Differential D5594 Diff 18104 extern/quadriflow/3rd/lemon-1.3.1/lemon/hao_orlin.h

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				/* -- mode: C++; indent-tabs-mode: nil; --
				*
				* This file is a part of LEMON, a generic C++ optimization library.
				*
				* Copyright (C) 2003-2013
				* 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 <vector>
				#include <list>
				#include <limits>

				#include <lemon/maps.h>
				#include <lemon/core.h>
				#include <lemon/tolerance.h>

				/// \file
				/// \ingroup min_cut
				/// \brief Implementation of the Hao-Orlin algorithm.
				///
				/// Implementation of the Hao-Orlin algorithm for finding a minimum cut
				/// in a digraph.

				namespace lemon {

				/// \ingroup min_cut
				///
				/// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph.
				///
				/// This class implements the Hao-Orlin algorithm for finding a minimum
				/// value 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 outgoing
				/// capacity) 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 outgoing
				/// capacity). Obviously, the smaller of these two cuts will be a
				/// minimum cut of \f$ D \f$. The algorithm is a modified
				/// preflow push-relabel algorithm. Our implementation calculates
				/// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
				/// highest-label rule), or in \f$O(nm)\f$ for unit capacities. A notable
				/// use of this algorithm is testing network reliability.
				///
				/// For an undirected graph you can run just the first phase of the
				/// algorithm or you can use the algorithm of Nagamochi and Ibaraki,
				/// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$
				/// time. It is implemented in the NagamochiIbaraki algorithm class.
				///
				/// \tparam GR The type of the digraph the algorithm runs on.
				/// \tparam CAP The type of the arc map containing the capacities,
				/// which can be any numreric type. The default map type is
				/// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
				/// \tparam TOL Tolerance class for handling inexact computations. The
				/// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>".
				#ifdef DOXYGEN
				template <typename GR, typename CAP, typename TOL>
				#else
				template <typename GR,
				typename CAP = typename GR::template ArcMap<int>,
				typename TOL = Tolerance<typename CAP::Value> >
				#endif
				class HaoOrlin {
				public:

				/// The digraph type of the algorithm
				typedef GR Digraph;
				/// The capacity map type of the algorithm
				typedef CAP CapacityMap;
				/// The tolerance type of the algorithm
				typedef TOL Tolerance;

				private:

				typedef typename CapacityMap::Value Value;

				TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

				const Digraph& _graph;
				const CapacityMap* _capacity;

				typedef typename Digraph::template ArcMap<Value> FlowMap;
				FlowMap* _flow;

				Node _source;

				int _node_num;

				// Bucketing structure
				std::vector<Node> _first, _last;
				typename Digraph::template NodeMap<Node>* _next;
				typename Digraph::template NodeMap<Node>* _prev;
				typename Digraph::template NodeMap<bool>* _active;
				typename Digraph::template NodeMap<int>* _bucket;

				std::vector<bool> _dormant;

				std::list<std::list<int> > _sets;
				std::list<int>::iterator _highest;

				typedef typename Digraph::template NodeMap<Value> ExcessMap;
				ExcessMap* _excess;

				typedef typename Digraph::template NodeMap<bool> SourceSetMap;
				SourceSetMap* _source_set;

				Value _min_cut;

				typedef typename Digraph::template NodeMap<bool> MinCutMap;
				MinCutMap* _min_cut_map;

				Tolerance _tolerance;

				public:

				/// \brief Constructor
				///
				/// Constructor of the algorithm class.
				HaoOrlin(const Digraph& graph, const CapacityMap& capacity,
				const Tolerance& tolerance = Tolerance()) :
				_graph(graph), _capacity(&capacity), _flow(0), _source(),
				_node_num(), _first(), _last(), _next(0), _prev(0),
				_active(0), _bucket(0), _dormant(), _sets(), _highest(),
				_excess(0), _source_set(0), _min_cut(), _min_cut_map(0),
				_tolerance(tolerance) {}

