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/* -*- 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) 2003-2008
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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 class for testing network
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/// reliability.
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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 to find a minimum cut in directed graphs.
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///
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/// Hao-Orlin calculates a minimum cut in a directed graph
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/// \f$D=(V,A)\f$. 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
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/// out-degree) 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
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/// out-degree). Obviously, the smaller of these two cuts will be a
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/// minimum cut of \f$ D \f$. The algorithm is a modified
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/// push-relabel preflow algorithm and our implementation calculates
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/// the minimum cut in \f$ 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. The
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/// purpose of such algorithm is testing network reliability. For an
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/// 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
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/// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the
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/// NagamochiIbaraki algorithm class.
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///
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/// \param _Digraph is the graph type of the algorithm.
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/// \param _CapacityMap is an edge map of capacities which should
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/// be any numreric type. The default type is _Digraph::ArcMap<int>.
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/// \param _Tolerance is the handler of the inexact computation. The
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/// default type for this is Tolerance<CapacityMap::Value>.
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#ifdef DOXYGEN
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template <typename _Digraph, typename _CapacityMap, typename _Tolerance>
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#else
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template <typename _Digraph,
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typename _CapacityMap = typename _Digraph::template ArcMap<int>,
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typename _Tolerance = Tolerance<typename _CapacityMap::Value> >
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#endif
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class HaoOrlin {
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private:
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typedef _Digraph Digraph;
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typedef _CapacityMap CapacityMap;
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typedef _Tolerance Tolerance;
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typedef typename CapacityMap::Value Value;
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TEMPLATE_GRAPH_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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private:
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void activate(const Node& i) {
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_active->set(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->set((*_prev)[i], (*_next)[i]);
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if ((*_next)[i] != INVALID) {
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_prev->set((*_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->set(i, _first[bucket]);
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_prev->set(_first[bucket], i);
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_prev->set(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->set(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->set((*_next)[i], (*_prev)[i]);
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if ((*_prev)[i] != INVALID) {
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_next->set((*_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->set(i, _last[bucket]);
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_next->set(_last[bucket], i);
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_next->set(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->set(i, _last[bucket]);
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_next->set(_last[bucket], i);
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_next->set(i, INVALID);
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_last[bucket] = i;
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} else {
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_prev->set(i, INVALID);
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_first[bucket] = i;
