1016 lines
31 KiB
C++
Executable File
1016 lines
31 KiB
C++
Executable File
/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2013
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_HAO_ORLIN_H
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#define LEMON_HAO_ORLIN_H
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#include <vector>
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#include <list>
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#include <limits>
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#include <lemon/maps.h>
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#include <lemon/core.h>
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#include <lemon/tolerance.h>
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/// \file
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/// \ingroup min_cut
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/// \brief Implementation of the Hao-Orlin algorithm.
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///
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/// Implementation of the Hao-Orlin algorithm for finding a minimum cut
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/// in a digraph.
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namespace lemon {
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/// \ingroup min_cut
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///
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/// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph.
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///
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/// This class implements the Hao-Orlin algorithm for finding a minimum
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/// value cut in a directed graph \f$D=(V,A)\f$.
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/// It takes a fixed node \f$ source \in V \f$ and
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/// consists of two phases: in the first phase it determines a
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/// minimum cut with \f$ source \f$ on the source-side (i.e. a set
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/// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal outgoing
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/// capacity) and in the second phase it determines a minimum cut
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/// with \f$ source \f$ on the sink-side (i.e. a set
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/// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal outgoing
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/// capacity). Obviously, the smaller of these two cuts will be a
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/// minimum cut of \f$ D \f$. The algorithm is a modified
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/// preflow push-relabel algorithm. Our implementation calculates
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/// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the
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/// highest-label rule), or in \f$O(nm)\f$ for unit capacities. A notable
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/// use of this algorithm is testing network reliability.
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///
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/// For an undirected graph you can run just the first phase of the
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/// algorithm or you can use the algorithm of Nagamochi and Ibaraki,
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/// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$
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/// time. It is implemented in the NagamochiIbaraki algorithm class.
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///
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/// \tparam GR The type of the digraph the algorithm runs on.
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/// \tparam CAP The type of the arc map containing the capacities,
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/// which can be any numreric type. The default map type is
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/// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
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/// \tparam TOL Tolerance class for handling inexact computations. The
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/// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>".
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#ifdef DOXYGEN
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template <typename GR, typename CAP, typename TOL>
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#else
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template <typename GR,
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typename CAP = typename GR::template ArcMap<int>,
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typename TOL = Tolerance<typename CAP::Value> >
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#endif
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class HaoOrlin {
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public:
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/// The digraph type of the algorithm
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typedef GR Digraph;
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/// The capacity map type of the algorithm
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typedef CAP CapacityMap;
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/// The tolerance type of the algorithm
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typedef TOL Tolerance;
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private:
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typedef typename CapacityMap::Value Value;
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TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
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const Digraph& _graph;
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const CapacityMap* _capacity;
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typedef typename Digraph::template ArcMap<Value> FlowMap;
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FlowMap* _flow;
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Node _source;
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int _node_num;
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// Bucketing structure
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std::vector<Node> _first, _last;
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typename Digraph::template NodeMap<Node>* _next;
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typename Digraph::template NodeMap<Node>* _prev;
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typename Digraph::template NodeMap<bool>* _active;
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typename Digraph::template NodeMap<int>* _bucket;
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std::vector<bool> _dormant;
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std::list<std::list<int> > _sets;
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std::list<int>::iterator _highest;
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typedef typename Digraph::template NodeMap<Value> ExcessMap;
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ExcessMap* _excess;
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typedef typename Digraph::template NodeMap<bool> SourceSetMap;
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SourceSetMap* _source_set;
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Value _min_cut;
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typedef typename Digraph::template NodeMap<bool> MinCutMap;
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MinCutMap* _min_cut_map;
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Tolerance _tolerance;
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public:
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/// \brief Constructor
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///
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/// Constructor of the algorithm class.
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HaoOrlin(const Digraph& graph, const CapacityMap& capacity,
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const Tolerance& tolerance = Tolerance()) :
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_graph(graph), _capacity(&capacity), _flow(0), _source(),
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_node_num(), _first(), _last(), _next(0), _prev(0),
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_active(0), _bucket(0), _dormant(), _sets(), _highest(),
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_excess(0), _source_set(0), _min_cut(), _min_cut_map(0),
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_tolerance(tolerance) {}
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~HaoOrlin() {
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if (_min_cut_map) {
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delete _min_cut_map;
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}
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if (_source_set) {
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delete _source_set;
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}
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if (_excess) {
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delete _excess;
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}
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if (_next) {
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delete _next;
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}
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if (_prev) {
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delete _prev;
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}
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if (_active) {
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delete _active;
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}
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if (_bucket) {
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delete _bucket;
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}
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if (_flow) {
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delete _flow;
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}
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}
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/// \brief Set the tolerance used by the algorithm.
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///
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/// This function sets the tolerance object used by the algorithm.
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/// \return <tt>(*this)</tt>
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HaoOrlin& tolerance(const Tolerance& tolerance) {
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_tolerance = tolerance;
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return *this;
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}
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/// \brief Returns a const reference to the tolerance.
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///
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/// This function returns a const reference to the tolerance object
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/// used by the algorithm.