				~HaoOrlin() {
				if (_min_cut_map) {
				delete _min_cut_map;
				}
				if (_source_set) {
				delete _source_set;
				}
				if (_excess) {
				delete _excess;
				}
				if (_next) {
				delete _next;
				}
				if (_prev) {
				delete _prev;
				}
				if (_active) {
				delete _active;
				}
				if (_bucket) {
				delete _bucket;
				}
				if (_flow) {
				delete _flow;
				}
				}

				/// \brief Set the tolerance used by the algorithm.
				///
				/// This function sets the tolerance object used by the algorithm.
				/// \return <tt>(*this)</tt>
				HaoOrlin& tolerance(const Tolerance& tolerance) {
				_tolerance = tolerance;
				return *this;
				}

				/// \brief Returns a const reference to the tolerance.
				///
				/// This function returns a const reference to the tolerance object
				/// used by the algorithm.
				const Tolerance& tolerance() const {
				return _tolerance;
				}

				private:

				void activate(const Node& i) {
				(*_active)[i] = true;

				int bucket = (*_bucket)[i];

				if ((_prev)[i] == INVALID \|\| (_active)[(*_prev)[i]]) return;
				//unlace
				(_next)[(_prev)[i]] = (*_next)[i];
				if ((*_next)[i] != INVALID) {
				(_prev)[(_next)[i]] = (*_prev)[i];
				} else {
				_last[bucket] = (*_prev)[i];
				}
				//lace
				(*_next)[i] = _first[bucket];
				(*_prev)[_first[bucket]] = i;
				(*_prev)[i] = INVALID;
				_first[bucket] = i;
				}

				void deactivate(const Node& i) {
				(*_active)[i] = false;
				int bucket = (*_bucket)[i];

				if ((_next)[i] == INVALID \|\| !(_active)[(*_next)[i]]) return;

				//unlace
				(_prev)[(_next)[i]] = (*_prev)[i];
				if ((*_prev)[i] != INVALID) {
				(_next)[(_prev)[i]] = (*_next)[i];
				} else {
				_first[bucket] = (*_next)[i];
				}
				//lace
				(*_prev)[i] = _last[bucket];
				(*_next)[_last[bucket]] = i;
				(*_next)[i] = INVALID;
				_last[bucket] = i;
				}

				void addItem(const Node& i, int bucket) {
				(*_bucket)[i] = bucket;
				if (_last[bucket] != INVALID) {
				(*_prev)[i] = _last[bucket];
				(*_next)[_last[bucket]] = i;
				(*_next)[i] = INVALID;
				_last[bucket] = i;
				} else {
				(*_prev)[i] = INVALID;
				_first[bucket] = i;
				(*_next)[i] = INVALID;
				_last[bucket] = i;
				}
				}

				void findMinCutOut() {

				for (NodeIt n(_graph); n != INVALID; ++n) {
				(*_excess)[n] = 0;
				(*_source_set)[n] = false;
				}

				for (ArcIt a(_graph); a != INVALID; ++a) {
				(*_flow)[a] = 0;
				}

				int bucket_num = 0;
				std::vector<Node> queue(_node_num);
				int qfirst = 0, qlast = 0, qsep = 0;

				{
				typename Digraph::template NodeMap<bool> reached(_graph, false);

				reached[_source] = true;
				bool first_set = true;

				for (NodeIt t(_graph); t != INVALID; ++t) {
				if (reached[t]) continue;
				_sets.push_front(std::list<int>());

				queue[qlast++] = t;
				reached[t] = true;

				while (qfirst != qlast) {
				if (qsep == qfirst) {
				++bucket_num;
				_sets.front().push_front(bucket_num);
				_dormant[bucket_num] = !first_set;
				_first[bucket_num] = _last[bucket_num] = INVALID;
				qsep = qlast;
				}

				Node n = queue[qfirst++];
				addItem(n, bucket_num);

				for (InArcIt a(_graph, n); a != INVALID; ++a) {
				Node u = _graph.source(a);
				if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
				reached[u] = true;
				queue[qlast++] = u;
				}
				}
				}
				first_set = false;
				}

