deba@409: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@409:  *
deba@409:  * This file is a part of LEMON, a generic C++ optimization library.
deba@409:  *
deba@409:  * Copyright (C) 2003-2008
deba@409:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@409:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@409:  *
deba@409:  * Permission to use, modify and distribute this software is granted
deba@409:  * provided that this copyright notice appears in all copies. For
deba@409:  * precise terms see the accompanying LICENSE file.
deba@409:  *
deba@409:  * This software is provided "AS IS" with no warranty of any kind,
deba@409:  * express or implied, and with no claim as to its suitability for any
deba@409:  * purpose.
deba@409:  *
deba@409:  */
deba@409: 
deba@409: #ifndef LEMON_HAO_ORLIN_H
deba@409: #define LEMON_HAO_ORLIN_H
deba@409: 
deba@409: #include <vector>
deba@409: #include <list>
deba@409: #include <limits>
deba@409: 
deba@409: #include <lemon/maps.h>
deba@409: #include <lemon/core.h>
deba@409: #include <lemon/tolerance.h>
deba@409: 
deba@409: /// \file
deba@409: /// \ingroup min_cut
deba@409: /// \brief Implementation of the Hao-Orlin algorithm.
deba@409: ///
deba@409: /// Implementation of the Hao-Orlin algorithm class for testing network
deba@409: /// reliability.
deba@409: 
deba@409: namespace lemon {
deba@409: 
deba@409:   /// \ingroup min_cut
deba@409:   ///
deba@409:   /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs.
deba@409:   ///
deba@409:   /// Hao-Orlin calculates a minimum cut in a directed graph
deba@409:   /// \f$D=(V,A)\f$. It takes a fixed node \f$ source \in V \f$ and
deba@409:   /// consists of two phases: in the first phase it determines a
deba@409:   /// minimum cut with \f$ source \f$ on the source-side (i.e. a set
deba@409:   /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal
deba@409:   /// out-degree) and in the second phase it determines a minimum cut
deba@409:   /// with \f$ source \f$ on the sink-side (i.e. a set
deba@409:   /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal
deba@409:   /// out-degree). Obviously, the smaller of these two cuts will be a
deba@409:   /// minimum cut of \f$ D \f$. The algorithm is a modified
deba@409:   /// push-relabel preflow algorithm and our implementation calculates
deba@409:   /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
deba@409:   /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The
deba@409:   /// purpose of such algorithm is testing network reliability. For an
deba@409:   /// undirected graph you can run just the first phase of the
deba@409:   /// algorithm or you can use the algorithm of Nagamochi and Ibaraki
deba@409:   /// which solves the undirected problem in
deba@409:   /// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the
deba@409:   /// NagamochiIbaraki algorithm class.
deba@409:   ///
deba@409:   /// \param _Digraph is the graph type of the algorithm.
deba@409:   /// \param _CapacityMap is an edge map of capacities which should
deba@409:   /// be any numreric type. The default type is _Digraph::ArcMap<int>.
deba@409:   /// \param _Tolerance is the handler of the inexact computation. The
deba@409:   /// default type for this is Tolerance<CapacityMap::Value>.
deba@409: #ifdef DOXYGEN
deba@409:   template <typename _Digraph, typename _CapacityMap, typename _Tolerance>
deba@409: #else
deba@409:   template <typename _Digraph,
deba@409:             typename _CapacityMap = typename _Digraph::template ArcMap<int>,
deba@409:             typename _Tolerance = Tolerance<typename _CapacityMap::Value> >
deba@409: #endif
deba@409:   class HaoOrlin {
deba@409:   private:
deba@409: 
deba@409:     typedef _Digraph Digraph;
deba@409:     typedef _CapacityMap CapacityMap;
deba@409:     typedef _Tolerance Tolerance;
deba@409: 
deba@409:     typedef typename CapacityMap::Value Value;
deba@409: 
deba@409:     TEMPLATE_GRAPH_TYPEDEFS(Digraph);
deba@409: 
deba@409:     const Digraph& _graph;
deba@409:     const CapacityMap* _capacity;
deba@409: 
deba@409:     typedef typename Digraph::template ArcMap<Value> FlowMap;
deba@409:     FlowMap* _flow;
deba@409: 
deba@409:     Node _source;
deba@409: 
deba@409:     int _node_num;
deba@409: 
deba@409:     // Bucketing structure
deba@409:     std::vector<Node> _first, _last;
deba@409:     typename Digraph::template NodeMap<Node>* _next;
deba@409:     typename Digraph::template NodeMap<Node>* _prev;
deba@409:     typename Digraph::template NodeMap<bool>* _active;
deba@409:     typename Digraph::template NodeMap<int>* _bucket;
deba@409: 
deba@409:     std::vector<bool> _dormant;
deba@409: 
deba@409:     std::list<std::list<int> > _sets;
deba@409:     std::list<int>::iterator _highest;
deba@409: 
deba@409:     typedef typename Digraph::template NodeMap<Value> ExcessMap;
deba@409:     ExcessMap* _excess;
deba@409: 
deba@409:     typedef typename Digraph::template NodeMap<bool> SourceSetMap;
deba@409:     SourceSetMap* _source_set;
deba@409: 
deba@409:     Value _min_cut;
deba@409: 
deba@409:     typedef typename Digraph::template NodeMap<bool> MinCutMap;
deba@409:     MinCutMap* _min_cut_map;
deba@409: 
deba@409:     Tolerance _tolerance;
deba@409: 
deba@409:   public:
deba@409: 
deba@409:     /// \brief Constructor
deba@409:     ///
deba@409:     /// Constructor of the algorithm class.