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const Tolerance& tolerance() const {
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return _tolerance;
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}
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private:
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void activate(const Node& i) {
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(*_active)[i] = true;
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int bucket = (*_bucket)[i];
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if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;
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//unlace
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(*_next)[(*_prev)[i]] = (*_next)[i];
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if ((*_next)[i] != INVALID) {
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(*_prev)[(*_next)[i]] = (*_prev)[i];
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} else {
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_last[bucket] = (*_prev)[i];
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}
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//lace
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(*_next)[i] = _first[bucket];
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(*_prev)[_first[bucket]] = i;
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(*_prev)[i] = INVALID;
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_first[bucket] = i;
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}
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void deactivate(const Node& i) {
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(*_active)[i] = false;
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int bucket = (*_bucket)[i];
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if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;
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//unlace
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(*_prev)[(*_next)[i]] = (*_prev)[i];
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if ((*_prev)[i] != INVALID) {
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(*_next)[(*_prev)[i]] = (*_next)[i];
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} else {
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_first[bucket] = (*_next)[i];
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}
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//lace
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(*_prev)[i] = _last[bucket];
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(*_next)[_last[bucket]] = i;
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(*_next)[i] = INVALID;
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_last[bucket] = i;
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}
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void addItem(const Node& i, int bucket) {
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(*_bucket)[i] = bucket;
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if (_last[bucket] != INVALID) {
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(*_prev)[i] = _last[bucket];
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(*_next)[_last[bucket]] = i;
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(*_next)[i] = INVALID;
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_last[bucket] = i;
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} else {
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(*_prev)[i] = INVALID;
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_first[bucket] = i;
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(*_next)[i] = INVALID;
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_last[bucket] = i;
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}
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}
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void findMinCutOut() {
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for (NodeIt n(_graph); n != INVALID; ++n) {
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(*_excess)[n] = 0;
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(*_source_set)[n] = false;
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}
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for (ArcIt a(_graph); a != INVALID; ++a) {
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(*_flow)[a] = 0;
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}
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int bucket_num = 0;
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std::vector<Node> queue(_node_num);
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int qfirst = 0, qlast = 0, qsep = 0;
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{
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typename Digraph::template NodeMap<bool> reached(_graph, false);
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reached[_source] = true;
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bool first_set = true;
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for (NodeIt t(_graph); t != INVALID; ++t) {
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if (reached[t]) continue;
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_sets.push_front(std::list<int>());
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queue[qlast++] = t;
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reached[t] = true;
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while (qfirst != qlast) {
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if (qsep == qfirst) {
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++bucket_num;
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_sets.front().push_front(bucket_num);
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_dormant[bucket_num] = !first_set;
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_first[bucket_num] = _last[bucket_num] = INVALID;
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qsep = qlast;
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}
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Node n = queue[qfirst++];
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addItem(n, bucket_num);
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for (InArcIt a(_graph, n); a != INVALID; ++a) {
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Node u = _graph.source(a);
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if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
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reached[u] = true;
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queue[qlast++] = u;
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}
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}
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}
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first_set = false;
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}
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++bucket_num;
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(*_bucket)[_source] = 0;
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_dormant[0] = true;
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}
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(*_source_set)[_source] = true;
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Node target = _last[_sets.back().back()];
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{
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for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
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if (_tolerance.positive((*_capacity)[a])) {
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Node u = _graph.target(a);
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(*_flow)[a] = (*_capacity)[a];
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(*_excess)[u] += (*_capacity)[a];
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if (!(*_active)[u] && u != _source) {
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activate(u);
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}
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}
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}
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if ((*_active)[target]) {
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deactivate(target);
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}
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_highest = _sets.back().begin();
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while (_highest != _sets.back().end() &&
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!(*_active)[_first[*_highest]]) {
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++_highest;
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}
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}
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while (true) {
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while (_highest != _sets.back().end()) {
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Node n = _first[*_highest];
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Value excess = (*_excess)[n];
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int next_bucket = _node_num;
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int under_bucket;
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if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
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under_bucket = -1;
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} else {
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under_bucket = *(++std::list<int>::iterator(_highest));
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}
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for (OutArcIt a(_graph, n); a != INVALID; ++a) {
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Node v = _graph.target(a);
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if (_dormant[(*_bucket)[v]]) continue;
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Value rem = (*_capacity)[a] - (*_flow)[a];
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if (!_tolerance.positive(rem)) continue;
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if ((*_bucket)[v] == under_bucket) {
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if (!(*_active)[v] && v != target) {
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activate(v);
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}
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if (!_tolerance.less(rem, excess)) {
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(*_flow)[a] += excess;
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(*_excess)[v] += excess;
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excess = 0;
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goto no_more_push;
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} else {
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excess -= rem;
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(*_excess)[v] += rem;
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(*_flow)[a] = (*_capacity)[a];
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}
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} else if (next_bucket > (*_bucket)[v]) {
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next_bucket = (*_bucket)[v];
