dust3d/thirdparty/QuadriFlow/3rd/lemon-1.3.1/lemon/nagamochi_ibaraki.h

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/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2013
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
* (Egervary Research Group on Combinatorial Optimization, EGRES).
*
* Permission to use, modify and distribute this software is granted
* provided that this copyright notice appears in all copies. For
* precise terms see the accompanying LICENSE file.
*
* This software is provided "AS IS" with no warranty of any kind,
* express or implied, and with no claim as to its suitability for any
* purpose.
*
*/
#ifndef LEMON_NAGAMOCHI_IBARAKI_H
#define LEMON_NAGAMOCHI_IBARAKI_H
/// \ingroup min_cut
/// \file
/// \brief Implementation of the Nagamochi-Ibaraki algorithm.
#include <lemon/core.h>
#include <lemon/bin_heap.h>
#include <lemon/bucket_heap.h>
#include <lemon/maps.h>
#include <lemon/radix_sort.h>
#include <lemon/unionfind.h>
#include <cassert>
namespace lemon {
/// \brief Default traits class for NagamochiIbaraki class.
///
/// Default traits class for NagamochiIbaraki class.
/// \param GR The undirected graph type.
/// \param CM Type of capacity map.
template <typename GR, typename CM>
struct NagamochiIbarakiDefaultTraits {
/// The type of the capacity map.
typedef typename CM::Value Value;
/// The undirected graph type the algorithm runs on.
typedef GR Graph;
/// \brief The type of the map that stores the edge capacities.
///
/// The type of the map that stores the edge capacities.
/// It must meet the \ref concepts::ReadMap "ReadMap" concept.
typedef CM CapacityMap;
/// \brief Instantiates a CapacityMap.
///
/// This function instantiates a \ref CapacityMap.
#ifdef DOXYGEN
static CapacityMap *createCapacityMap(const Graph& graph)
#else
static CapacityMap *createCapacityMap(const Graph&)
#endif
{
LEMON_ASSERT(false, "CapacityMap is not initialized");
return 0; // ignore warnings
}
/// \brief The cross reference type used by heap.
///
/// The cross reference type used by heap.
/// Usually \c Graph::NodeMap<int>.
typedef typename Graph::template NodeMap<int> HeapCrossRef;
/// \brief Instantiates a HeapCrossRef.
///
/// This function instantiates a \ref HeapCrossRef.
/// \param g is the graph, to which we would like to define the
/// \ref HeapCrossRef.
static HeapCrossRef *createHeapCrossRef(const Graph& g) {
return new HeapCrossRef(g);
}
/// \brief The heap type used by NagamochiIbaraki algorithm.
///
/// The heap type used by NagamochiIbaraki algorithm. It has to
/// maximize the priorities.
///
/// \sa BinHeap
/// \sa NagamochiIbaraki
typedef BinHeap<Value, HeapCrossRef, std::greater<Value> > Heap;
/// \brief Instantiates a Heap.
///
/// This function instantiates a \ref Heap.
/// \param r is the cross reference of the heap.
static Heap *createHeap(HeapCrossRef& r) {
return new Heap(r);
}
};
/// \ingroup min_cut
///
/// \brief Calculates the minimum cut in an undirected graph.
///
/// Calculates the minimum cut in an undirected graph with the
/// Nagamochi-Ibaraki algorithm. The algorithm separates the graph's
/// nodes into two partitions with the minimum sum of edge capacities
/// between the two partitions. The algorithm can be used to test
/// the network reliability, especially to test how many links have
/// to be destroyed in the network to split it to at least two
/// distinict subnetworks.
///
/// The complexity of the algorithm is \f$ O(nm\log(n)) \f$ but with
/// \ref FibHeap "Fibonacci heap" it can be decreased to
/// \f$ O(nm+n^2\log(n)) \f$. When the edges have unit capacities,
/// \c BucketHeap can be used which yields \f$ O(nm) \f$ time
/// complexity.
///
/// \warning The value type of the capacity map should be able to
/// hold any cut value of the graph, otherwise the result can
/// overflow.
/// \note This capacity is supposed to be integer type.