deba@409:     HaoOrlin(const Digraph& graph, const CapacityMap& capacity,
deba@409:              const Tolerance& tolerance = Tolerance()) :
deba@409:       _graph(graph), _capacity(&capacity), _flow(0), _source(),
deba@409:       _node_num(), _first(), _last(), _next(0), _prev(0),
deba@409:       _active(0), _bucket(0), _dormant(), _sets(), _highest(),
deba@409:       _excess(0), _source_set(0), _min_cut(), _min_cut_map(0),
deba@409:       _tolerance(tolerance) {}
deba@409: 
deba@409:     ~HaoOrlin() {
deba@409:       if (_min_cut_map) {
deba@409:         delete _min_cut_map;
deba@409:       }
deba@409:       if (_source_set) {
deba@409:         delete _source_set;
deba@409:       }
deba@409:       if (_excess) {
deba@409:         delete _excess;
deba@409:       }
deba@409:       if (_next) {
deba@409:         delete _next;
deba@409:       }
deba@409:       if (_prev) {
deba@409:         delete _prev;
deba@409:       }
deba@409:       if (_active) {
deba@409:         delete _active;
deba@409:       }
deba@409:       if (_bucket) {
deba@409:         delete _bucket;
deba@409:       }
deba@409:       if (_flow) {
deba@409:         delete _flow;
deba@409:       }
deba@409:     }
deba@409: 
deba@409:   private:
deba@409: 
deba@409:     void activate(const Node& i) {
deba@409:       _active->set(i, true);
deba@409: 
deba@409:       int bucket = (*_bucket)[i];
deba@409: 
deba@409:       if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;
deba@409:       //unlace
deba@409:       _next->set((*_prev)[i], (*_next)[i]);
deba@409:       if ((*_next)[i] != INVALID) {
deba@409:         _prev->set((*_next)[i], (*_prev)[i]);
deba@409:       } else {
deba@409:         _last[bucket] = (*_prev)[i];
deba@409:       }
deba@409:       //lace
deba@409:       _next->set(i, _first[bucket]);
deba@409:       _prev->set(_first[bucket], i);
deba@409:       _prev->set(i, INVALID);
deba@409:       _first[bucket] = i;
deba@409:     }
deba@409: 
deba@409:     void deactivate(const Node& i) {
deba@409:       _active->set(i, false);
deba@409:       int bucket = (*_bucket)[i];
deba@409: 
deba@409:       if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;
deba@409: 
deba@409:       //unlace
deba@409:       _prev->set((*_next)[i], (*_prev)[i]);
deba@409:       if ((*_prev)[i] != INVALID) {
deba@409:         _next->set((*_prev)[i], (*_next)[i]);
deba@409:       } else {
deba@409:         _first[bucket] = (*_next)[i];
deba@409:       }
deba@409:       //lace
deba@409:       _prev->set(i, _last[bucket]);
deba@409:       _next->set(_last[bucket], i);
deba@409:       _next->set(i, INVALID);
deba@409:       _last[bucket] = i;
deba@409:     }
deba@409: 
deba@409:     void addItem(const Node& i, int bucket) {
deba@409:       (*_bucket)[i] = bucket;
deba@409:       if (_last[bucket] != INVALID) {
deba@409:         _prev->set(i, _last[bucket]);
deba@409:         _next->set(_last[bucket], i);
deba@409:         _next->set(i, INVALID);
deba@409:         _last[bucket] = i;
deba@409:       } else {
deba@409:         _prev->set(i, INVALID);
deba@409:         _first[bucket] = i;
deba@409:         _next->set(i, INVALID);
deba@409:         _last[bucket] = i;
deba@409:       }
deba@409:     }
deba@409: 
deba@409:     void findMinCutOut() {
deba@409: 
deba@409:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@409:         _excess->set(n, 0);
deba@409:       }
deba@409: 
deba@409:       for (ArcIt a(_graph); a != INVALID; ++a) {
deba@409:         _flow->set(a, 0);
deba@409:       }
deba@409: 
deba@411:       int bucket_num = 0;
deba@411:       std::vector<Node> queue(_node_num);
deba@411:       int qfirst = 0, qlast = 0, qsep = 0;
deba@409: 
deba@409:       {
deba@409:         typename Digraph::template NodeMap<bool> reached(_graph, false);
deba@409: 
deba@409:         reached.set(_source, true);
deba@409:         bool first_set = true;
deba@409: 
deba@409:         for (NodeIt t(_graph); t != INVALID; ++t) {
deba@409:           if (reached[t]) continue;
deba@409:           _sets.push_front(std::list<int>());
deba@411:           
deba@411:           queue[qlast++] = t;
deba@409:           reached.set(t, true);
deba@409: 
deba@411:           while (qfirst != qlast) {
deba@411:             if (qsep == qfirst) {
deba@411:               ++bucket_num;
deba@411:               _sets.front().push_front(bucket_num);
deba@411:               _dormant[bucket_num] = !first_set;
deba@411:               _first[bucket_num] = _last[bucket_num] = INVALID;
deba@411:               qsep = qlast;
deba@411:             }
deba@409: 
deba@411:             Node n = queue[qfirst++];
deba@411:             addItem(n, bucket_num);
deba@411: 
deba@411:             for (InArcIt a(_graph, n); a != INVALID; ++a) {
deba@411:               Node u = _graph.source(a);
deba@411:               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
deba@411:                 reached.set(u, true);
deba@411:                 queue[qlast++] = u;