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_next->set(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->set(n, 0);
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}
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for (ArcIt a(_graph); a != INVALID; ++a) {
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_flow->set(a, 0);
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}
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int bucket_num = 1;
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{
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typename Digraph::template NodeMap<bool> reached(_graph, false);
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reached.set(_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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_sets.front().push_front(bucket_num);
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_dormant[bucket_num] = !first_set;
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_bucket->set(t, bucket_num);
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_first[bucket_num] = _last[bucket_num] = t;
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_next->set(t, INVALID);
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_prev->set(t, INVALID);
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++bucket_num;
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std::vector<Node> queue;
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queue.push_back(t);
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reached.set(t, true);
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while (!queue.empty()) {
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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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258 |
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deba@409
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std::vector<Node> nqueue;
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for (int i = 0; i < int(queue.size()); ++i) {
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Node n = queue[i];
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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.set(u, true);
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addItem(u, bucket_num);
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nqueue.push_back(u);
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}
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}
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270 |
}
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deba@409
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queue.swap(nqueue);
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272 |
++bucket_num;
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273 |
}
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_sets.front().pop_front();
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deba@409
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--bucket_num;
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first_set = false;
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}
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278 |
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_bucket->set(_source, 0);
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280 |
_dormant[0] = true;
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281 |
}
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deba@409
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_source_set->set(_source, true);
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283 |
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deba@409
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Node target = _last[_sets.back().back()];
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deba@409
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{
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deba@409
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for (OutArcIt a(_graph, _source); a != INVALID; ++a) {
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deba@409
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287 |
if (_tolerance.positive((*_capacity)[a])) {
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deba@409
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Node u = _graph.target(a);
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deba@409
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289 |
_flow->set(a, (*_capacity)[a]);
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deba@409
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_excess->set(u, (*_excess)[u] + (*_capacity)[a]);
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deba@409
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if (!(*_active)[u] && u != _source) {
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deba@409
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activate(u);
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deba@409
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}
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deba@409
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}
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deba@409
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}
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deba@409