#ifdef DOXYGEN
template <typename GR, typename CM, typename TR>
#else
template <typename GR,
typename CM = typename GR::template EdgeMap<int>,
typename TR = NagamochiIbarakiDefaultTraits<GR, CM> >
#endif
class NagamochiIbaraki {
public:
typedef TR Traits;
/// The type of the underlying graph.
typedef typename Traits::Graph Graph;
/// The type of the capacity map.
typedef typename Traits::CapacityMap CapacityMap;
/// The value type of the capacity map.
typedef typename Traits::CapacityMap::Value Value;
/// The heap type used by the algorithm.
typedef typename Traits::Heap Heap;
/// The cross reference type used for the heap.
typedef typename Traits::HeapCrossRef HeapCrossRef;
///\name Named template parameters
///@{
struct SetUnitCapacityTraits : public Traits {
typedef ConstMap<typename Graph::Edge, Const<int, 1> > CapacityMap;
static CapacityMap *createCapacityMap(const Graph&) {
return new CapacityMap();
}
};
/// \brief \ref named-templ-param "Named parameter" for setting
/// the capacity map to a constMap<Edge, int, 1>() instance
///
/// \ref named-templ-param "Named parameter" for setting
/// the capacity map to a constMap<Edge, int, 1>() instance
struct SetUnitCapacity
: public NagamochiIbaraki<Graph, CapacityMap,
SetUnitCapacityTraits> {
typedef NagamochiIbaraki<Graph, CapacityMap,
SetUnitCapacityTraits> Create;
};
template <class H, class CR>
struct SetHeapTraits : public Traits {
typedef CR HeapCrossRef;
typedef H Heap;
static HeapCrossRef *createHeapCrossRef(int num) {
LEMON_ASSERT(false, "HeapCrossRef is not initialized");
return 0; // ignore warnings
}
static Heap *createHeap(HeapCrossRef &) {
LEMON_ASSERT(false, "Heap is not initialized");
return 0; // ignore warnings
}
};
/// \brief \ref named-templ-param "Named parameter" for setting
/// heap and cross reference type
///
/// \ref named-templ-param "Named parameter" for setting heap and
/// cross reference type. The heap has to maximize the priorities.
template <class H, class CR = RangeMap<int> >
struct SetHeap
: public NagamochiIbaraki<Graph, CapacityMap, SetHeapTraits<H, CR> > {
typedef NagamochiIbaraki< Graph, CapacityMap, SetHeapTraits<H, CR> >
Create;
};
template <class H, class CR>
struct SetStandardHeapTraits : public Traits {
typedef CR HeapCrossRef;
typedef H Heap;
static HeapCrossRef *createHeapCrossRef(int size) {
return new HeapCrossRef(size);
}
static Heap *createHeap(HeapCrossRef &crossref) {
return new Heap(crossref);
}
};
/// \brief \ref named-templ-param "Named parameter" for setting
/// heap and cross reference type with automatic allocation
///
/// \ref named-templ-param "Named parameter" for setting heap and
/// cross reference type with automatic allocation. They should
/// have standard constructor interfaces to be able to
/// automatically created by the algorithm (i.e. the graph should
/// be passed to the constructor of the cross reference and the
/// cross reference should be passed to the constructor of the
/// heap). However, external heap and cross reference objects
/// could also be passed to the algorithm using the \ref heap()
/// function before calling \ref run() or \ref init(). The heap
/// has to maximize the priorities.