deba@409:               }
deba@409:             }
deba@409:           }
deba@409:           first_set = false;
deba@409:         }
deba@409: 
deba@411:         ++bucket_num;
deba@409:         _bucket->set(_source, 0);
deba@409:         _dormant[0] = true;
deba@409:       }
deba@409:       _source_set->set(_source, true);
deba@409: 
deba@409:       Node target = _last[_sets.back().back()];
deba@409:       {
deba@409:         for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
deba@409:           if (_tolerance.positive((*_capacity)[a])) {
deba@409:             Node u = _graph.target(a);
deba@409:             _flow->set(a, (*_capacity)[a]);
deba@409:             _excess->set(u, (*_excess)[u] + (*_capacity)[a]);
deba@409:             if (!(*_active)[u] && u != _source) {
deba@409:               activate(u);
deba@409:             }
deba@409:           }
deba@409:         }
deba@409: 
deba@409:         if ((*_active)[target]) {
deba@409:           deactivate(target);
deba@409:         }
deba@409: 
deba@409:         _highest = _sets.back().begin();
deba@409:         while (_highest != _sets.back().end() &&
deba@409:                !(*_active)[_first[*_highest]]) {
deba@409:           ++_highest;
deba@409:         }
deba@409:       }
deba@409: 
deba@409:       while (true) {
deba@409:         while (_highest != _sets.back().end()) {
deba@409:           Node n = _first[*_highest];
deba@409:           Value excess = (*_excess)[n];
deba@409:           int next_bucket = _node_num;
deba@409: 
deba@409:           int under_bucket;
deba@409:           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
deba@409:             under_bucket = -1;
deba@409:           } else {
deba@409:             under_bucket = *(++std::list<int>::iterator(_highest));
deba@409:           }
deba@409: 
deba@409:           for (OutArcIt a(_graph, n); a != INVALID; ++a) {
deba@409:             Node v = _graph.target(a);
deba@409:             if (_dormant[(*_bucket)[v]]) continue;
deba@409:             Value rem = (*_capacity)[a] - (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             if ((*_bucket)[v] == under_bucket) {
deba@409:               if (!(*_active)[v] && v != target) {
deba@409:                 activate(v);
deba@409:               }
deba@409:               if (!_tolerance.less(rem, excess)) {
deba@409:                 _flow->set(a, (*_flow)[a] + excess);
deba@409:                 _excess->set(v, (*_excess)[v] + excess);
deba@409:                 excess = 0;
deba@409:                 goto no_more_push;
deba@409:               } else {
deba@409:                 excess -= rem;
deba@409:                 _excess->set(v, (*_excess)[v] + rem);
deba@409:                 _flow->set(a, (*_capacity)[a]);
deba@409:               }
deba@409:             } else if (next_bucket > (*_bucket)[v]) {
deba@409:               next_bucket = (*_bucket)[v];
deba@409:             }
deba@409:           }
deba@409: 
deba@409:           for (InArcIt a(_graph, n); a != INVALID; ++a) {
deba@409:             Node v = _graph.source(a);
deba@409:             if (_dormant[(*_bucket)[v]]) continue;
deba@409:             Value rem = (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             if ((*_bucket)[v] == under_bucket) {
deba@409:               if (!(*_active)[v] && v != target) {
deba@409:                 activate(v);
deba@409:               }
deba@409:               if (!_tolerance.less(rem, excess)) {
deba@409:                 _flow->set(a, (*_flow)[a] - excess);
deba@409:                 _excess->set(v, (*_excess)[v] + excess);
deba@409:                 excess = 0;
deba@409:                 goto no_more_push;
deba@409:               } else {
deba@409:                 excess -= rem;
deba@409:                 _excess->set(v, (*_excess)[v] + rem);
deba@409:                 _flow->set(a, 0);
deba@409:               }
deba@409:             } else if (next_bucket > (*_bucket)[v]) {
deba@409:               next_bucket = (*_bucket)[v];
deba@409:             }
deba@409:           }
deba@409: 
deba@409:         no_more_push:
deba@409: 
deba@409:           _excess->set(n, excess);
deba@409: 
deba@409:           if (excess != 0) {
deba@409:             if ((*_next)[n] == INVALID) {
deba@409:               typename std::list<std::list<int> >::iterator new_set =
deba@409:                 _sets.insert(--_sets.end(), std::list<int>());
deba@409:               new_set->splice(new_set->end(), _sets.back(),
deba@409:                               _sets.back().begin(), ++_highest);
deba@409:               for (std::list<int>::iterator it = new_set->begin();
deba@409:                    it != new_set->end(); ++it) {
deba@409:                 _dormant[*it] = true;
deba@409:               }
deba@409:               while (_highest != _sets.back().end() &&
deba@409:                      !(*_active)[_first[*_highest]]) {
deba@409:                 ++_highest;
deba@409:               }