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deba@409
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297 |
if ((*_active)[target]) {
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deba@409
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deactivate(target);
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deba@409
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299 |
}
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deba@409
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300 |
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deba@409
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301 |
_highest = _sets.back().begin();
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deba@409
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302 |
while (_highest != _sets.back().end() &&
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deba@409
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303 |
!(*_active)[_first[*_highest]]) {
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deba@409
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304 |
++_highest;
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deba@409
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305 |
}
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deba@409
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306 |
}
|
deba@409
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307 |
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deba@409
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308 |
while (true) {
|
deba@409
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309 |
while (_highest != _sets.back().end()) {
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deba@409
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310 |
Node n = _first[*_highest];
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deba@409
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311 |
Value excess = (*_excess)[n];
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deba@409
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312 |
int next_bucket = _node_num;
|
deba@409
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313 |
|
deba@409
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314 |
int under_bucket;
|
deba@409
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315 |
if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
|
deba@409
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316 |
under_bucket = -1;
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deba@409
|
317 |
} else {
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deba@409
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318 |
under_bucket = *(++std::list<int>::iterator(_highest));
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deba@409
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319 |
}
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deba@409
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320 |
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deba@409
|
321 |
for (OutArcIt a(_graph, n); a != INVALID; ++a) {
|
deba@409
|
322 |
Node v = _graph.target(a);
|
deba@409
|
323 |
if (_dormant[(*_bucket)[v]]) continue;
|
deba@409
|
324 |
Value rem = (*_capacity)[a] - (*_flow)[a];
|
deba@409
|
325 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
326 |
if ((*_bucket)[v] == under_bucket) {
|
deba@409
|
327 |
if (!(*_active)[v] && v != target) {
|
deba@409
|
328 |
activate(v);
|
deba@409
|
329 |
}
|
deba@409
|
330 |
if (!_tolerance.less(rem, excess)) {
|
deba@409
|
331 |
_flow->set(a, (*_flow)[a] + excess);
|
deba@409
|
332 |
_excess->set(v, (*_excess)[v] + excess);
|
deba@409
|
333 |
excess = 0;
|
deba@409
|
334 |
goto no_more_push;
|
deba@409
|
335 |
} else {
|
deba@409
|
336 |
excess -= rem;
|
deba@409
|
337 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
338 |
_flow->set(a, (*_capacity)[a]);
|
deba@409
|
339 |
}
|
deba@409
|
340 |
} else if (next_bucket > (*_bucket)[v]) {
|
deba@409
|
341 |
next_bucket = (*_bucket)[v];
|
deba@409
|
342 |
}
|
deba@409
|
343 |
}
|
deba@409
|
344 |
|
deba@409
|
345 |
for (InArcIt a(_graph, n); a != INVALID; ++a) {
|
deba@409
|
346 |
Node v = _graph.source(a);
|
deba@409
|
347 |
if (_dormant[(*_bucket)[v]]) continue;
|
deba@409
|
348 |
Value rem = (*_flow)[a];
|
deba@409
|
349 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
350 |
if ((*_bucket)[v] == under_bucket) {
|
deba@409
|
351 |
if (!(*_active)[v] && v != target) {
|
deba@409
|
352 |
activate(v);
|
deba@409
|
353 |
}
|
deba@409
|
354 |
if (!_tolerance.less(rem, excess)) {
|
deba@409
|
355 |
_flow->set(a, (*_flow)[a] - excess);
|
deba@409
|
356 |
_excess->set(v, (*_excess)[v] + excess);
|
deba@409
|
357 |
excess = 0;
|
deba@409
|
358 |
goto no_more_push;
|
deba@409
|
359 |
} else {
|
deba@409
|
360 |
excess -= rem;
|
deba@409
|
361 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
362 |
_flow->set(a, 0);
|
deba@409
|
363 |
}
|
deba@409
|
364 |
} else if (next_bucket > (*_bucket)[v]) {
|
deba@409
|
365 |
next_bucket = (*_bucket)[v];
|
deba@409
|
366 |
}
|
deba@409
|
367 |
}
|
deba@409
|
368 |
|
deba@409
|
369 |
no_more_push:
|
deba@409
|
370 |
|
deba@409
|
371 |
_excess->set(n, excess);
|
deba@409
|
372 |
|
deba@409
|
373 |
if (excess != 0) {
|
deba@409
|
374 |
if ((*_next)[n] == INVALID) {
|
deba@409
|
375 |
typename std::list<std::list<int> >::iterator new_set =
|
deba@409
|
376 |