/// \sa SetHeap
template <class H, class CR = RangeMap<int> >
struct SetStandardHeap
: public NagamochiIbaraki<Graph, CapacityMap,
SetStandardHeapTraits<H, CR> > {
typedef NagamochiIbaraki<Graph, CapacityMap,
SetStandardHeapTraits<H, CR> > Create;
};
///@}
private:
const Graph &_graph;
const CapacityMap *_capacity;
bool _local_capacity; // unit capacity
struct ArcData {
typename Graph::Node target;
int prev, next;
};
struct EdgeData {
Value capacity;
Value cut;
};
struct NodeData {
int first_arc;
typename Graph::Node prev, next;
int curr_arc;
typename Graph::Node last_rep;
Value sum;
};
typename Graph::template NodeMap<NodeData> *_nodes;
std::vector<ArcData> _arcs;
std::vector<EdgeData> _edges;
typename Graph::Node _first_node;
int _node_num;
Value _min_cut;
HeapCrossRef *_heap_cross_ref;
bool _local_heap_cross_ref;
Heap *_heap;
bool _local_heap;
typedef typename Graph::template NodeMap<typename Graph::Node> NodeList;
NodeList *_next_rep;
typedef typename Graph::template NodeMap<bool> MinCutMap;
MinCutMap *_cut_map;
void createStructures() {
if (!_nodes) {
_nodes = new (typename Graph::template NodeMap<NodeData>)(_graph);
}
if (!_capacity) {
_local_capacity = true;
_capacity = Traits::createCapacityMap(_graph);
}
if (!_heap_cross_ref) {
_local_heap_cross_ref = true;
_heap_cross_ref = Traits::createHeapCrossRef(_graph);
}
if (!_heap) {
_local_heap = true;
_heap = Traits::createHeap(*_heap_cross_ref);
}
if (!_next_rep) {
_next_rep = new NodeList(_graph);
}
if (!_cut_map) {
_cut_map = new MinCutMap(_graph);
}
}
protected:
//This is here to avoid a gcc-3.3 compilation error.
//It should never be called.
NagamochiIbaraki() {}
public:
typedef NagamochiIbaraki Create;
/// \brief Constructor.
///
/// \param graph The graph the algorithm runs on.
/// \param capacity The capacity map used by the algorithm.
NagamochiIbaraki(const Graph& graph, const CapacityMap& capacity)
: _graph(graph), _capacity(&capacity), _local_capacity(false),
_nodes(0), _arcs(), _edges(), _min_cut(),
_heap_cross_ref(0), _local_heap_cross_ref(false),
_heap(0), _local_heap(false),
_next_rep(0), _cut_map(0) {}
/// \brief Constructor.
///
/// This constructor can be used only when the Traits class
/// defines how can the local capacity map be instantiated.
/// If the SetUnitCapacity used the algorithm automatically
/// constructs the capacity map.
///
///\param graph The graph the algorithm runs on.
NagamochiIbaraki(const Graph& graph)
: _graph(graph), _capacity(0), _local_capacity(false),
_nodes(0), _arcs(), _edges(), _min_cut(),
_heap_cross_ref(0), _local_heap_cross_ref(false),
_heap(0), _local_heap(false),
_next_rep(0), _cut_map(0) {}
/// \brief Destructor.
///
/// Destructor.
~NagamochiIbaraki() {
if (_local_capacity) delete _capacity;
if (_nodes) delete _nodes;
if (_local_heap) delete _heap;
if (_local_heap_cross_ref) delete _heap_cross_ref;
if (_next_rep) delete _next_rep;
if (_cut_map) delete _cut_map;
}
/// \brief Sets the heap and the cross reference used by algorithm.
///
/// Sets the heap and the cross reference used by algorithm.
/// If you don't use this function before calling \ref run(),
/// it will allocate one. The destuctor deallocates this
/// automatically allocated heap and cross reference, of course.
/// \return <tt> (*this) </tt>
NagamochiIbaraki &heap(Heap& hp, HeapCrossRef &cr)
{
if (_local_heap_cross_ref) {
delete _heap_cross_ref;
_local_heap_cross_ref = false;
}
_heap_cross_ref = &cr;
if (_local_heap) {
delete _heap;
_local_heap = false;
}
_heap = &hp;
return *this;
}
/// \name Execution control
/// The simplest way to execute the algorithm is to use
/// one of the member functions called \c run().
/// \n
/// If you need more control on the execution,
/// first you must call \ref init() and then call the start()
/// or proper times the processNextPhase() member functions.
///@{
/// \brief Initializes the internal data structures.
///
/// Initializes the internal data structures.