				++bucket_num;
				(*_bucket)[_source] = 0;
				_dormant[0] = true;
				}
				(*_source_set)[_source] = true;

				Node target = _last[_sets.back().back()];
				{
				for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
				if (_tolerance.positive((*_capacity)[a])) {
				Node u = _graph.target(a);
				(_flow)[a] = (_capacity)[a];
				(_excess)[u] += (_capacity)[a];
				if (!(*_active)[u] && u != _source) {
				activate(u);
				}
				}
				}

				if ((*_active)[target]) {
				deactivate(target);
				}

				_highest = _sets.back().begin();
				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				}

				while (true) {
				while (_highest != _sets.back().end()) {
				Node n = _first[*_highest];
				Value excess = (*_excess)[n];
				int next_bucket = _node_num;

				int under_bucket;
				if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
				under_bucket = -1;
				} else {
				under_bucket = *(++std::list<int>::iterator(_highest));
				}

				for (OutArcIt a(_graph, n); a != INVALID; ++a) {
				Node v = _graph.target(a);
				if (_dormant[(*_bucket)[v]]) continue;
				Value rem = (_capacity)[a] - (_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				if ((*_bucket)[v] == under_bucket) {
				if (!(*_active)[v] && v != target) {
				activate(v);
				}
				if (!_tolerance.less(rem, excess)) {
				(*_flow)[a] += excess;
				(*_excess)[v] += excess;
				excess = 0;
				goto no_more_push;
				} else {
				excess -= rem;
				(*_excess)[v] += rem;
				(_flow)[a] = (_capacity)[a];
				}
				} else if (next_bucket > (*_bucket)[v]) {
				next_bucket = (*_bucket)[v];
				}
				}

				for (InArcIt a(_graph, n); a != INVALID; ++a) {
				Node v = _graph.source(a);
				if (_dormant[(*_bucket)[v]]) continue;
				Value rem = (*_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				if ((*_bucket)[v] == under_bucket) {
				if (!(*_active)[v] && v != target) {
				activate(v);
				}
				if (!_tolerance.less(rem, excess)) {
				(*_flow)[a] -= excess;
				(*_excess)[v] += excess;
				excess = 0;
				goto no_more_push;
				} else {
				excess -= rem;
				(*_excess)[v] += rem;
				(*_flow)[a] = 0;
				}
				} else if (next_bucket > (*_bucket)[v]) {
				next_bucket = (*_bucket)[v];
				}
				}

				no_more_push:

				(*_excess)[n] = excess;

				if (excess != 0) {
				if ((*_next)[n] == INVALID) {
				typename std::list<std::list<int> >::iterator new_set =
				_sets.insert(--_sets.end(), std::list<int>());
				new_set->splice(new_set->end(), _sets.back(),
				_sets.back().begin(), ++_highest);
				for (std::list<int>::iterator it = new_set->begin();
				it != new_set->end(); ++it) {
				_dormant[*it] = true;
				}
				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				} else if (next_bucket == _node_num) {
				_first[(_bucket)[n]] = (_next)[n];
				(_prev)[(_next)[n]] = INVALID;

				std::list<std::list<int> >::iterator new_set =
				_sets.insert(--_sets.end(), std::list<int>());

				new_set->push_front(bucket_num);
				(*_bucket)[n] = bucket_num;
				_first[bucket_num] = _last[bucket_num] = n;
				(*_next)[n] = INVALID;
				(*_prev)[n] = INVALID;
				_dormant[bucket_num] = true;
				++bucket_num;

				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				} else {
				_first[_highest] = (_next)[n];
				(_prev)[(_next)[n]] = INVALID;

				while (next_bucket != *_highest) {
				--_highest;
				}

				if (_highest == _sets.back().begin()) {
				_sets.back().push_front(bucket_num);
				_dormant[bucket_num] = false;
				_first[bucket_num] = _last[bucket_num] = INVALID;
				++bucket_num;
				}
				--_highest;