_sets.insert(--_sets.end(), std::list<int>());
|
deba@409
|
377 |
new_set->splice(new_set->end(), _sets.back(),
|
deba@409
|
378 |
_sets.back().begin(), ++_highest);
|
deba@409
|
379 |
for (std::list<int>::iterator it = new_set->begin();
|
deba@409
|
380 |
it != new_set->end(); ++it) {
|
deba@409
|
381 |
_dormant[*it] = true;
|
deba@409
|
382 |
}
|
deba@409
|
383 |
while (_highest != _sets.back().end() &&
|
deba@409
|
384 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
385 |
++_highest;
|
deba@409
|
386 |
}
|
deba@409
|
387 |
} else if (next_bucket == _node_num) {
|
deba@409
|
388 |
_first[(*_bucket)[n]] = (*_next)[n];
|
deba@409
|
389 |
_prev->set((*_next)[n], INVALID);
|
deba@409
|
390 |
|
deba@409
|
391 |
std::list<std::list<int> >::iterator new_set =
|
deba@409
|
392 |
_sets.insert(--_sets.end(), std::list<int>());
|
deba@409
|
393 |
|
deba@409
|
394 |
new_set->push_front(bucket_num);
|
deba@409
|
395 |
_bucket->set(n, bucket_num);
|
deba@409
|
396 |
_first[bucket_num] = _last[bucket_num] = n;
|
deba@409
|
397 |
_next->set(n, INVALID);
|
deba@409
|
398 |
_prev->set(n, INVALID);
|
deba@409
|
399 |
_dormant[bucket_num] = true;
|
deba@409
|
400 |
++bucket_num;
|
deba@409
|
401 |
|
deba@409
|
402 |
while (_highest != _sets.back().end() &&
|
deba@409
|
403 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
404 |
++_highest;
|
deba@409
|
405 |
}
|
deba@409
|
406 |
} else {
|
deba@409
|
407 |
_first[*_highest] = (*_next)[n];
|
deba@409
|
408 |
_prev->set((*_next)[n], INVALID);
|
deba@409
|
409 |
|
deba@409
|
410 |
while (next_bucket != *_highest) {
|
deba@409
|
411 |
--_highest;
|
deba@409
|
412 |
}
|
deba@409
|
413 |
|
deba@409
|
414 |
if (_highest == _sets.back().begin()) {
|
deba@409
|
415 |
_sets.back().push_front(bucket_num);
|
deba@409
|
416 |
_dormant[bucket_num] = false;
|
deba@409
|
417 |
_first[bucket_num] = _last[bucket_num] = INVALID;
|
deba@409
|
418 |
++bucket_num;
|
deba@409
|
419 |
}
|
deba@409
|
420 |
--_highest;
|
deba@409
|
421 |
|
deba@409
|
422 |
_bucket->set(n, *_highest);
|
deba@409
|
423 |
_next->set(n, _first[*_highest]);
|
deba@409
|
424 |
if (_first[*_highest] != INVALID) {
|
deba@409
|
425 |
_prev->set(_first[*_highest], n);
|
deba@409
|
426 |
} else {
|
deba@409
|
427 |
_last[*_highest] = n;
|
deba@409
|
428 |
}
|
deba@409
|
429 |
_first[*_highest] = n;
|
deba@409
|
430 |
}
|
deba@409
|
431 |
} else {
|
deba@409
|
432 |
|
deba@409
|
433 |
deactivate(n);
|
deba@409
|
434 |
if (!(*_active)[_first[*_highest]]) {
|
deba@409
|
435 |
++_highest;
|
deba@409
|
436 |
if (_highest != _sets.back().end() &&
|
deba@409
|
437 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
438 |
_highest = _sets.back().end();
|
deba@409
|
439 |
}
|
deba@409
|
440 |
}
|
deba@409
|
441 |
}
|
deba@409
|
442 |
}
|
deba@409
|
443 |
|
deba@409
|
444 |
if ((*_excess)[target] < _min_cut) {
|
deba@409
|
445 |
_min_cut = (*_excess)[target];
|
deba@409
|
446 |
for (NodeIt i(_graph); i != INVALID; ++i) {
|
deba@409
|
447 |
_min_cut_map->set(i, true);
|
deba@409
|
448 |
}
|
deba@409
|
449 |
for (std::list<int>::iterator it = _sets.back().begin();
|
deba@409
|
450 |
it != _sets.back().end(); ++it) {
|
deba@409
|
451 |
Node n = _first[*it];
|
deba@409
|
452 |
while (n != INVALID) {
|
deba@409
|
453 |
_min_cut_map->set(n, false);
|
deba@409
|
454 |
n = (*_next)[n];
|
deba@409
|
455 |
}
|
deba@409
|
456 |
}
|
deba@409
|
457 |
}
|
deba@409
|
458 |
|
deba@409
|
459 |
{
|
deba@409
|
460 |
Node new_target;
|
deba@409
|
461 |
if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
|
deba@409
|
462 |
if ((*_next)[target] == INVALID) {
|
deba@409
|
463 |
_last[(*_bucket)[target]] = (*_prev)[target];
|
deba@409
|
464 |
new_target = (*_prev)[target];
|
deba@409
|
465 |
} else {
|
deba@409
|
466 |
_prev->set((*_next)[target], (*_prev)[target]);
|
deba@409
|
467 |
new_target = (*_next)[target];
|
deba@409
|
468 |
}
|
deba@409
|
469 |
if ((*_prev)[target] == INVALID) {
|
deba@409
|
470 |
_first[(*_bucket)[target]] = (*_next)[target];
|
deba@409
|
471 |
} else {
|
deba@409
|
472 |
_next->set((*_prev)[target], (*_next)[target]);
|
deba@409
|
473 |
}
|
deba@409
|
474 |
} else {
|
deba@409
|
475 |
_sets.back().pop_back();
|
deba@409
|
476 |
if (_sets.back().empty()) {
|
deba@409
|
477 |
_sets.pop_back();
|
deba@409
|
478 |
if (_sets.empty())
|
deba@409
|
479 |
break;
|
deba@409
|
480 |
for (std::list<int>::iterator it = _sets.back().begin();
|
deba@409
|
481 |
it != _sets.back().end(); ++it) {
|
deba@409
|
482 |
_dormant[*it] = false;
|
deba@409
|
483 |
}
|
deba@409
|
484 |
}
|
deba@409
|
485 |
new_target = _last[_sets.back().back()];
|
deba@409
|
486 |
}
|
deba@409
|
487 |
|
deba@409
|
488 |
_bucket->set(target, 0);
|
deba@409
|
489 |
|
deba@409
|
490 |
_source_set->set(target, true);
|
deba@409
|
491 |
for (OutArcIt a(_graph, target); a != INVALID; ++a) {
|
deba@409
|
492 |
Value rem = (*_capacity)[a] - (*_flow)[a];
|
deba@409
|
493 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
494 |
Node v = _graph.target(a);
|
deba@409
|
495 |
if (!(*_active)[v] && !(*_source_set)[v]) {
|
deba@409
|
496 |
activate(v);
|
deba@409
|
497 |
}
|
deba@409
|
498 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
499 |
_flow->set(a, (*_capacity)[a]);
|
deba@409
|
500 |
}
|
deba@409
|
501 |
|
deba@409
|
502 |
for (InArcIt a(_graph, target); a != INVALID; ++a) {
|
deba@409
|
503 |
Value rem = (*_flow)[a];
|
deba@409
|
504 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
