prev)[target], INVALID);
deba@2530: 	    new_target = (*_prev)[target];
deba@2530: 	  } else {
deba@2530: 	    _sets.back().pop_back();
deba@2530: 	    if (_sets.back().empty()) {
deba@2530: 	      _sets.pop_back();
deba@2530: 	      if (_sets.empty())
deba@2530: 		break;
deba@2530: 	      for (std::list<int>::iterator it = _sets.back().begin();
deba@2530: 		   it != _sets.back().end(); ++it) {
deba@2530: 		_dormant[*it] = false;
deba@2530: 	      }
deba@2530: 	    }
deba@2530: 	    new_target = _last[_sets.back().back()];
deba@2530: 	  }
deba@2530: 
deba@2530: 	  _bucket->set(target, 0);
deba@2530: 
deba@2530: 	  _source_set->set(target, true);	  
deba@2530: 	  for (OutEdgeIt e(_graph, target); e != INVALID; ++e) {
deba@2530: 	    Value rem = (*_capacity)[e] - (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    Node v = _graph.target(e);
deba@2530: 	    if (!(*_active)[v] && !(*_source_set)[v]) {
deba@2530: 	      activate(v);
deba@2530: 	    }
deba@2530: 	    _excess->set(v, (*_excess)[v] + rem);
deba@2530: 	    _flow->set(e, (*_capacity)[e]);
deba@2530: 	  }
deba@2530: 	  
deba@2530: 	  for (InEdgeIt e(_graph, target); e != INVALID; ++e) {
deba@2530: 	    Value rem = (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    Node v = _graph.source(e);
deba@2530: 	    if (!(*_active)[v] && !(*_source_set)[v]) {
deba@2530: 	      activate(v);
deba@2530: 	    }
deba@2530: 	    _excess->set(v, (*_excess)[v] + rem);
deba@2530: 	    _flow->set(e, 0);
deba@2530: 	  }
deba@2530: 	  
deba@2530: 	  target = new_target;
deba@2530: 	  if ((*_active)[target]) {
deba@2530: 	    deactivate(target);
deba@2530: 	  }
deba@2530: 
deba@2530: 	  _highest = _sets.back().begin();
deba@2530: 	  while (_highest != _sets.back().end() && 
deba@2530: 		 !(*_active)[_first[*_highest]]) {
deba@2530: 	    ++_highest;
deba@2530: 	  }
deba@2530: 	}
deba@2530:       }
deba@2530:     }    
deba@2530: 
deba@2530:     void findMinCutIn() {
deba@2530: 
deba@2530:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@2530: 	_excess->set(n, 0);
deba@2530:       }
deba@2530: 
deba@2530:       for (EdgeIt e(_graph); e != INVALID; ++e) {
deba@2530: 	_flow->set(e, 0);
deba@2530:       }
deba@2530: 
deba@2530:       int bucket_num = 1;
deba@2530:       
deba@2530:       {
deba@2530: 	typename Graph::template NodeMap<bool> reached(_graph, false);
deba@2530: 	
deba@2530: 	reached.set(_source, true);
deba@2530: 
deba@2530: 	bool first_set = true;
deba@2530: 
deba@2530: 	for (NodeIt t(_graph); t != INVALID; ++t) {
deba@2530: 	  if (reached[t]) continue;
deba@2530: 	  _sets.push_front(std::list<int>());
deba@2530: 	  _sets.front().push_front(bucket_num);
deba@2530: 	  _dormant[bucket_num] = !first_set;
deba@2530: 
deba@2530: 	  _bucket->set(t, bucket_num);
deba@2530: 	  _first[bucket_num] = _last[bucket_num] = t;
deba@2530: 	  _next->set(t, INVALID);
deba@2530: 	  _prev->set(t, INVALID);
deba@2530: 
deba@2530: 	  ++bucket_num;
deba@2530: 	  
deba@2530: 	  std::vector<Node> queue;
deba@2530: 	  queue.push_back(t);
deba@2530: 	  reached.set(t, true);
deba@2530: 	  
deba@2530: 	  while (!queue.empty()) {
deba@2530: 	    _sets.front().push_front(bucket_num);
deba@2530: 	    _dormant[bucket_num] = !first_set;
deba@2530: 	    _first[bucket_num] = _last[bucket_num] = INVALID;
deba@2530: 	    
deba@2530: 	    std::vector<Node> nqueue;
deba@2530: 	    for (int i = 0; i < int(queue.size()); ++i) {
deba@2530: 	      Node n = queue[i];
deba@2530: 	      for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2530: 		Node u = _graph.target(e);