				(_bucket)[n] = _highest;
				(_next)[n] = _first[_highest];
				if (_first[*_highest] != INVALID) {
				(_prev)[_first[_highest]] = n;
				} else {
				_last[*_highest] = n;
				}
				_first[*_highest] = n;
				}
				} else {

				deactivate(n);
				if (!(_active)[_first[_highest]]) {
				++_highest;
				if (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				_highest = _sets.back().end();
				}
				}
				}
				}

				if ((*_excess)[target] < _min_cut) {
				_min_cut = (*_excess)[target];
				for (NodeIt i(_graph); i != INVALID; ++i) {
				(*_min_cut_map)[i] = true;
				}
				for (std::list<int>::iterator it = _sets.back().begin();
				it != _sets.back().end(); ++it) {
				Node n = _first[*it];
				while (n != INVALID) {
				(*_min_cut_map)[n] = false;
				n = (*_next)[n];
				}
				}
				}

				{
				Node new_target;
				if ((_prev)[target] != INVALID \|\| (_next)[target] != INVALID) {
				if ((*_next)[target] == INVALID) {
				_last[(_bucket)[target]] = (_prev)[target];
				new_target = (*_prev)[target];
				} else {
				(_prev)[(_next)[target]] = (*_prev)[target];
				new_target = (*_next)[target];
				}
				if ((*_prev)[target] == INVALID) {
				_first[(_bucket)[target]] = (_next)[target];
				} else {
				(_next)[(_prev)[target]] = (*_next)[target];
				}
				} else {
				_sets.back().pop_back();
				if (_sets.back().empty()) {
				_sets.pop_back();
				if (_sets.empty())
				break;
				for (std::list<int>::iterator it = _sets.back().begin();
				it != _sets.back().end(); ++it) {
				_dormant[*it] = false;
				}
				}
				new_target = _last[_sets.back().back()];
				}

				(*_bucket)[target] = 0;

				(*_source_set)[target] = true;
				for (OutArcIt a(_graph, target); a != INVALID; ++a) {
				Value rem = (_capacity)[a] - (_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				Node v = _graph.target(a);
				if (!(_active)[v] && !(_source_set)[v]) {
				activate(v);
				}
				(*_excess)[v] += rem;
				(_flow)[a] = (_capacity)[a];
				}

				for (InArcIt a(_graph, target); a != INVALID; ++a) {
				Value rem = (*_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				Node v = _graph.source(a);
				if (!(_active)[v] && !(_source_set)[v]) {
				activate(v);
				}
				(*_excess)[v] += rem;
				(*_flow)[a] = 0;
				}

				target = new_target;
				if ((*_active)[target]) {
				deactivate(target);
				}

				_highest = _sets.back().begin();
				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				}
				}
				}

				void findMinCutIn() {

				for (NodeIt n(_graph); n != INVALID; ++n) {
				(*_excess)[n] = 0;
				(*_source_set)[n] = false;
				}

				for (ArcIt a(_graph); a != INVALID; ++a) {
				(*_flow)[a] = 0;
				}

				int bucket_num = 0;
				std::vector<Node> queue(_node_num);
				int qfirst = 0, qlast = 0, qsep = 0;

				{
				typename Digraph::template NodeMap<bool> reached(_graph, false);

				reached[_source] = true;

				bool first_set = true;

				for (NodeIt t(_graph); t != INVALID; ++t) {
				if (reached[t]) continue;
				_sets.push_front(std::list<int>());

				queue[qlast++] = t;
				reached[t] = true;

				while (qfirst != qlast) {
				if (qsep == qfirst) {
				++bucket_num;
				_sets.front().push_front(bucket_num);
				_dormant[bucket_num] = !first_set;
				_first[bucket_num] = _last[bucket_num] = INVALID;
				qsep = qlast;
				}