505 |
Node v = _graph.source(a);
|
deba@409
|
506 |
if (!(*_active)[v] && !(*_source_set)[v]) {
|
deba@409
|
507 |
activate(v);
|
deba@409
|
508 |
}
|
deba@409
|
509 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
510 |
_flow->set(a, 0);
|
deba@409
|
511 |
}
|
deba@409
|
512 |
|
deba@409
|
513 |
target = new_target;
|
deba@409
|
514 |
if ((*_active)[target]) {
|
deba@409
|
515 |
deactivate(target);
|
deba@409
|
516 |
}
|
deba@409
|
517 |
|
deba@409
|
518 |
_highest = _sets.back().begin();
|
deba@409
|
519 |
while (_highest != _sets.back().end() &&
|
deba@409
|
520 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
521 |
++_highest;
|
deba@409
|
522 |
}
|
deba@409
|
523 |
}
|
deba@409
|
524 |
}
|
deba@409
|
525 |
}
|
deba@409
|
526 |
|
deba@409
|
527 |
void findMinCutIn() {
|
deba@409
|
528 |
|
deba@409
|
529 |
for (NodeIt n(_graph); n != INVALID; ++n) {
|
deba@409
|
530 |
_excess->set(n, 0);
|
deba@409
|
531 |
}
|
deba@409
|
532 |
|
deba@409
|
533 |
for (ArcIt a(_graph); a != INVALID; ++a) {
|
deba@409
|
534 |
_flow->set(a, 0);
|
deba@409
|
535 |
}
|
deba@409
|
536 |
|
deba@409
|
537 |
int bucket_num = 1;
|
deba@409
|
538 |
|
deba@409
|
539 |
{
|
deba@409
|
540 |
typename Digraph::template NodeMap<bool> reached(_graph, false);
|
deba@409
|
541 |
|
deba@409
|
542 |
reached.set(_source, true);
|
deba@409
|
543 |
|
deba@409
|
544 |
bool first_set = true;
|
deba@409
|
545 |
|
deba@409
|
546 |
for (NodeIt t(_graph); t != INVALID; ++t) {
|
deba@409
|
547 |
if (reached[t]) continue;
|
deba@409
|
548 |
_sets.push_front(std::list<int>());
|
deba@409
|
549 |
_sets.front().push_front(bucket_num);
|
deba@409
|
550 |
_dormant[bucket_num] = !first_set;
|
deba@409
|
551 |
|
deba@409
|
552 |
_bucket->set(t, bucket_num);
|
deba@409
|
553 |
_first[bucket_num] = _last[bucket_num] = t;
|
deba@409
|
554 |
_next->set(t, INVALID);
|
deba@409
|
555 |
_prev->set(t, INVALID);
|
deba@409
|
556 |
|
deba@409
|
557 |
++bucket_num;
|
deba@409
|
558 |
|
deba@409
|
559 |
std::vector<Node> queue;
|
deba@409
|
560 |
queue.push_back(t);
|
deba@409
|
561 |
reached.set(t, true);
|
deba@409
|
562 |
|
deba@409
|
563 |
while (!queue.empty()) {
|
deba@409
|
564 |
_sets.front().push_front(bucket_num);
|
deba@409
|
565 |
_dormant[bucket_num] = !first_set;
|
deba@409
|
566 |
_first[bucket_num] = _last[bucket_num] = INVALID;
|
deba@409
|
567 |
|
deba@409
|
568 |
std::vector<Node> nqueue;
|
deba@409
|
569 |
for (int i = 0; i < int(queue.size()); ++i) {
|
deba@409
|
570 |
Node n = queue[i];
|
deba@409
|
571 |
for (OutArcIt a(_graph, n); a != INVALID; ++a) {
|
deba@409
|
572 |
Node u = _graph.target(a);
|
deba@409
|
573 |
if (!reached[u] && _tolerance.positive((*_capacity)[a])) {
|
deba@409
|
574 |
reached.set(u, true);
|
deba@409
|
575 |
addItem(u, bucket_num);
|
deba@409
|
576 |
nqueue.push_back(u);
|
deba@409
|
577 |
}
|
deba@409
|
578 |
}
|
deba@409
|
579 |
}
|
deba@409
|
580 |
queue.swap(nqueue);
|
deba@409
|
581 |
++bucket_num;
|
deba@409
|
582 |
}
|
deba@409
|
583 |
_sets.front().pop_front();
|
deba@409
|
584 |
--bucket_num;
|
deba@409
|
585 |
first_set = false;
|
deba@409
|
586 |
}
|
deba@409
|
587 |
|
deba@409
|
588 |
_bucket->set(_source, 0);
|
deba@409
|
589 |
_dormant[0] = true;
|
deba@409
|
590 |
}
|
deba@409
|
591 |
_source_set->set(_source, true);
|
deba@409
|
592 |
|
deba@409
|
593 |
Node target = _last[_sets.back().back()];
|
deba@409
|
594 |
{
|
deba@409
|
595 |
for (InArcIt a(_graph, _source); a != INVALID; ++a) {
|
deba@409
|
596 |
if (_tolerance.positive((*_capacity)[a])) {
|
deba@409
|
597 |
Node u = _graph.source(a);
|
deba@409
|
598 |
_flow->set(a, (*_capacity)[a]);
|
deba@409
|
599 |
_excess->set(u, (*_excess)[u] + (*_capacity)[a]);
|
deba@409
|
600 |
if (!(*_active)[u] && u != _source) {
|
deba@409
|
601 |
activate(u);
|
deba@409
|
602 |
}
|
deba@409
|
603 |
}
|
deba@409
|
604 |
}
|
deba@409
|
605 |
if ((*_active)[target]) {
|
deba@409
|
606 |
deactivate(target);
|
deba@409
|
607 |
}
|
deba@409
|
608 |
|
deba@409
|
609 |
_highest = _sets.back().begin();
|
deba@409
|
610 |
while (_highest != _sets.back().end() &&
|
deba@409
|
611 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
612 |
++_highest;
|
deba@409
|
613 |
}
|
deba@409
|
614 |
}
|
deba@409
|
615 |
|
deba@409
|
616 |
|
deba@409
|
617 |
while (true) {
|
deba@409
|
618 |
while (_highest != _sets.back().end()) {
|
deba@409
|
619 |
Node n = _first[*_highest];
|
deba@409
|
620 |
Value excess = (*_excess)[n];
|
deba@409
|
621 |
int next_bucket = _node_num;
|
deba@409
|
622 |
|
deba@409
|
623 |
int under_bucket;
|
deba@409
|
624 |
if (++std::list<int>::iterator(_highest) == _sets.back().end()) {
|
deba@409
|
625 |
under_bucket = -1;
|
deba@409
|
626 |
} else {
|
deba@409
|
627 |
under_bucket = *(++std::list<int>::iterator(_highest));
|
deba@409
|
628 |
}
|
deba@409
|
629 |
|
deba@409
|
630 |
for (InArcIt a(_graph, n); a != INVALID; ++a) {
|
deba@409
|
631 |
Node v = _graph.source(a);
|
deba@409
|
632 |
if (_dormant[(*_bucket)[v]]) continue;
|
deba@409
|
633 |
Value rem = (*_capacity)[a] - (*_flow)[a];
|
deba@409
|
634 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
635 |
if ((*_bucket)[v] == under_bucket) {
|
deba@409
|
636 |
if (!(*_active)[v] && v != target) {
|
deba@409
|
637 |
activate(v);
|
deba@409
|
638 |
}
|
deba@409
|
639 |
if (!_tolerance.less(rem, excess)) {
|
deba@409
|
640 |
_flow->set(a, (*_flow)[a] + excess);
|
deba@409
|
641 |
_excess->set(v, (*_excess)[v] + excess);
|