deba@409:             } else if (next_bucket == _node_num) {
deba@409:               _first[(*_bucket)[n]] = (*_next)[n];
deba@409:               _prev->set((*_next)[n], INVALID);
deba@409: 
deba@409:               std::list<std::list<int> >::iterator new_set =
deba@409:                 _sets.insert(--_sets.end(), std::list<int>());
deba@409: 
deba@409:               new_set->push_front(bucket_num);
deba@409:               _bucket->set(n, bucket_num);
deba@409:               _first[bucket_num] = _last[bucket_num] = n;
deba@409:               _next->set(n, INVALID);
deba@409:               _prev->set(n, INVALID);
deba@409:               _dormant[bucket_num] = true;
deba@409:               ++bucket_num;
deba@409: 
deba@409:               while (_highest != _sets.back().end() &&
deba@409:                      !(*_active)[_first[*_highest]]) {
deba@409:                 ++_highest;
deba@409:               }
deba@409:             } else {
deba@409:               _first[*_highest] = (*_next)[n];
deba@409:               _prev->set((*_next)[n], INVALID);
deba@409: 
deba@409:               while (next_bucket != *_highest) {
deba@409:                 --_highest;
deba@409:               }
deba@409: 
deba@409:               if (_highest == _sets.back().begin()) {
deba@409:                 _sets.back().push_front(bucket_num);
deba@409:                 _dormant[bucket_num] = false;
deba@409:                 _first[bucket_num] = _last[bucket_num] = INVALID;
deba@409:                 ++bucket_num;
deba@409:               }
deba@409:               --_highest;
deba@409: 
deba@409:               _bucket->set(n, *_highest);
deba@409:               _next->set(n, _first[*_highest]);
deba@409:               if (_first[*_highest] != INVALID) {
deba@409:                 _prev->set(_first[*_highest], n);
deba@409:               } else {
deba@409:                 _last[*_highest] = n;
deba@409:               }
deba@409:               _first[*_highest] = n;
deba@409:             }
deba@409:           } else {
deba@409: 
deba@409:             deactivate(n);
deba@409:             if (!(*_active)[_first[*_highest]]) {
deba@409:               ++_highest;
deba@409:               if (_highest != _sets.back().end() &&
deba@409:                   !(*_active)[_first[*_highest]]) {
deba@409:                 _highest = _sets.back().end();
deba@409:               }
deba@409:             }
deba@409:           }
deba@409:         }
deba@409: 
deba@409:         if ((*_excess)[target] < _min_cut) {
deba@409:           _min_cut = (*_excess)[target];
deba@409:           for (NodeIt i(_graph); i != INVALID; ++i) {
deba@409:             _min_cut_map->set(i, true);
deba@409:           }
deba@409:           for (std::list<int>::iterator it = _sets.back().begin();
deba@409:                it != _sets.back().end(); ++it) {
deba@409:             Node n = _first[*it];
deba@409:             while (n != INVALID) {
deba@409:               _min_cut_map->set(n, false);
deba@409:               n = (*_next)[n];
deba@409:             }
deba@409:           }
deba@409:         }
deba@409: 
deba@409:         {
deba@409:           Node new_target;
deba@409:           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
deba@409:             if ((*_next)[target] == INVALID) {
deba@409:               _last[(*_bucket)[target]] = (*_prev)[target];
deba@409:               new_target = (*_prev)[target];
deba@409:             } else {
deba@409:               _prev->set((*_next)[target], (*_prev)[target]);
deba@409:               new_target = (*_next)[target];
deba@409:             }
deba@409:             if ((*_prev)[target] == INVALID) {
deba@409:               _first[(*_bucket)[target]] = (*_next)[target];
deba@409:             } else {
deba@409:               _next->set((*_prev)[target], (*_next)[target]);
deba@409:             }
deba@409:           } else {
deba@409:             _sets.back().pop_back();
deba@409:             if (_sets.back().empty()) {
deba@409:               _sets.pop_back();
deba@409:               if (_sets.empty())
deba@409:                 break;
deba@409:               for (std::list<int>::iterator it = _sets.back().begin();
deba@409:                    it != _sets.back().end(); ++it) {
deba@409:                 _dormant[*it] = false;
deba@409:               }
deba@409:             }
deba@409:             new_target = _last[_sets.back().back()];
deba@409:           }
deba@409: 
deba@409:           _bucket->set(target, 0);
deba@409: 
deba@409:           _source_set->set(target, true);
deba@409:           for (OutArcIt a(_graph, target); a != INVALID; ++a) {
deba@409:             Value rem = (*_capacity)[a] - (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             Node v = _graph.target(a);
deba@409:             if (!(*_active)[v] && !(*_source_set)[v]) {
deba@409:               activate(v);
deba@409:             }
deba@409:             _excess->set(v, (*_excess)[v] + rem);