				Node n = queue[qfirst++];
				addItem(n, bucket_num);

				for (OutArcIt a(_graph, n); a != INVALID; ++a) {
				Node u = _graph.target(a);
				if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
				reached[u] = true;
				queue[qlast++] = u;
				}
				}
				}
				first_set = false;
				}

				++bucket_num;
				(*_bucket)[_source] = 0;
				_dormant[0] = true;
				}
				(*_source_set)[_source] = true;

				Node target = _last[_sets.back().back()];
				{
				for (InArcIt a(_graph, _source); a != INVALID; ++a) {
				if (_tolerance.positive((*_capacity)[a])) {
				Node u = _graph.source(a);
				(_flow)[a] = (_capacity)[a];
				(_excess)[u] += (_capacity)[a];
				if (!(*_active)[u] && u != _source) {
				activate(u);
				}
				}
				}
				if ((*_active)[target]) {
				deactivate(target);
				}

				_highest = _sets.back().begin();
				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				}


				while (true) {
				while (_highest != _sets.back().end()) {
				Node n = _first[*_highest];
				Value excess = (*_excess)[n];
				int next_bucket = _node_num;

				int under_bucket;
				if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
				under_bucket = -1;
				} else {
				under_bucket = *(++std::list<int>::iterator(_highest));
				}

				for (InArcIt a(_graph, n); a != INVALID; ++a) {
				Node v = _graph.source(a);
				if (_dormant[(*_bucket)[v]]) continue;
				Value rem = (_capacity)[a] - (_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				if ((*_bucket)[v] == under_bucket) {
				if (!(*_active)[v] && v != target) {
				activate(v);
				}
				if (!_tolerance.less(rem, excess)) {
				(*_flow)[a] += excess;
				(*_excess)[v] += excess;
				excess = 0;
				goto no_more_push;
				} else {
				excess -= rem;
				(*_excess)[v] += rem;
				(_flow)[a] = (_capacity)[a];
				}
				} else if (next_bucket > (*_bucket)[v]) {
				next_bucket = (*_bucket)[v];
				}
				}

				for (OutArcIt a(_graph, n); a != INVALID; ++a) {
				Node v = _graph.target(a);
				if (_dormant[(*_bucket)[v]]) continue;
				Value rem = (*_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				if ((*_bucket)[v] == under_bucket) {
				if (!(*_active)[v] && v != target) {
				activate(v);
				}
				if (!_tolerance.less(rem, excess)) {
				(*_flow)[a] -= excess;
				(*_excess)[v] += excess;
				excess = 0;
				goto no_more_push;
				} else {
				excess -= rem;
				(*_excess)[v] += rem;
				(*_flow)[a] = 0;
				}
				} else if (next_bucket > (*_bucket)[v]) {
				next_bucket = (*_bucket)[v];
				}
				}

				no_more_push:

				(*_excess)[n] = excess;

				if (excess != 0) {
				if ((*_next)[n] == INVALID) {
				typename std::list<std::list<int> >::iterator new_set =
				_sets.insert(--_sets.end(), std::list<int>());
				new_set->splice(new_set->end(), _sets.back(),
				_sets.back().begin(), ++_highest);
				for (std::list<int>::iterator it = new_set->begin();
				it != new_set->end(); ++it) {
				_dormant[*it] = true;
				}
				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				} else if (next_bucket == _node_num) {
				_first[(_bucket)[n]] = (_next)[n];
				(_prev)[(_next)[n]] = INVALID;

				std::list<std::list<int> >::iterator new_set =
				_sets.insert(--_sets.end(), std::list<int>());

				new_set->push_front(bucket_num);
				(*_bucket)[n] = bucket_num;
				_first[bucket_num] = _last[bucket_num] = n;
				(*_next)[n] = INVALID;
				(*_prev)[n] = INVALID;
				_dormant[bucket_num] = true;
				++bucket_num;