deba@2530: 		if (!reached[u] && _tolerance.positive((*_capacity)[e])) {
deba@2530: 		  reached.set(u, true);
deba@2530: 		  addItem(u, bucket_num);
deba@2530: 		  nqueue.push_back(u);
deba@2530: 		}
deba@2530: 	      }
deba@2530: 	    }
deba@2530: 	    queue.swap(nqueue);
deba@2530: 	    ++bucket_num;
deba@2530: 	  }
deba@2530: 	  _sets.front().pop_front();
deba@2530: 	  --bucket_num;
deba@2530: 	  first_set = false;
deba@2530: 	}
deba@2530: 
deba@2530: 	_bucket->set(_source, 0);
deba@2530: 	_dormant[0] = true;
deba@2530:       }
deba@2530:       _source_set->set(_source, true);	  
deba@2530: 	  
deba@2530:       Node target = _last[_sets.back().back()];
deba@2530:       {
deba@2530: 	for (InEdgeIt e(_graph, _source); e != INVALID; ++e) {
deba@2530: 	  if (_tolerance.positive((*_capacity)[e])) {
deba@2530: 	    Node u = _graph.source(e);
deba@2530: 	    _flow->set(e, (*_capacity)[e]);
deba@2530: 	    _excess->set(u, (*_excess)[u] + (*_capacity)[e]);
deba@2530: 	    if (!(*_active)[u] && u != _source) {
deba@2530: 	      activate(u);
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	}
deba@2530: 	if ((*_active)[target]) {
deba@2530: 	  deactivate(target);
deba@2530: 	}
deba@2530: 	
deba@2530: 	_highest = _sets.back().begin();
deba@2530: 	while (_highest != _sets.back().end() && 
deba@2530: 	       !(*_active)[_first[*_highest]]) {
deba@2530: 	  ++_highest;
deba@2530: 	}
deba@2530:       }
deba@2530: 
deba@2530: 
deba@2530:       while (true) {
deba@2530: 	while (_highest != _sets.back().end()) {
deba@2530: 	  Node n = _first[*_highest];
deba@2530: 	  Value excess = (*_excess)[n];
deba@2530: 	  int next_bucket = _node_num;
deba@2530: 
deba@2530: 	  int under_bucket;
deba@2530: 	  if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
deba@2530: 	    under_bucket = -1;
deba@2530: 	  } else {
deba@2530: 	    under_bucket = *(++std::list<int>::iterator(_highest));
deba@2530: 	  }
deba@2530: 
deba@2530: 	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2530: 	    Node v = _graph.source(e);
deba@2530: 	    if (_dormant[(*_bucket)[v]]) continue;
deba@2530: 	    Value rem = (*_capacity)[e] - (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    if ((*_bucket)[v] == under_bucket) {
deba@2530: 	      if (!(*_active)[v] && v != target) {
deba@2530: 		activate(v);
deba@2530: 	      }
deba@2530: 	      if (!_tolerance.less(rem, excess)) {
deba@2530: 		_flow->set(e, (*_flow)[e] + excess);
deba@2530: 		_excess->set(v, (*_excess)[v] + excess);
deba@2530: 		excess = 0;
deba@2530: 		goto no_more_push;
deba@2530: 	      } else {
deba@2530: 		excess -= rem;
deba@2530: 		_excess->set(v, (*_excess)[v] + rem);
deba@2530: 		_flow->set(e, (*_capacity)[e]);
deba@2530: 	      }
deba@2530: 	    } else if (next_bucket > (*_bucket)[v]) {
deba@2530: 	      next_bucket = (*_bucket)[v];
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 
deba@2530: 	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
deba@2530: 	    Node v = _graph.target(e);
deba@2530: 	    if (_dormant[(*_bucket)[v]]) continue;
deba@2530: 	    Value rem = (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    if ((*_bucket)[v] == under_bucket) {
deba@2530: 	      if (!(*_active)[v] && v != target) {
deba@2530: 		activate(v);
deba@2530: 	      }
deba@2530: 	      if (!_tolerance.less(rem, excess)) {
deba@2530: 		_flow->set(e, (*_flow)[e] - excess);
deba@2530: 		_excess->set(v, (*_excess)[v] + excess);
deba@2530: 		excess = 0;
deba@2530: 		goto no_more_push;