deba@409:             _flow->set(a, (*_capacity)[a]);
deba@409:           }
deba@409: 
deba@409:           for (InArcIt a(_graph, target); a != INVALID; ++a) {
deba@409:             Value rem = (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             Node v = _graph.source(a);
deba@409:             if (!(*_active)[v] && !(*_source_set)[v]) {
deba@409:               activate(v);
deba@409:             }
deba@409:             _excess->set(v, (*_excess)[v] + rem);
deba@409:             _flow->set(a, 0);
deba@409:           }
deba@409: 
deba@409:           target = new_target;
deba@409:           if ((*_active)[target]) {
deba@409:             deactivate(target);
deba@409:           }
deba@409: 
deba@409:           _highest = _sets.back().begin();
deba@409:           while (_highest != _sets.back().end() &&
deba@409:                  !(*_active)[_first[*_highest]]) {
deba@409:             ++_highest;
deba@409:           }
deba@409:         }
deba@409:       }
deba@409:     }
deba@409: 
deba@409:     void findMinCutIn() {
deba@409: 
deba@409:       for (NodeIt n(_graph); n != INVALID; ++n) {
deba@409:         _excess->set(n, 0);
deba@409:       }
deba@409: 
deba@409:       for (ArcIt a(_graph); a != INVALID; ++a) {
deba@409:         _flow->set(a, 0);
deba@409:       }
deba@409: 
deba@411:       int bucket_num = 0;
deba@411:       std::vector<Node> queue(_node_num);
deba@411:       int qfirst = 0, qlast = 0, qsep = 0;
deba@409: 
deba@409:       {
deba@409:         typename Digraph::template NodeMap<bool> reached(_graph, false);
deba@409: 
deba@409:         reached.set(_source, true);
deba@409: 
deba@409:         bool first_set = true;
deba@409: 
deba@409:         for (NodeIt t(_graph); t != INVALID; ++t) {
deba@409:           if (reached[t]) continue;
deba@409:           _sets.push_front(std::list<int>());
deba@411:           
deba@411:           queue[qlast++] = t;
deba@409:           reached.set(t, true);
deba@409: 
deba@411:           while (qfirst != qlast) {
deba@411:             if (qsep == qfirst) {
deba@411:               ++bucket_num;
deba@411:               _sets.front().push_front(bucket_num);
deba@411:               _dormant[bucket_num] = !first_set;
deba@411:               _first[bucket_num] = _last[bucket_num] = INVALID;
deba@411:               qsep = qlast;
deba@411:             }
deba@409: 
deba@411:             Node n = queue[qfirst++];
deba@411:             addItem(n, bucket_num);
deba@411: 
deba@411:             for (OutArcIt a(_graph, n); a != INVALID; ++a) {
deba@411:               Node u = _graph.target(a);
deba@411:               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
deba@411:                 reached.set(u, true);
deba@411:                 queue[qlast++] = u;
deba@409:               }
deba@409:             }
deba@409:           }
deba@409:           first_set = false;
deba@409:         }
deba@409: 
deba@411:         ++bucket_num;
deba@409:         _bucket->set(_source, 0);
deba@409:         _dormant[0] = true;
deba@409:       }
deba@409:       _source_set->set(_source, true);
deba@409: 
deba@409:       Node target = _last[_sets.back().back()];
deba@409:       {
deba@409:         for (InArcIt a(_graph, _source); a != INVALID; ++a) {
deba@409:           if (_tolerance.positive((*_capacity)[a])) {
deba@409:             Node u = _graph.source(a);
deba@409:             _flow->set(a, (*_capacity)[a]);
deba@409:             _excess->set(u, (*_excess)[u] + (*_capacity)[a]);
deba@409:             if (!(*_active)[u] && u != _source) {
deba@409:               activate(u);
deba@409:             }
deba@409:           }
deba@409:         }
deba@409:         if ((*_active)[target]) {
deba@409:           deactivate(target);
deba@409:         }
deba@409: 
deba@409:         _highest = _sets.back().begin();
deba@409:         while (_highest != _sets.back().end() &&
deba@409:                !(*_active)[_first[*_highest]]) {
deba@409:           ++_highest;
deba@409:         }
deba@409:       }
deba@409: 
deba@409: 
deba@409:       while (true) {
deba@409:         while (_highest != _sets.back().end()) {
deba@409:           Node n = _first[*_highest];
deba@409:           Value excess = (*_excess)[n];
deba@409:           int next_bucket = _node_num;
deba@409: 
deba@409:           int under_bucket;
deba@409:           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
deba@409:             under_bucket = -1;
deba@409:           } else {
deba@409:             under_bucket = *(++std::list<int>::iterator(_highest));
deba@409:           }
deba@409: 
deba@409:           for (InArcIt a(_graph, n); a != INVALID; ++a) {
deba@409:             Node v = _graph.source(a);
deba@409:             if (_dormant[(*_bucket)[v]]) continue;
deba@409:             Value rem = (*_capacity)[a] - (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             if ((*_bucket)[v] == under_bucket) {
deba@409:               if (!(*_active)[v] && v != target) {