				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				} else {
				_first[_highest] = (_next)[n];
				(_prev)[(_next)[n]] = INVALID;

				while (next_bucket != *_highest) {
				--_highest;
				}
				if (_highest == _sets.back().begin()) {
				_sets.back().push_front(bucket_num);
				_dormant[bucket_num] = false;
				_first[bucket_num] = _last[bucket_num] = INVALID;
				++bucket_num;
				}
				--_highest;

				(_bucket)[n] = _highest;
				(_next)[n] = _first[_highest];
				if (_first[*_highest] != INVALID) {
				(_prev)[_first[_highest]] = n;
				} else {
				_last[*_highest] = n;
				}
				_first[*_highest] = n;
				}
				} else {

				deactivate(n);
				if (!(_active)[_first[_highest]]) {
				++_highest;
				if (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				_highest = _sets.back().end();
				}
				}
				}
				}

				if ((*_excess)[target] < _min_cut) {
				_min_cut = (*_excess)[target];
				for (NodeIt i(_graph); i != INVALID; ++i) {
				(*_min_cut_map)[i] = false;
				}
				for (std::list<int>::iterator it = _sets.back().begin();
				it != _sets.back().end(); ++it) {
				Node n = _first[*it];
				while (n != INVALID) {
				(*_min_cut_map)[n] = true;
				n = (*_next)[n];
				}
				}
				}

				{
				Node new_target;
				if ((_prev)[target] != INVALID \|\| (_next)[target] != INVALID) {
				if ((*_next)[target] == INVALID) {
				_last[(_bucket)[target]] = (_prev)[target];
				new_target = (*_prev)[target];
				} else {
				(_prev)[(_next)[target]] = (*_prev)[target];
				new_target = (*_next)[target];
				}
				if ((*_prev)[target] == INVALID) {
				_first[(_bucket)[target]] = (_next)[target];
				} else {
				(_next)[(_prev)[target]] = (*_next)[target];
				}
				} else {
				_sets.back().pop_back();
				if (_sets.back().empty()) {
				_sets.pop_back();
				if (_sets.empty())
				break;
				for (std::list<int>::iterator it = _sets.back().begin();
				it != _sets.back().end(); ++it) {
				_dormant[*it] = false;
				}
				}
				new_target = _last[_sets.back().back()];
				}

				(*_bucket)[target] = 0;

				(*_source_set)[target] = true;
				for (InArcIt a(_graph, target); a != INVALID; ++a) {
				Value rem = (_capacity)[a] - (_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				Node v = _graph.source(a);
				if (!(_active)[v] && !(_source_set)[v]) {
				activate(v);
				}
				(*_excess)[v] += rem;
				(_flow)[a] = (_capacity)[a];
				}

				for (OutArcIt a(_graph, target); a != INVALID; ++a) {
				Value rem = (*_flow)[a];
				if (!_tolerance.positive(rem)) continue;
				Node v = _graph.target(a);
				if (!(_active)[v] && !(_source_set)[v]) {
				activate(v);
				}
				(*_excess)[v] += rem;
				(*_flow)[a] = 0;
				}

				target = new_target;
				if ((*_active)[target]) {
				deactivate(target);
				}

				_highest = _sets.back().begin();
				while (_highest != _sets.back().end() &&
				!(_active)[_first[_highest]]) {
				++_highest;
				}
				}
				}
				}

				public:

				/// \name Execution Control
				/// The simplest way to execute the algorithm is to use
				/// one of the member functions called \ref run().
				/// \n
				/// If you need better control on the execution,
				/// you have to call one of the \ref init() functions first, then
				/// \ref calculateOut() and/or \ref calculateIn().