deba@2530: 	      } else {
deba@2530: 		excess -= rem;
deba@2530: 		_excess->set(v, (*_excess)[v] + rem);
deba@2530: 		_flow->set(e, 0);
deba@2530: 	      }
deba@2530: 	    } else if (next_bucket > (*_bucket)[v]) {
deba@2530: 	      next_bucket = (*_bucket)[v];
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	  
deba@2530: 	no_more_push:
deba@2530: 	  
deba@2530: 	  _excess->set(n, excess);
deba@2530: 	  
deba@2530: 	  if (excess != 0) {
deba@2530: 	    if ((*_next)[n] == INVALID) {
deba@2530: 	      typename std::list<std::list<int> >::iterator new_set = 
deba@2530: 		_sets.insert(--_sets.end(), std::list<int>());
deba@2530: 	      new_set->splice(new_set->end(), _sets.back(), 
deba@2530: 			      _sets.back().begin(), ++_highest);
deba@2530: 	      for (std::list<int>::iterator it = new_set->begin();
deba@2530: 		   it != new_set->end(); ++it) {
deba@2530: 		_dormant[*it] = true;
deba@2530: 	      }
deba@2530: 	      while (_highest != _sets.back().end() && 
deba@2530: 		     !(*_active)[_first[*_highest]]) {
deba@2530: 		++_highest;
deba@2530: 	      }
deba@2530: 	    } else if (next_bucket == _node_num) {
deba@2530: 	      _first[(*_bucket)[n]] = (*_next)[n];
deba@2530: 	      _prev->set((*_next)[n], INVALID);
deba@2530: 	      
deba@2530: 	      std::list<std::list<int> >::iterator new_set = 
deba@2530: 		_sets.insert(--_sets.end(), std::list<int>());
deba@2530: 	      
deba@2530: 	      new_set->push_front(bucket_num);
deba@2530: 	      _bucket->set(n, bucket_num);
deba@2530: 	      _first[bucket_num] = _last[bucket_num] = n;
deba@2530: 	      _next->set(n, INVALID);
deba@2530: 	      _prev->set(n, INVALID);
deba@2530: 	      _dormant[bucket_num] = true;
deba@2530: 	      ++bucket_num;
deba@2530: 
deba@2530: 	      while (_highest != _sets.back().end() && 
deba@2530: 		     !(*_active)[_first[*_highest]]) {
deba@2530: 		++_highest;
deba@2530: 	      }
deba@2530: 	    } else {
deba@2530: 	      _first[*_highest] = (*_next)[n];
deba@2530: 	      _prev->set((*_next)[n], INVALID);
deba@2530: 
deba@2530: 	      while (next_bucket != *_highest) {
deba@2530: 		--_highest;
deba@2530: 	      }
deba@2530: 	      if (_highest == _sets.back().begin()) {
deba@2530: 		_sets.back().push_front(bucket_num);
deba@2530: 		_dormant[bucket_num] = false;
deba@2530: 		_first[bucket_num] = _last[bucket_num] = INVALID;
deba@2530: 		++bucket_num;
deba@2530: 	      }
deba@2530: 	      --_highest;
deba@2530: 
deba@2530: 	      _bucket->set(n, *_highest);
deba@2530: 	      _next->set(n, _first[*_highest]);
deba@2530: 	      if (_first[*_highest] != INVALID) {
deba@2530: 		_prev->set(_first[*_highest], n);
deba@2530: 	      } else {
deba@2530: 		_last[*_highest] = n;
deba@2530: 	      }
deba@2530: 	      _first[*_highest] = n;	      
deba@2530: 	    }
deba@2530: 	  } else {
deba@2530: 
deba@2530: 	    deactivate(n);
deba@2530: 	    if (!(*_active)[_first[*_highest]]) {
deba@2530: 	      ++_highest;
deba@2530: 	      if (_highest != _sets.back().end() && 
deba@2530: 		  !(*_active)[_first[*_highest]]) {
deba@2530: 		_highest = _sets.back().end();
deba@2530: 	      }
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	}
deba@2530: 
deba@2530: 	if ((*_excess)[target] < _min_cut) {
deba@2530: 	  _min_cut = (*_excess)[target];
deba@2530: 	  for (NodeIt i(_graph); i != INVALID; ++i) {
deba@2530: 	    _min_cut_map->set(i, false);
deba@2530: 	  }
deba@2530: 	  for (std::list<int>::iterator it = _sets.back().begin();
deba@2530: 	       it != _sets.back().end(); ++it) {
deba@2530: 	    Node n = _first[*it];