deba@409
|
642 |
excess = 0;
|
deba@409
|
643 |
goto no_more_push;
|
deba@409
|
644 |
} else {
|
deba@409
|
645 |
excess -= rem;
|
deba@409
|
646 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
647 |
_flow->set(a, (*_capacity)[a]);
|
deba@409
|
648 |
}
|
deba@409
|
649 |
} else if (next_bucket > (*_bucket)[v]) {
|
deba@409
|
650 |
next_bucket = (*_bucket)[v];
|
deba@409
|
651 |
}
|
deba@409
|
652 |
}
|
deba@409
|
653 |
|
deba@409
|
654 |
for (OutArcIt a(_graph, n); a != INVALID; ++a) {
|
deba@409
|
655 |
Node v = _graph.target(a);
|
deba@409
|
656 |
if (_dormant[(*_bucket)[v]]) continue;
|
deba@409
|
657 |
Value rem = (*_flow)[a];
|
deba@409
|
658 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
659 |
if ((*_bucket)[v] == under_bucket) {
|
deba@409
|
660 |
if (!(*_active)[v] && v != target) {
|
deba@409
|
661 |
activate(v);
|
deba@409
|
662 |
}
|
deba@409
|
663 |
if (!_tolerance.less(rem, excess)) {
|
deba@409
|
664 |
_flow->set(a, (*_flow)[a] - excess);
|
deba@409
|
665 |
_excess->set(v, (*_excess)[v] + excess);
|
deba@409
|
666 |
excess = 0;
|
deba@409
|
667 |
goto no_more_push;
|
deba@409
|
668 |
} else {
|
deba@409
|
669 |
excess -= rem;
|
deba@409
|
670 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
671 |
_flow->set(a, 0);
|
deba@409
|
672 |
}
|
deba@409
|
673 |
} else if (next_bucket > (*_bucket)[v]) {
|
deba@409
|
674 |
next_bucket = (*_bucket)[v];
|
deba@409
|
675 |
}
|
deba@409
|
676 |
}
|
deba@409
|
677 |
|
deba@409
|
678 |
no_more_push:
|
deba@409
|
679 |
|
deba@409
|
680 |
_excess->set(n, excess);
|
deba@409
|
681 |
|
deba@409
|
682 |
if (excess != 0) {
|
deba@409
|
683 |
if ((*_next)[n] == INVALID) {
|
deba@409
|
684 |
typename std::list<std::list<int> >::iterator new_set =
|
deba@409
|
685 |
_sets.insert(--_sets.end(), std::list<int>());
|
deba@409
|
686 |
new_set->splice(new_set->end(), _sets.back(),
|
deba@409
|
687 |
_sets.back().begin(), ++_highest);
|
deba@409
|
688 |
for (std::list<int>::iterator it = new_set->begin();
|
deba@409
|
689 |
it != new_set->end(); ++it) {
|
deba@409
|
690 |
_dormant[*it] = true;
|
deba@409
|
691 |
}
|
deba@409
|
692 |
while (_highest != _sets.back().end() &&
|
deba@409
|
693 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
694 |
++_highest;
|
deba@409
|
695 |
}
|
deba@409
|
696 |
} else if (next_bucket == _node_num) {
|
deba@409
|
697 |
_first[(*_bucket)[n]] = (*_next)[n];
|
deba@409
|
698 |
_prev->set((*_next)[n], INVALID);
|
deba@409
|
699 |
|
deba@409
|
700 |
std::list<std::list<int> >::iterator new_set =
|
deba@409
|
701 |
_sets.insert(--_sets.end(), std::list<int>());
|
deba@409
|
702 |
|
deba@409
|
703 |
new_set->push_front(bucket_num);
|
deba@409
|
704 |
_bucket->set(n, bucket_num);
|
deba@409
|
705 |
_first[bucket_num] = _last[bucket_num] = n;
|
deba@409
|
706 |
_next->set(n, INVALID);
|
deba@409
|
707 |
_prev->set(n, INVALID);
|
deba@409
|
708 |
_dormant[bucket_num] = true;
|
deba@409
|
709 |
++bucket_num;
|
deba@409
|
710 |
|
deba@409
|
711 |
while (_highest != _sets.back().end() &&
|
deba@409
|
712 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
713 |
++_highest;
|
deba@409
|
714 |
}
|
deba@409
|
715 |
} else {
|
deba@409
|
716 |
_first[*_highest] = (*_next)[n];
|
deba@409
|
717 |
_prev->set((*_next)[n], INVALID);
|
deba@409
|
718 |
|
deba@409
|
719 |
while (next_bucket != *_highest) {
|
deba@409
|
720 |
--_highest;
|
deba@409
|
721 |
}
|
deba@409
|
722 |
if (_highest == _sets.back().begin()) {
|
deba@409
|
723 |
_sets.back().push_front(bucket_num);
|
deba@409
|
724 |
_dormant[bucket_num] = false;
|
deba@409
|
725 |
_first[bucket_num] = _last[bucket_num] = INVALID;
|
deba@409
|
726 |
++bucket_num;
|
deba@409
|
727 |
}
|
deba@409
|
728 |
--_highest;
|
deba@409
|
729 |
|
deba@409
|
730 |
_bucket->set(n, *_highest);
|
deba@409
|
731 |
_next->set(n, _first[*_highest]);
|
deba@409
|
732 |
if (_first[*_highest] != INVALID) {
|
deba@409
|
733 |
_prev->set(_first[*_highest], n);
|
deba@409
|
734 |
} else {
|
deba@409
|
735 |
_last[*_highest] = n;
|
deba@409
|
736 |
}
|
deba@409
|
737 |
_first[*_highest] = n;
|
deba@409
|
738 |
}
|
deba@409
|
739 |
} else {
|
deba@409
|
740 |
|
deba@409
|
741 |
deactivate(n);
|
deba@409
|
742 |
if (!(*_active)[_first[*_highest]]) {
|
deba@409
|
743 |
++_highest;
|
deba@409
|
744 |
if (_highest != _sets.back().end() &&
|
deba@409
|
745 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
746 |
_highest = _sets.back().end();
|
deba@409
|
747 |
}
|
deba@409
|
748 |
}
|
deba@409
|
749 |
}
|
deba@409
|
750 |
}
|
deba@409
|
751 |
|
deba@409
|
752 |
if ((*_excess)[target] < _min_cut) {
|
deba@409
|
753 |
_min_cut = (*_excess)[target];
|
deba@409
|
754 |
for (NodeIt i(_graph); i != INVALID; ++i) {
|
deba@409
|
755 |
_min_cut_map->set(i, false);
|
deba@409
|
756 |
}
|
deba@409
|
757 |
for (std::list<int>::iterator it = _sets.back().begin();
|
deba@409
|
758 |
it != _sets.back().end(); ++it) {
|
deba@409
|
759 |
Node n = _first[*it];
|
deba@409
|
760 |
while (n != INVALID) {
|
deba@409
|
761 |
_min_cut_map->set(n, true);
|
deba@409
|
762 |
n = (*_next)[n];
|
deba@409
|
763 |
}
|
deba@409
|
764 |
}
|
deba@409
|
765 |
}
|
deba@409
|
766 |
|
deba@409
|
767 |
{
|
deba@409
|
768 |
Node new_target;
|
deba@409
|
769 |
if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {
|
deba@409
|
770 |
if ((*_next)[target] == INVALID) {
|
deba@409
|
771 |
_last[(*_bucket)[target]] = (*_prev)[target];
|
deba@409
|
772 |
new_target = (*_prev)[target];