void init() {
createStructures();
int edge_num = countEdges(_graph);
_edges.resize(edge_num);
_arcs.resize(2 * edge_num);
typename Graph::Node prev = INVALID;
_node_num = 0;
for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
(*_cut_map)[n] = false;
(*_next_rep)[n] = INVALID;
(*_nodes)[n].last_rep = n;
(*_nodes)[n].first_arc = -1;
(*_nodes)[n].curr_arc = -1;
(*_nodes)[n].prev = prev;
if (prev != INVALID) {
(*_nodes)[prev].next = n;
}
(*_nodes)[n].next = INVALID;
(*_nodes)[n].sum = 0;
prev = n;
++_node_num;
}
_first_node = typename Graph::NodeIt(_graph);
int index = 0;
for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
for (typename Graph::OutArcIt a(_graph, n); a != INVALID; ++a) {
typename Graph::Node m = _graph.target(a);
if (!(n < m)) continue;
(*_nodes)[n].sum += (*_capacity)[a];
(*_nodes)[m].sum += (*_capacity)[a];
int c = (*_nodes)[m].curr_arc;
if (c != -1 && _arcs[c ^ 1].target == n) {
_edges[c >> 1].capacity += (*_capacity)[a];
} else {
_edges[index].capacity = (*_capacity)[a];
_arcs[index << 1].prev = -1;
if ((*_nodes)[n].first_arc != -1) {
_arcs[(*_nodes)[n].first_arc].prev = (index << 1);
}
_arcs[index << 1].next = (*_nodes)[n].first_arc;
(*_nodes)[n].first_arc = (index << 1);
_arcs[index << 1].target = m;
(*_nodes)[m].curr_arc = (index << 1);
_arcs[(index << 1) | 1].prev = -1;
if ((*_nodes)[m].first_arc != -1) {
_arcs[(*_nodes)[m].first_arc].prev = ((index << 1) | 1);
}
_arcs[(index << 1) | 1].next = (*_nodes)[m].first_arc;
(*_nodes)[m].first_arc = ((index << 1) | 1);
_arcs[(index << 1) | 1].target = n;
++index;
}
}
}
typename Graph::Node cut_node = INVALID;
_min_cut = std::numeric_limits<Value>::max();
for (typename Graph::Node n = _first_node;
n != INVALID; n = (*_nodes)[n].next) {
if ((*_nodes)[n].sum < _min_cut) {
cut_node = n;
_min_cut = (*_nodes)[n].sum;
}
}
(*_cut_map)[cut_node] = true;
if (_min_cut == 0) {
_first_node = INVALID;
}
}
public:
/// \brief Processes the next phase
///
/// Processes the next phase in the algorithm. It must be called
/// at most one less the number of the nodes in the graph.
///
///\return %True when the algorithm finished.
bool processNextPhase() {
if (_first_node == INVALID) return true;
_heap->clear();
for (typename Graph::Node n = _first_node;
n != INVALID; n = (*_nodes)[n].next) {
(*_heap_cross_ref)[n] = Heap::PRE_HEAP;
}
std::vector<typename Graph::Node> order;
order.reserve(_node_num);
int sep = 0;
Value alpha = 0;
Value pmc = std::numeric_limits<Value>::max();
_heap->push(_first_node, static_cast<Value>(0));
while (!_heap->empty()) {
typename Graph::Node n = _heap->top();
Value v = _heap->prio();
_heap->pop();
for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
switch (_heap->state(_arcs[a].target)) {
case Heap::PRE_HEAP:
{
Value nv = _edges[a >> 1].capacity;
_heap->push(_arcs[a].target, nv);
_edges[a >> 1].cut = nv;
} break;
case Heap::IN_HEAP:
{
Value nv = _edges[a >> 1].capacity + (*_heap)[_arcs[a].target];
_heap->decrease(_arcs[a].target, nv);
_edges[a >> 1].cut = nv;
} break;
case Heap::POST_HEAP:
break;
}
}
alpha += (*_nodes)[n].sum;
alpha -= 2 * v;
order.push_back(n);
if (!_heap->empty()) {
if (alpha < pmc) {
pmc = alpha;
sep = order.size();
}
}
}
if (static_cast<int>(order.size()) < _node_num) {
_first_node = INVALID;
for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
(*_cut_map)[n] = false;
}
for (int i = 0; i < static_cast<int>(order.size()); ++i) {
typename Graph::Node n = order[i];
while (n != INVALID) {
(*_cut_map)[n] = true;
n = (*_next_rep)[n];
}
}