deba@2530: 	    while (n != INVALID) {
deba@2530: 	      _min_cut_map->set(n, true);
deba@2530: 	      n = (*_next)[n];
deba@2530: 	    }
deba@2530: 	  }
deba@2530: 	}
deba@2530: 
deba@2530: 	{
deba@2530: 	  Node new_target;
deba@2530: 	  if ((*_prev)[target] != INVALID) {
deba@2530: 	    _last[(*_bucket)[target]] = (*_prev)[target];
deba@2530: 	    _next->set((*_prev)[target], INVALID);
deba@2530: 	    new_target = (*_prev)[target];
deba@2530: 	  } else {
deba@2530: 	    _sets.back().pop_back();
deba@2530: 	    if (_sets.back().empty()) {
deba@2530: 	      _sets.pop_back();
deba@2530: 	      if (_sets.empty())
deba@2530: 		break;
deba@2530: 	      for (std::list<int>::iterator it = _sets.back().begin();
deba@2530: 		   it != _sets.back().end(); ++it) {
deba@2530: 		_dormant[*it] = false;
deba@2530: 	      }
deba@2530: 	    }
deba@2530: 	    new_target = _last[_sets.back().back()];
deba@2530: 	  }
deba@2530: 
deba@2530: 	  _bucket->set(target, 0);
deba@2530: 
deba@2530: 	  _source_set->set(target, true);	  
deba@2530: 	  for (InEdgeIt e(_graph, target); e != INVALID; ++e) {
deba@2530: 	    Value rem = (*_capacity)[e] - (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    Node v = _graph.source(e);
deba@2530: 	    if (!(*_active)[v] && !(*_source_set)[v]) {
deba@2530: 	      activate(v);
deba@2530: 	    }
deba@2530: 	    _excess->set(v, (*_excess)[v] + rem);
deba@2530: 	    _flow->set(e, (*_capacity)[e]);
deba@2530: 	  }
deba@2530: 	  
deba@2530: 	  for (OutEdgeIt e(_graph, target); e != INVALID; ++e) {
deba@2530: 	    Value rem = (*_flow)[e];
deba@2530: 	    if (!_tolerance.positive(rem)) continue;
deba@2530: 	    Node v = _graph.target(e);
deba@2530: 	    if (!(*_active)[v] && !(*_source_set)[v]) {
deba@2530: 	      activate(v);
deba@2530: 	    }
deba@2530: 	    _excess->set(v, (*_excess)[v] + rem);
deba@2530: 	    _flow->set(e, 0);
deba@2530: 	  }
deba@2530: 	  
deba@2530: 	  target = new_target;
deba@2530: 	  if ((*_active)[target]) {
deba@2530: 	    deactivate(target);
deba@2530: 	  }
deba@2530: 
deba@2530: 	  _highest = _sets.back().begin();
deba@2530: 	  while (_highest != _sets.back().end() && 
deba@2530: 		 !(*_active)[_first[*_highest]]) {
deba@2530: 	    ++_highest;
deba@2530: 	  }
deba@2211: 	}
deba@2211:       }
deba@2211:     }
deba@2211: 
deba@2211:   public:
deba@2211: 
deba@2225:     /// \name Execution control
deba@2225:     /// The simplest way to execute the algorithm is to use
deba@2225:     /// one of the member functions called \c run(...).
deba@2225:     /// \n
deba@2225:     /// If you need more control on the execution,
deba@2225:     /// first you must call \ref init(), then the \ref calculateIn() or
deba@2225:     /// \ref calculateIn() functions.
deba@2225: 
deba@2225:     /// @{
deba@2225: 
deba@2211:     /// \brief Initializes the internal data structures.
deba@2211:     ///
deba@2211:     /// Initializes the internal data structures. It creates
deba@2225:     /// the maps, residual graph adaptors and some bucket structures
deba@2211:     /// for the algorithm. 
deba@2211:     void init() {
deba@2530:       init(NodeIt(_graph));
deba@2211:     }
deba@2211: 
deba@2211:     /// \brief Initializes the internal data structures.
deba@2211:     ///
deba@2211:     /// Initializes the internal data structures. It creates
deba@2211:     /// the maps, residual graph adaptor and some bucket structures
athos@2228:     /// for the algorithm. Node \c source  is used as the push-relabel
deba@2211:     /// algorithm's source.