|
deba@409
|
773 |
} else {
|
deba@409
|
774 |
_prev->set((*_next)[target], (*_prev)[target]);
|
deba@409
|
775 |
new_target = (*_next)[target];
|
deba@409
|
776 |
}
|
deba@409
|
777 |
if ((*_prev)[target] == INVALID) {
|
deba@409
|
778 |
_first[(*_bucket)[target]] = (*_next)[target];
|
deba@409
|
779 |
} else {
|
deba@409
|
780 |
_next->set((*_prev)[target], (*_next)[target]);
|
deba@409
|
781 |
}
|
deba@409
|
782 |
} else {
|
deba@409
|
783 |
_sets.back().pop_back();
|
deba@409
|
784 |
if (_sets.back().empty()) {
|
deba@409
|
785 |
_sets.pop_back();
|
deba@409
|
786 |
if (_sets.empty())
|
deba@409
|
787 |
break;
|
deba@409
|
788 |
for (std::list<int>::iterator it = _sets.back().begin();
|
deba@409
|
789 |
it != _sets.back().end(); ++it) {
|
deba@409
|
790 |
_dormant[*it] = false;
|
deba@409
|
791 |
}
|
deba@409
|
792 |
}
|
deba@409
|
793 |
new_target = _last[_sets.back().back()];
|
deba@409
|
794 |
}
|
deba@409
|
795 |
|
deba@409
|
796 |
_bucket->set(target, 0);
|
deba@409
|
797 |
|
deba@409
|
798 |
_source_set->set(target, true);
|
deba@409
|
799 |
for (InArcIt a(_graph, target); a != INVALID; ++a) {
|
deba@409
|
800 |
Value rem = (*_capacity)[a] - (*_flow)[a];
|
deba@409
|
801 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
802 |
Node v = _graph.source(a);
|
deba@409
|
803 |
if (!(*_active)[v] && !(*_source_set)[v]) {
|
deba@409
|
804 |
activate(v);
|
deba@409
|
805 |
}
|
deba@409
|
806 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
807 |
_flow->set(a, (*_capacity)[a]);
|
deba@409
|
808 |
}
|
deba@409
|
809 |
|
deba@409
|
810 |
for (OutArcIt a(_graph, target); a != INVALID; ++a) {
|
deba@409
|
811 |
Value rem = (*_flow)[a];
|
deba@409
|
812 |
if (!_tolerance.positive(rem)) continue;
|
deba@409
|
813 |
Node v = _graph.target(a);
|
deba@409
|
814 |
if (!(*_active)[v] && !(*_source_set)[v]) {
|
deba@409
|
815 |
activate(v);
|
deba@409
|
816 |
}
|
deba@409
|
817 |
_excess->set(v, (*_excess)[v] + rem);
|
deba@409
|
818 |
_flow->set(a, 0);
|
deba@409
|
819 |
}
|
deba@409
|
820 |
|
deba@409
|
821 |
target = new_target;
|
deba@409
|
822 |
if ((*_active)[target]) {
|
deba@409
|
823 |
deactivate(target);
|
deba@409
|
824 |
}
|
deba@409
|
825 |
|
deba@409
|
826 |
_highest = _sets.back().begin();
|
deba@409
|
827 |
while (_highest != _sets.back().end() &&
|
deba@409
|
828 |
!(*_active)[_first[*_highest]]) {
|
deba@409
|
829 |
++_highest;
|
deba@409
|
830 |
}
|
deba@409
|
831 |
}
|
deba@409
|
832 |
}
|
deba@409
|
833 |
}
|
deba@409
|
834 |
|
deba@409
|
835 |
public:
|
deba@409
|
836 |
|
deba@409
|
837 |
/// \name Execution control
|
deba@409
|
838 |
/// The simplest way to execute the algorithm is to use
|
deba@409
|
839 |
/// one of the member functions called \c run(...).
|
deba@409
|
840 |
/// \n
|
deba@409
|
841 |
/// If you need more control on the execution,
|
deba@409
|
842 |
/// first you must call \ref init(), then the \ref calculateIn() or
|
deba@409
|
843 |
/// \ref calculateIn() functions.
|
deba@409
|
844 |
|
deba@409
|
845 |
/// @{
|
deba@409
|
846 |
|
deba@409
|
847 |
/// \brief Initializes the internal data structures.
|
deba@409
|
848 |
///
|
deba@409
|
849 |
/// Initializes the internal data structures. It creates
|
deba@409
|
850 |
/// the maps, residual graph adaptors and some bucket structures
|
deba@409
|
851 |
/// for the algorithm.
|
deba@409
|
852 |
void init() {
|
deba@409
|
853 |
init(NodeIt(_graph));
|
deba@409
|
854 |
}
|
deba@409
|
855 |
|
deba@409
|
856 |
/// \brief Initializes the internal data structures.
|
deba@409
|
857 |
///
|
deba@409
|
858 |
/// Initializes the internal data structures. It creates
|
deba@409
|
859 |
/// the maps, residual graph adaptor and some bucket structures
|
deba@409
|
860 |
/// for the algorithm. Node \c source is used as the push-relabel
|
deba@409
|
861 |
/// algorithm's source.
|
deba@409
|
862 |
void init(const Node& source) {
|
deba@409
|
863 |
_source = source;
|
deba@409
|
864 |
|
deba@409
|
865 |
_node_num = countNodes(_graph);
|
deba@409
|
866 |
|
deba@409
|
867 |
_first.resize(_node_num + 1);
|
deba@409
|
868 |
_last.resize(_node_num + 1);
|
deba@409
|
869 |
|
deba@409
|
870 |
_dormant.resize(_node_num + 1);
|
deba@409
|
871 |
|
deba@409
|
872 |
if (!_flow) {
|
deba@409
|
873 |
_flow = new FlowMap(_graph);
|
deba@409
|
874 |
}
|
deba@409
|
875 |
if (!_next) {
|
deba@409
|
876 |
_next = new typename Digraph::template NodeMap<Node>(_graph);
|
deba@409
|
877 |
}
|
deba@409
|
878 |
if (!_prev) {
|
deba@409
|
879 |
_prev = new typename Digraph::template NodeMap<Node>(_graph);
|
deba@409
|
880 |
}
|
deba@409
|
881 |
if (!_active) {
|
deba@409
|
882 |
_active = new typename Digraph::template NodeMap<bool>(_graph);
|
deba@409
|
883 |
}
|
deba@409
|
884 |
if (!_bucket) {
|
deba@409
|
885 |
_bucket = new typename Digraph::template NodeMap<int>(_graph);
|
deba@409
|
886 |
}
|
deba@409
|
887 |
if (!_excess) {
|
deba@409
|
888 |
_excess = new ExcessMap(_graph);
|
deba@409
|
889 |
}
|
deba@409
|
890 |
if (!_source_set) {
|
deba@409
|
891 |
_source_set = new SourceSetMap(_graph);
|
deba@409
|
892 |
}
|
deba@409
|
893 |
if (!_min_cut_map) {
|
deba@409
|
894 |
_min_cut_map = new MinCutMap(_graph);
|
deba@409
|
895 |
}
|
deba@409
|
896 |
|
deba@409
|
897 |
_min_cut = std::numeric_limits<Value>::max();
|
deba@409
|
898 |
}
|
deba@409
|
899 |
|
deba@409
|
900 |
|
deba@409
|
901 |
/// \brief Calculates a minimum cut with \f$ source \f$ on the
|
deba@409
|
902 |
/// source-side.