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}
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}
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for (InArcIt a(_graph, n); a != INVALID; ++a) {
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Node v = _graph.source(a);
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if (_dormant[(*_bucket)[v]]) continue;
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Value rem = (*_flow)[a];
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if (!_tolerance.positive(rem)) continue;
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if ((*_bucket)[v] == under_bucket) {
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if (!(*_active)[v] && v != target) {
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activate(v);
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}
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if (!_tolerance.less(rem, excess)) {
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(*_flow)[a] -= excess;
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(*_excess)[v] += excess;
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excess = 0;
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goto no_more_push;
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} else {
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excess -= rem;
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(*_excess)[v] += rem;
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(*_flow)[a] = 0;
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}
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} else if (next_bucket > (*_bucket)[v]) {
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next_bucket = (*_bucket)[v];
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}
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}
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no_more_push:
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(*_excess)[n] = excess;
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if (excess != 0) {
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if ((*_next)[n] == INVALID) {
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typename std::list<std::list<int> >::iterator new_set =
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_sets.insert(--_sets.end(), std::list<int>());
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new_set->splice(new_set->end(), _sets.back(),
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_sets.back().begin(), ++_highest);
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for (std::list<int>::iterator it = new_set->begin();
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it != new_set->end(); ++it) {
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_dormant[*it] = true;
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}
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while (_highest != _sets.back().end() &&
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!(*_active)[_first[*_highest]]) {
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++_highest;
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}
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} else if (next_bucket == _node_num) {
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_first[(*_bucket)[n]] = (*_next)[n];
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(*_prev)[(*_next)[n]] = INVALID;
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std::list<std::list<int> >::iterator new_set =
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_sets.insert(--_sets.end(), std::list<int>());
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new_set->push_front(bucket_num);
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(*_bucket)[n] = bucket_num;
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_first[bucket_num] = _last[bucket_num] = n;
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(*_next)[n] = INVALID;
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(*_prev)[n] = INVALID;
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_dormant[bucket_num] = true;
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++bucket_num;
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while (_highest != _sets.back().end() &&
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!(*_active)[_first[*_highest]]) {
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++_highest;
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}
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} else {
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_first[*_highest] = (*_next)[n];
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(*_prev)[(*_next)[n]] = INVALID;
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while (next_bucket != *_highest) {
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--_highest;
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}
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if (_highest == _sets.back().begin()) {
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_sets.back().push_front(bucket_num);
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_dormant[bucket_num] = false;
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_first[bucket_num] = _last[bucket_num] = INVALID;
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++bucket_num;
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}
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--_highest;
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(*_bucket)[n] = *_highest;
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(*_next)[n] = _first[*_highest];
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if (_first[*_highest] != INVALID) {
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(*_prev)[_first[*_highest]] = n;
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} else {
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_last[*_highest] = n;
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}
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_first[*_highest] = n;
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}
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} else {
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deactivate(n);
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if (!(*_active)[_first[*_highest]]) {
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++_highest;
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if (_highest != _sets.back().end() &&
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!(*_active)[_first[*_highest]]) {
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_highest = _sets.back().end();
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}
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}
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}
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}
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if ((*_excess)[target] < _min_cut) {
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_min_cut = (*_excess)[target];
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for (NodeIt i(_graph); i != INVALID; ++i) {
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(*_min_cut_map)[i] = true;
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}
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for (std::list<int>::iterator it = _sets.back().begin();
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it != _sets.back().end(); ++it) {
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Node n = _first[*it];
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while (n != INVALID) {
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(*_min_cut_map)[n] = false;
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n = (*_next)[n];
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}
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}
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}
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{
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Node new_target;
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if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
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if ((*_next)[target] == INVALID) {
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_last[(*_bucket)[target]] = (*_prev)[target];
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new_target = (*_prev)[target];
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} else {
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(*_prev)[(*_next)[target]] = (*_prev)[target];
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new_target = (*_next)[target];
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}
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if ((*_prev)[target] == INVALID) {
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_first[(*_bucket)[target]] = (*_next)[target];
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} else {
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(*_next)[(*_prev)[target]] = (*_next)[target];
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}
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} else {
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_sets.back().pop_back();
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if (_sets.back().empty()) {
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_sets.pop_back();
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if (_sets.empty())
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break;
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for (std::list<int>::iterator it = _sets.back().begin();
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it != _sets.back().end(); ++it) {
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_dormant[*it] = false;
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}
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}
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new_target = _last[_sets.back().back()];
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}
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(*_bucket)[target] = 0;
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(*_source_set)[target] = true;
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for (OutArcIt a(_graph, target); a != INVALID; ++a) {
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Value rem = (*_capacity)[a] - (*_flow)[a];
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if (!_tolerance.positive(rem)) continue;
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Node v = _graph.target(a);
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if (!(*_active)[v] && !(*_source_set)[v]) {
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activate(v);
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}
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(*_excess)[v] += rem;
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(*_flow)[a] = (*_capacity)[a];
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}
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for (InArcIt a(_graph, target); a != INVALID; ++a) {
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Value rem = (*_flow)[a];
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if (!_tolerance.positive(rem)) continue;
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|
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
|