deba@409:                 activate(v);
deba@409:               }
deba@409:               if (!_tolerance.less(rem, excess)) {
deba@409:                 _flow->set(a, (*_flow)[a] + excess);
deba@409:                 _excess->set(v, (*_excess)[v] + excess);
deba@409:                 excess = 0;
deba@409:                 goto no_more_push;
deba@409:               } else {
deba@409:                 excess -= rem;
deba@409:                 _excess->set(v, (*_excess)[v] + rem);
deba@409:                 _flow->set(a, (*_capacity)[a]);
deba@409:               }
deba@409:             } else if (next_bucket > (*_bucket)[v]) {
deba@409:               next_bucket = (*_bucket)[v];
deba@409:             }
deba@409:           }
deba@409: 
deba@409:           for (OutArcIt a(_graph, n); a != INVALID; ++a) {
deba@409:             Node v = _graph.target(a);
deba@409:             if (_dormant[(*_bucket)[v]]) continue;
deba@409:             Value rem = (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             if ((*_bucket)[v] == under_bucket) {
deba@409:               if (!(*_active)[v] && v != target) {
deba@409:                 activate(v);
deba@409:               }
deba@409:               if (!_tolerance.less(rem, excess)) {
deba@409:                 _flow->set(a, (*_flow)[a] - excess);
deba@409:                 _excess->set(v, (*_excess)[v] + excess);
deba@409:                 excess = 0;
deba@409:                 goto no_more_push;
deba@409:               } else {
deba@409:                 excess -= rem;
deba@409:                 _excess->set(v, (*_excess)[v] + rem);
deba@409:                 _flow->set(a, 0);
deba@409:               }
deba@409:             } else if (next_bucket > (*_bucket)[v]) {
deba@409:               next_bucket = (*_bucket)[v];
deba@409:             }
deba@409:           }
deba@409: 
deba@409:         no_more_push:
deba@409: 
deba@409:           _excess->set(n, excess);
deba@409: 
deba@409:           if (excess != 0) {
deba@409:             if ((*_next)[n] == INVALID) {
deba@409:               typename std::list<std::list<int> >::iterator new_set =
deba@409:                 _sets.insert(--_sets.end(), std::list<int>());
deba@409:               new_set->splice(new_set->end(), _sets.back(),
deba@409:                               _sets.back().begin(), ++_highest);
deba@409:               for (std::list<int>::iterator it = new_set->begin();
deba@409:                    it != new_set->end(); ++it) {
deba@409:                 _dormant[*it] = true;
deba@409:               }
deba@409:               while (_highest != _sets.back().end() &&
deba@409:                      !(*_active)[_first[*_highest]]) {
deba@409:                 ++_highest;
deba@409:               }
deba@409:             } else if (next_bucket == _node_num) {
deba@409:               _first[(*_bucket)[n]] = (*_next)[n];
deba@409:               _prev->set((*_next)[n], INVALID);
deba@409: 
deba@409:               std::list<std::list<int> >::iterator new_set =
deba@409:                 _sets.insert(--_sets.end(), std::list<int>());
deba@409: 
deba@409:               new_set->push_front(bucket_num);
deba@409:               _bucket->set(n, bucket_num);
deba@409:               _first[bucket_num] = _last[bucket_num] = n;
deba@409:               _next->set(n, INVALID);
deba@409:               _prev->set(n, INVALID);
deba@409:               _dormant[bucket_num] = true;
deba@409:               ++bucket_num;
deba@409: 
deba@409:               while (_highest != _sets.back().end() &&
deba@409:                      !(*_active)[_first[*_highest]]) {
deba@409:                 ++_highest;
deba@409:               }
deba@409:             } else {
deba@409:               _first[*_highest] = (*_next)[n];
deba@409:               _prev->set((*_next)[n], INVALID);
deba@409: 
deba@409:               while (next_bucket != *_highest) {
deba@409:                 --_highest;
deba@409:               }
deba@409:               if (_highest == _sets.back().begin()) {
deba@409:                 _sets.back().push_front(bucket_num);
deba@409:                 _dormant[bucket_num] = false;
deba@409:                 _first[bucket_num] = _last[bucket_num] = INVALID;
deba@409:                 ++bucket_num;
deba@409:               }
deba@409:               --_highest;
deba@409: 
deba@409:               _bucket->set(n, *_highest);
deba@409:               _next->set(n, _first[*_highest]);
deba@409:               if (_first[*_highest] != INVALID) {
deba@409:                 _prev->set(_first[*_highest], n);
deba@409:               } else {
deba@409:                 _last[*_highest] = n;
deba@409:               }
deba@409:               _first[*_highest] = n;
deba@409:             }
deba@409:           } else {
deba@409: 
deba@409:             deactivate(n);
deba@409:             if (!(*_active)[_first[*_highest]]) {
deba@409:               ++_highest;
deba@409:               if (_highest != _sets.back().end() &&