deba@2211:     void init(const Node& source) {
deba@2211:       _source = source;
deba@2530:       
deba@2530:       _node_num = countNodes(_graph);
deba@2530:       
deba@2530:       _first.resize(_node_num);
deba@2530:       _last.resize(_node_num);
deba@2211: 
deba@2211:       _dormant.resize(_node_num);
deba@2211: 
deba@2530:       if (!_flow) {
deba@2530: 	_flow = new FlowMap(_graph);
deba@2211:       }
deba@2530:       if (!_next) {
deba@2530: 	_next = new typename Graph::template NodeMap<Node>(_graph);
deba@2211:       }
deba@2530:       if (!_prev) {
deba@2530: 	_prev = new typename Graph::template NodeMap<Node>(_graph);
deba@2530:       }
deba@2530:       if (!_active) {
deba@2530: 	_active = new typename Graph::template NodeMap<bool>(_graph);
deba@2530:       }
deba@2530:       if (!_bucket) {
deba@2530: 	_bucket = new typename Graph::template NodeMap<int>(_graph);
deba@2211:       }
deba@2211:       if (!_excess) {
deba@2530: 	_excess = new ExcessMap(_graph);
deba@2211:       }
deba@2211:       if (!_source_set) {
deba@2530: 	_source_set = new SourceSetMap(_graph);
deba@2225:       }
deba@2211:       if (!_min_cut_map) {
deba@2530: 	_min_cut_map = new MinCutMap(_graph);
deba@2211:       }
deba@2211: 
deba@2211:       _min_cut = std::numeric_limits<Value>::max();
deba@2211:     }
deba@2211: 
deba@2211: 
athos@2228:     /// \brief Calculates a minimum cut with \f$ source \f$ on the
athos@2228:     /// source-side.
deba@2211:     ///
deba@2530:     /// Calculates a minimum cut with \f$ source \f$ on the
deba@2530:     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source
deba@2530:     /// \in X \f$ and minimal out-degree).
deba@2211:     void calculateOut() {
deba@2530:       findMinCutOut();
deba@2211:     }
deba@2211: 
athos@2228:     /// \brief Calculates a minimum cut with \f$ source \f$ on the
deba@2530:     /// target-side.
deba@2211:     ///
deba@2530:     /// Calculates a minimum cut with \f$ source \f$ on the
deba@2530:     /// target-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source
deba@2530:     /// \in X \f$ and minimal out-degree).
deba@2530:     void calculateIn() {
deba@2530:       findMinCutIn();
deba@2211:     }
deba@2211: 
deba@2225: 
deba@2225:     /// \brief Runs the algorithm.
deba@2225:     ///
athos@2228:     /// Runs the algorithm. It finds nodes \c source and \c target
athos@2228:     /// arbitrarily and then calls \ref init(), \ref calculateOut()
athos@2228:     /// and \ref calculateIn().
deba@2211:     void run() {
deba@2211:       init();
deba@2530:       calculateOut();
deba@2530:       calculateIn();
deba@2211:     }
deba@2211: 
deba@2225:     /// \brief Runs the algorithm.
deba@2225:     ///
athos@2228:     /// Runs the algorithm. It uses the given \c source node, finds a
athos@2228:     /// proper \c target and then calls the \ref init(), \ref
athos@2228:     /// calculateOut() and \ref calculateIn().
deba@2211:     void run(const Node& s) {
deba@2211:       init(s);
deba@2530:       calculateOut();
deba@2530:       calculateIn();
deba@2211:     }
deba@2225: 
deba@2225:     /// @}
deba@2211:     
athos@2275:     /// \name Query Functions 
athos@2275:     /// The result of the %HaoOrlin algorithm
deba@2225:     /// can be obtained using these functions.
deba@2225:     /// \n
athos@2275:     /// Before using these functions, either \ref run(), \ref
deba@2225:     /// calculateOut() or \ref calculateIn() must be called.
deba@2225:     
deba@2225:     /// @{
deba@2225: 
deba@2225:     /// \brief Returns the value of the minimum value cut.
deba@2211:     /// 
deba@2225:     /// Returns the value of the minimum value cut.
deba@2211:     Value minCut() const {
deba@2211:       return _min_cut;
deba@2211:     }
deba@2211: 
deba@2211: 
athos@2228:     /// \brief Returns a minimum cut.
deba@2211:     ///
deba@2211:     /// Sets \c nodeMap to the characteristic vector of a minimum
athos@2228:     /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$
athos@2228:     /// with minimal out-degree (i.e. \c nodeMap will be true exactly
athos@2275:     /// for the nodes of \f$ X \f$).  \pre nodeMap should be a
athos@2228:     /// bool-valued node-map.
deba@2211:     template <typename NodeMap>
deba@2211:     Value minCut(NodeMap& nodeMap) const {
deba@2530:       for (NodeIt it(_graph); it != INVALID; ++it) {
deba@2211: 	nodeMap.set(it, (*_min_cut_map)[it]);
deba@2211:       }
deba@2211:       return minCut();
deba@2211:     }
deba@2225: 
deba@2225:     /// @}
deba@2211:     
deba@2211:   }; //class HaoOrlin 
deba@2211: 
deba@2211: 
deba@2211: } //namespace lemon
deba@2211: 
deba@2211: #endif //LEMON_HAO_ORLIN_H