				/// @{

				/// \brief Initialize the internal data structures.
				///
				/// This function initializes the internal data structures. It creates
				/// the maps and some bucket structures for the algorithm.
				/// The first node is used as the source node for the push-relabel
				/// algorithm.
				void init() {
				init(NodeIt(_graph));
				}

				/// \brief Initialize the internal data structures.
				///
				/// This function initializes the internal data structures. It creates
				/// the maps and some bucket structures for the algorithm.
				/// The given node is used as the source node for the push-relabel
				/// algorithm.
				void init(const Node& source) {
				_source = source;

				_node_num = countNodes(_graph);

				_first.resize(_node_num);
				_last.resize(_node_num);

				_dormant.resize(_node_num);

				if (!_flow) {
				_flow = new FlowMap(_graph);
				}
				if (!_next) {
				_next = new typename Digraph::template NodeMap<Node>(_graph);
				}
				if (!_prev) {
				_prev = new typename Digraph::template NodeMap<Node>(_graph);
				}
				if (!_active) {
				_active = new typename Digraph::template NodeMap<bool>(_graph);
				}
				if (!_bucket) {
				_bucket = new typename Digraph::template NodeMap<int>(_graph);
				}
				if (!_excess) {
				_excess = new ExcessMap(_graph);
				}
				if (!_source_set) {
				_source_set = new SourceSetMap(_graph);
				}
				if (!_min_cut_map) {
				_min_cut_map = new MinCutMap(_graph);
				}

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


				/// \brief Calculate a minimum cut with \f$ source \f$ on the
				/// source-side.
				///
				/// This function 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 outgoing capacity).
				/// It updates the stored cut if (and only if) the newly found one
				/// is better.
				///
				/// \pre \ref init() must be called before using this function.
				void calculateOut() {
				findMinCutOut();
				}

				/// \brief Calculate a minimum cut with \f$ source \f$ on the
				/// sink-side.
				///
				/// This function 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 outgoing capacity).
				/// It updates the stored cut if (and only if) the newly found one
				/// is better.
				///
				/// \pre \ref init() must be called before using this function.
				void calculateIn() {
				findMinCutIn();
				}


				/// \brief Run the algorithm.
				///
				/// This function runs the algorithm. It chooses source node,
				/// then calls \ref init(), \ref calculateOut()
				/// and \ref calculateIn().
				void run() {
				init();
				calculateOut();
				calculateIn();
				}

				/// \brief Run the algorithm.
				///
				/// This function runs the algorithm. It calls \ref init(),
				/// \ref calculateOut() and \ref calculateIn() with the given
				/// source node.
				void run(const Node& s) {
				init(s);
				calculateOut();
				calculateIn();
				}

				/// @}

				/// \name Query Functions
				/// The result of the %HaoOrlin algorithm
				/// can be obtained using these functions.\n
				/// \ref run(), \ref calculateOut() or \ref calculateIn()
				/// should be called before using them.

				/// @{

				/// \brief Return the value of the minimum cut.
				///
				/// This function returns the value of the best cut found by the
				/// previously called \ref run(), \ref calculateOut() or \ref
				/// calculateIn().
				///
				/// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
				/// must be called before using this function.
				Value minCutValue() const {
				return _min_cut;
				}


				/// \brief Return a minimum cut.
				///
				/// This function gives the best cut found by the
				/// previously called \ref run(), \ref calculateOut() or \ref
				/// calculateIn().
				///
				/// It sets \c cutMap to the characteristic vector of the found
				/// minimum value cut - a non-empty set \f$ X\subsetneq V \f$
				/// of minimum outgoing capacity (i.e. \c cutMap will be \c true exactly
				/// for the nodes of \f$ X \f$).
				///
				/// \param cutMap A \ref concepts::WriteMap "writable" node map with
				/// \c bool (or convertible) value type.
				///
				/// \return The value of the minimum cut.
				///
				/// \pre \ref run(), \ref calculateOut() or \ref calculateIn()
				/// must be called before using this function.
				template <typename CutMap>
				Value minCutMap(CutMap& cutMap) const {
				for (NodeIt it(_graph); it != INVALID; ++it) {
				cutMap.set(it, (*_min_cut_map)[it]);
				}
				return _min_cut;
				}

				/// @}

				}; //class HaoOrlin

				} //namespace lemon

				#endif //LEMON_HAO_ORLIN_H