deba@409:                   !(*_active)[_first[*_highest]]) {
deba@409:                 _highest = _sets.back().end();
deba@409:               }
deba@409:             }
deba@409:           }
deba@409:         }
deba@409: 
deba@409:         if ((*_excess)[target] < _min_cut) {
deba@409:           _min_cut = (*_excess)[target];
deba@409:           for (NodeIt i(_graph); i != INVALID; ++i) {
deba@409:             _min_cut_map->set(i, false);
deba@409:           }
deba@409:           for (std::list<int>::iterator it = _sets.back().begin();
deba@409:                it != _sets.back().end(); ++it) {
deba@409:             Node n = _first[*it];
deba@409:             while (n != INVALID) {
deba@409:               _min_cut_map->set(n, true);
deba@409:               n = (*_next)[n];
deba@409:             }
deba@409:           }
deba@409:         }
deba@409: 
deba@409:         {
deba@409:           Node new_target;
deba@409:           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
deba@409:             if ((*_next)[target] == INVALID) {
deba@409:               _last[(*_bucket)[target]] = (*_prev)[target];
deba@409:               new_target = (*_prev)[target];
deba@409:             } else {
deba@409:               _prev->set((*_next)[target], (*_prev)[target]);
deba@409:               new_target = (*_next)[target];
deba@409:             }
deba@409:             if ((*_prev)[target] == INVALID) {
deba@409:               _first[(*_bucket)[target]] = (*_next)[target];
deba@409:             } else {
deba@409:               _next->set((*_prev)[target], (*_next)[target]);
deba@409:             }
deba@409:           } else {
deba@409:             _sets.back().pop_back();
deba@409:             if (_sets.back().empty()) {
deba@409:               _sets.pop_back();
deba@409:               if (_sets.empty())
deba@409:                 break;
deba@409:               for (std::list<int>::iterator it = _sets.back().begin();
deba@409:                    it != _sets.back().end(); ++it) {
deba@409:                 _dormant[*it] = false;
deba@409:               }
deba@409:             }
deba@409:             new_target = _last[_sets.back().back()];
deba@409:           }
deba@409: 
deba@409:           _bucket->set(target, 0);
deba@409: 
deba@409:           _source_set->set(target, true);
deba@409:           for (InArcIt a(_graph, target); a != INVALID; ++a) {
deba@409:             Value rem = (*_capacity)[a] - (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             Node v = _graph.source(a);
deba@409:             if (!(*_active)[v] && !(*_source_set)[v]) {
deba@409:               activate(v);
deba@409:             }
deba@409:             _excess->set(v, (*_excess)[v] + rem);
deba@409:             _flow->set(a, (*_capacity)[a]);
deba@409:           }
deba@409: 
deba@409:           for (OutArcIt a(_graph, target); a != INVALID; ++a) {
deba@409:             Value rem = (*_flow)[a];
deba@409:             if (!_tolerance.positive(rem)) continue;
deba@409:             Node v = _graph.target(a);
deba@409:             if (!(*_active)[v] && !(*_source_set)[v]) {
deba@409:               activate(v);
deba@409:             }
deba@409:             _excess->set(v, (*_excess)[v] + rem);
deba@409:             _flow->set(a, 0);
deba@409:           }
deba@409: 
deba@409:           target = new_target;
deba@409:           if ((*_active)[target]) {
deba@409:             deactivate(target);
deba@409:           }
deba@409: 
deba@409:           _highest = _sets.back().begin();
deba@409:           while (_highest != _sets.back().end() &&
deba@409:                  !(*_active)[_first[*_highest]]) {
deba@409:             ++_highest;
deba@409:           }
deba@409:         }
deba@409:       }
deba@409:     }
deba@409: 
deba@409:   public:
deba@409: 
deba@409:     /// \name Execution control
deba@409:     /// The simplest way to execute the algorithm is to use
deba@409:     /// one of the member functions called \c run(...).
deba@409:     /// \n
deba@409:     /// If you need more control on the execution,
deba@409:     /// first you must call \ref init(), then the \ref calculateIn() or
alpar@412:     /// \ref calculateOut() functions.
deba@409: 
deba@409:     /// @{
deba@409: 
deba@409:     /// \brief Initializes the internal data structures.
deba@409:     ///
deba@409:     /// Initializes the internal data structures. It creates
deba@409:     /// the maps, residual graph adaptors and some bucket structures
deba@409:     /// for the algorithm.
deba@409:     void init() {
deba@409:       init(NodeIt(_graph));
deba@409:     }
deba@409: 
deba@409:     /// \brief Initializes the internal data structures.
deba@409:     ///
deba@409:     /// Initializes the internal data structures. It creates
deba@409:     /// the maps, residual graph adaptor and some bucket structures
deba@409:     /// for the algorithm. Node \c source  is used as the push-relabel
deba@409:     /// algorithm's source.