_min_cut = 0;
return true;
}
if (pmc < _min_cut) {
for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
(*_cut_map)[n] = false;
}
for (int i = 0; i < sep; ++i) {
typename Graph::Node n = order[i];
while (n != INVALID) {
(*_cut_map)[n] = true;
n = (*_next_rep)[n];
}
}
_min_cut = pmc;
}
for (typename Graph::Node n = _first_node;
n != INVALID; n = (*_nodes)[n].next) {
bool merged = false;
for (int a = (*_nodes)[n].first_arc; a != -1; a = _arcs[a].next) {
if (!(_edges[a >> 1].cut < pmc)) {
if (!merged) {
for (int b = (*_nodes)[n].first_arc; b != -1; b = _arcs[b].next) {
(*_nodes)[_arcs[b].target].curr_arc = b;
}
merged = true;
}
typename Graph::Node m = _arcs[a].target;
int nb = 0;
for (int b = (*_nodes)[m].first_arc; b != -1; b = nb) {
nb = _arcs[b].next;
if ((b ^ a) == 1) continue;
typename Graph::Node o = _arcs[b].target;
int c = (*_nodes)[o].curr_arc;
if (c != -1 && _arcs[c ^ 1].target == n) {
_edges[c >> 1].capacity += _edges[b >> 1].capacity;
(*_nodes)[n].sum += _edges[b >> 1].capacity;
if (_edges[b >> 1].cut < _edges[c >> 1].cut) {
_edges[b >> 1].cut = _edges[c >> 1].cut;
}
if (_arcs[b ^ 1].prev != -1) {
_arcs[_arcs[b ^ 1].prev].next = _arcs[b ^ 1].next;
} else {
(*_nodes)[o].first_arc = _arcs[b ^ 1].next;
}
if (_arcs[b ^ 1].next != -1) {
_arcs[_arcs[b ^ 1].next].prev = _arcs[b ^ 1].prev;
}
} else {
if (_arcs[a].next != -1) {
_arcs[_arcs[a].next].prev = b;
}
_arcs[b].next = _arcs[a].next;
_arcs[b].prev = a;
_arcs[a].next = b;
_arcs[b ^ 1].target = n;
(*_nodes)[n].sum += _edges[b >> 1].capacity;
(*_nodes)[o].curr_arc = b;
}
}
if (_arcs[a].prev != -1) {
_arcs[_arcs[a].prev].next = _arcs[a].next;
} else {
(*_nodes)[n].first_arc = _arcs[a].next;
}
if (_arcs[a].next != -1) {
_arcs[_arcs[a].next].prev = _arcs[a].prev;
}
(*_nodes)[n].sum -= _edges[a >> 1].capacity;
(*_next_rep)[(*_nodes)[n].last_rep] = m;
(*_nodes)[n].last_rep = (*_nodes)[m].last_rep;
if ((*_nodes)[m].prev != INVALID) {
(*_nodes)[(*_nodes)[m].prev].next = (*_nodes)[m].next;
} else{
_first_node = (*_nodes)[m].next;
}
if ((*_nodes)[m].next != INVALID) {
(*_nodes)[(*_nodes)[m].next].prev = (*_nodes)[m].prev;
}
--_node_num;
}
}
}
if (_node_num == 1) {
_first_node = INVALID;
return true;
}
return false;
}
/// \brief Executes the algorithm.
///
/// Executes the algorithm.
///
/// \pre init() must be called
void start() {
while (!processNextPhase()) {}
}
/// \brief Runs %NagamochiIbaraki algorithm.
///
/// This method runs the %Min cut algorithm
///
/// \note mc.run(s) is just a shortcut of the following code.
///\code
/// mc.init();
/// mc.start();
///\endcode
void run() {
init();
start();
}
///@}
/// \name Query Functions
///
/// The result of the %NagamochiIbaraki
/// algorithm can be obtained using these functions.\n
/// Before the use of these functions, either run() or start()
/// must be called.
///@{
/// \brief Returns the min cut value.
///
/// Returns the min cut value if the algorithm finished.
/// After the first processNextPhase() it is a value of a
/// valid cut in the graph.
Value minCutValue() const {
return _min_cut;
}
/// \brief Returns a min cut in a NodeMap.
///
/// It sets the nodes of one of the two partitions to true and
/// the other partition to false.
/// \param cutMap A \ref concepts::WriteMap "writable" node map with
/// \c bool (or convertible) value type.
template <typename CutMap>
Value minCutMap(CutMap& cutMap) const {
for (typename Graph::NodeIt n(_graph); n != INVALID; ++n) {
cutMap.set(n, (*_cut_map)[n]);
}
return minCutValue();
}
///@}
};
}
#endif