|
deba@409
|
903 |
///
|
deba@409
|
904 |
/// Calculates a minimum cut with \f$ source \f$ on the
|
deba@409
|
905 |
/// source-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source
|
deba@409
|
906 |
/// \in X \f$ and minimal out-degree).
|
deba@409
|
907 |
void calculateOut() {
|
deba@409
|
908 |
findMinCutOut();
|
deba@409
|
909 |
}
|
deba@409
|
910 |
|
deba@409
|
911 |
/// \brief Calculates a minimum cut with \f$ source \f$ on the
|
deba@409
|
912 |
/// target-side.
|
deba@409
|
913 |
///
|
deba@409
|
914 |
/// Calculates a minimum cut with \f$ source \f$ on the
|
deba@409
|
915 |
/// target-side (i.e. a set \f$ X\subsetneq V \f$ with \f$ source
|
deba@409
|
916 |
/// \in X \f$ and minimal out-degree).
|
deba@409
|
917 |
void calculateIn() {
|
deba@409
|
918 |
findMinCutIn();
|
deba@409
|
919 |
}
|
deba@409
|
920 |
|
deba@409
|
921 |
|
deba@409
|
922 |
/// \brief Runs the algorithm.
|
deba@409
|
923 |
///
|
deba@409
|
924 |
/// Runs the algorithm. It finds nodes \c source and \c target
|
deba@409
|
925 |
/// arbitrarily and then calls \ref init(), \ref calculateOut()
|
deba@409
|
926 |
/// and \ref calculateIn().
|
deba@409
|
927 |
void run() {
|
deba@409
|
928 |
init();
|
deba@409
|
929 |
calculateOut();
|
deba@409
|
930 |
calculateIn();
|
deba@409
|
931 |
}
|
deba@409
|
932 |
|
deba@409
|
933 |
/// \brief Runs the algorithm.
|
deba@409
|
934 |
///
|
deba@409
|
935 |
/// Runs the algorithm. It uses the given \c source node, finds a
|
deba@409
|
936 |
/// proper \c target and then calls the \ref init(), \ref
|
deba@409
|
937 |
/// calculateOut() and \ref calculateIn().
|
deba@409
|
938 |
void run(const Node& s) {
|
deba@409
|
939 |
init(s);
|
deba@409
|
940 |
calculateOut();
|
deba@409
|
941 |
calculateIn();
|
deba@409
|
942 |
}
|
deba@409
|
943 |
|
deba@409
|
944 |
/// @}
|
deba@409
|
945 |
|
deba@409
|
946 |
/// \name Query Functions
|
deba@409
|
947 |
/// The result of the %HaoOrlin algorithm
|
deba@409
|
948 |
/// can be obtained using these functions.
|
deba@409
|
949 |
/// \n
|
deba@409
|
950 |
/// Before using these functions, either \ref run(), \ref
|
deba@409
|
951 |
/// calculateOut() or \ref calculateIn() must be called.
|
deba@409
|
952 |
|
deba@409
|
953 |
/// @{
|
deba@409
|
954 |
|
deba@409
|
955 |
/// \brief Returns the value of the minimum value cut.
|
deba@409
|
956 |
///
|
deba@409
|
957 |
/// Returns the value of the minimum value cut.
|
deba@409
|
958 |
Value minCutValue() const {
|
deba@409
|
959 |
return _min_cut;
|
deba@409
|
960 |
}
|
deba@409
|
961 |
|
deba@409
|
962 |
|
deba@409
|
963 |
/// \brief Returns a minimum cut.
|
deba@409
|
964 |
///
|
deba@409
|
965 |
/// Sets \c nodeMap to the characteristic vector of a minimum
|
deba@409
|
966 |
/// value cut: it will give a nonempty set \f$ X\subsetneq V \f$
|
deba@409
|
967 |
/// with minimal out-degree (i.e. \c nodeMap will be true exactly
|
deba@409
|
968 |
/// for the nodes of \f$ X \f$). \pre nodeMap should be a
|
deba@409
|
969 |
/// bool-valued node-map.
|
deba@409
|
970 |
template <typename NodeMap>
|
deba@409
|
971 |
Value minCutMap(NodeMap& nodeMap) const {
|
deba@409
|
972 |
for (NodeIt it(_graph); it != INVALID; ++it) {
|
deba@409
|
973 |
nodeMap.set(it, (*_min_cut_map)[it]);
|
deba@409
|
974 |
}
|
deba@409
|
975 |
return _min_cut;
|
deba@409
|
976 |
}
|
deba@409
|
977 |
|
deba@409
|
978 |
/// @}
|
deba@409
|
979 |
|
deba@409
|
980 |
}; //class HaoOrlin
|
deba@409
|
981 |
|
deba@409
|
982 |
|
deba@409
|
983 |
} //namespace lemon
|
deba@409
|
984 |
|
deba@409
|
985 |
#endif //LEMON_HAO_ORLIN_H
|