deba@409:     void init(const Node& source) {
deba@409:       _source = source;
deba@409: 
deba@409:       _node_num = countNodes(_graph);
deba@409: 
deba@411:       _first.resize(_node_num);
deba@411:       _last.resize(_node_num);
deba@409: 
deba@411:       _dormant.resize(_node_num);
deba@409: 
deba@409:       if (!_flow) {
deba@409:         _flow = new FlowMap(_graph);
deba@409:       }
deba@409:       if (!_next) {
deba@409:         _next = new typename Digraph::template NodeMap<Node>(_graph);
deba@409:       }
deba@409:       if (!_prev) {
deba@409:         _prev = new typename Digraph::template NodeMap<Node>(_graph);
deba@409:       }
deba@409:       if (!_active) {
deba@409:         _active = new typename Digraph::template NodeMap<bool>(_graph);
deba@409:       }
deba@409:       if (!_bucket) {
deba@409:         _bucket = new typename Digraph::template NodeMap<int>(_graph);
deba@409:       }
deba@409:       if (!_excess) {
deba@409:         _excess = new ExcessMap(_graph);
deba@409:       }
deba@409:       if (!_source_set) {
deba@409:         _source_set = new SourceSetMap(_graph);
deba@409:       }
deba@409:       if (!_min_cut_map) {
deba@409:         _min_cut_map = new MinCutMap(_graph);
deba@409:       }
deba@409: 
deba@409:       _min_cut = std::numeric_limits<Value>::max();
deba@409:     }
deba@409: 
deba@409: 
deba@409:     /// \brief Calculates a minimum cut with \f$ source \f$ on the
deba@409:     /// source-side.
deba@409:     ///
deba@409:     /// Calculates a minimum cut with \f$ source \f$ on the
alpar@412:     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with
alpar@412:     /// \f$ source \in X \f$ and minimal out-degree).
deba@409:     void calculateOut() {
deba@409:       findMinCutOut();
deba@409:     }
deba@409: 
deba@409:     /// \brief Calculates a minimum cut with \f$ source \f$ on the
deba@409:     /// target-side.
deba@409:     ///
deba@409:     /// Calculates a minimum cut with \f$ source \f$ on the
alpar@412:     /// target-side (i.e. a set \f$ X\subsetneq V \f$ with
alpar@412:     /// \f$ source \in X \f$ and minimal out-degree).
deba@409:     void calculateIn() {
deba@409:       findMinCutIn();
deba@409:     }
deba@409: 
deba@409: 
deba@409:     /// \brief Runs the algorithm.
deba@409:     ///
deba@409:     /// Runs the algorithm. It finds nodes \c source and \c target
deba@409:     /// arbitrarily and then calls \ref init(), \ref calculateOut()
deba@409:     /// and \ref calculateIn().
deba@409:     void run() {
deba@409:       init();
deba@409:       calculateOut();
deba@409:       calculateIn();
deba@409:     }
deba@409: 
deba@409:     /// \brief Runs the algorithm.
deba@409:     ///
deba@409:     /// Runs the algorithm. It uses the given \c source node, finds a
deba@409:     /// proper \c target and then calls the \ref init(), \ref
deba@409:     /// calculateOut() and \ref calculateIn().
deba@409:     void run(const Node& s) {
deba@409:       init(s);
deba@409:       calculateOut();
deba@409:       calculateIn();
deba@409:     }
deba@409: 
deba@409:     /// @}
deba@409: 
deba@409:     /// \name Query Functions
deba@409:     /// The result of the %HaoOrlin algorithm
deba@409:     /// can be obtained using these functions.
deba@409:     /// \n
deba@409:     /// Before using these functions, either \ref run(), \ref
deba@409:     /// calculateOut() or \ref calculateIn() must be called.
deba@409: 
deba@409:     /// @{
deba@409: 
deba@409:     /// \brief Returns the value of the minimum value cut.
deba@409:     ///
deba@409:     /// Returns the value of the minimum value cut.
deba@409:     Value minCutValue() const {
deba@409:       return _min_cut;
deba@409:     }
deba@409: 
deba@409: 
deba@409:     /// \brief Returns a minimum cut.
deba@409:     ///
deba@409:     /// Sets \c nodeMap to the characteristic vector of a minimum
deba@409:     /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$
deba@409:     /// with minimal out-degree (i.e. \c nodeMap will be true exactly
deba@409:     /// for the nodes of \f$ X \f$).  \pre nodeMap should be a
deba@409:     /// bool-valued node-map.
deba@409:     template <typename NodeMap>
deba@409:     Value minCutMap(NodeMap& nodeMap) const {
deba@409:       for (NodeIt it(_graph); it != INVALID; ++it) {
deba@409:         nodeMap.set(it, (*_min_cut_map)[it]);
deba@409:       }
deba@409:       return _min_cut;
deba@409:     }
deba@409: 
deba@409:     /// @}
deba@409: 
deba@409:   }; //class HaoOrlin
deba@409: 
deba@409: 
deba@409: } //namespace lemon
deba@409: 
deba@409: #endif //LEMON_HAO_ORLIN_H