777 lines
23 KiB
C++
Executable File
777 lines
23 KiB
C++
Executable File
/* -*- 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_SUURBALLE_H
|
|
#define LEMON_SUURBALLE_H
|
|
|
|
///\ingroup shortest_path
|
|
///\file
|
|
///\brief An algorithm for finding arc-disjoint paths between two
|
|
/// nodes having minimum total length.
|
|
|
|
#include <vector>
|
|
#include <limits>
|
|
#include <lemon/bin_heap.h>
|
|
#include <lemon/path.h>
|
|
#include <lemon/list_graph.h>
|
|
#include <lemon/dijkstra.h>
|
|
#include <lemon/maps.h>
|
|
|
|
namespace lemon {
|
|
|
|
/// \brief Default traits class of Suurballe algorithm.
|
|
///
|
|
/// Default traits class of Suurballe algorithm.
|
|
/// \tparam GR The digraph type the algorithm runs on.
|
|
/// \tparam LEN The type of the length map.
|
|
/// The default value is <tt>GR::ArcMap<int></tt>.
|
|
#ifdef DOXYGEN
|
|
template <typename GR, typename LEN>
|
|
#else
|
|
template < typename GR,
|
|
typename LEN = typename GR::template ArcMap<int> >
|
|
#endif
|
|
struct SuurballeDefaultTraits
|
|
{
|
|
/// The type of the digraph.
|
|
typedef GR Digraph;
|
|
/// The type of the length map.
|
|
typedef LEN LengthMap;
|
|
/// The type of the lengths.
|
|
typedef typename LEN::Value Length;
|
|
/// The type of the flow map.
|
|
typedef typename GR::template ArcMap<int> FlowMap;
|
|
/// The type of the potential map.
|
|
typedef typename GR::template NodeMap<Length> PotentialMap;
|
|
|
|
/// \brief The path type
|
|
///
|
|
/// The type used for storing the found arc-disjoint paths.
|
|
/// It must conform to the \ref lemon::concepts::Path "Path" concept
|
|
/// and it must have an \c addBack() function.
|
|
typedef lemon::Path<Digraph> Path;
|
|
|
|
/// The cross reference type used for the heap.
|
|
typedef typename GR::template NodeMap<int> HeapCrossRef;
|
|
|
|
/// \brief The heap type used for internal Dijkstra computations.
|
|
///
|
|
/// The type of the heap used for internal Dijkstra computations.
|
|
/// It must conform to the \ref lemon::concepts::Heap "Heap" concept
|
|
/// and its priority type must be \c Length.
|
|
typedef BinHeap<Length, HeapCrossRef> Heap;
|
|
};
|
|
|
|
/// \addtogroup shortest_path
|
|
/// @{
|
|
|
|
/// \brief Algorithm for finding arc-disjoint paths between two nodes
|
|
/// having minimum total length.
|
|
///
|
|
/// \ref lemon::Suurballe "Suurballe" implements an algorithm for
|
|
/// finding arc-disjoint paths having minimum total length (cost)
|
|
/// from a given source node to a given target node in a digraph.
|
|
///
|
|
/// Note that this problem is a special case of the \ref min_cost_flow
|
|
/// "minimum cost flow problem". This implementation is actually an
|
|
/// efficient specialized version of the \ref CapacityScaling
|
|
/// "successive shortest path" algorithm directly for this problem.
|
|
/// Therefore this class provides query functions for flow values and
|
|
/// node potentials (the dual solution) just like the minimum cost flow
|
|
/// algorithms.
|
|
///
|
|
/// \tparam GR The digraph type the algorithm runs on.
|
|
/// \tparam LEN The type of the length map.
|
|
/// The default value is <tt>GR::ArcMap<int></tt>.
|
|
///
|
|
/// \warning Length values should be \e non-negative.
|
|
///
|
|
/// \note For finding \e node-disjoint paths, this algorithm can be used
|
|
/// along with the \ref SplitNodes adaptor.
|
|
#ifdef DOXYGEN
|
|
template <typename GR, typename LEN, typename TR>
|
|
#else
|
|
template < typename GR,
|
|
typename LEN = typename GR::template ArcMap<int>,
|
|
typename TR = SuurballeDefaultTraits<GR, LEN> >
|
|
#endif
|
|
class Suurballe
|
|
{
|
|
TEMPLATE_DIGRAPH_TYPEDEFS(GR);
|
|
|
|
typedef ConstMap<Arc, int> ConstArcMap;
|
|
typedef typename GR::template NodeMap<Arc> PredMap;
|
|
|
|
public:
|
|
|
|
/// The type of the digraph.
|
|
typedef typename TR::Digraph Digraph;
|
|
/// The type of the length map.
|
|
typedef typename TR::LengthMap LengthMap;
|
|
/// The type of the lengths.
|
|
typedef typename TR::Length Length;
|
|
|
|
/// The type of the flow map.
|
|
typedef typename TR::FlowMap FlowMap;
|
|
/// The type of the potential map.
|
|
typedef typename TR::PotentialMap PotentialMap;
|
|
/// The type of the path structures.
|
|
typedef typename TR::Path Path;
|
|
/// The cross reference type used for the heap.
|
|
typedef typename TR::HeapCrossRef HeapCrossRef;
|
|
/// The heap type used for internal Dijkstra computations.
|
|
typedef typename TR::Heap Heap;
|
|
|
|
/// The \ref lemon::SuurballeDefaultTraits "traits class" of the algorithm.
|
|
typedef TR Traits;
|
|
|
|
private:
|
|
|
|
// ResidualDijkstra is a special implementation of the
|
|
// Dijkstra algorithm for finding shortest paths in the
|
|
// residual network with respect to the reduced arc lengths
|
|
// and modifying the node potentials according to the
|
|
// distance of the nodes.
|
|
class ResidualDijkstra
|
|
{
|
|
private:
|
|
|
|
const Digraph &_graph;
|
|
const LengthMap &_length;
|
|
const FlowMap &_flow;
|
|
PotentialMap &_pi;
|
|
PredMap &_pred;
|
|
Node _s;
|
|
Node _t;
|
|
|
|
PotentialMap _dist;
|
|
std::vector<Node> _proc_nodes;
|
|
|
|
public:
|
|
|
|
// Constructor
|
|
ResidualDijkstra(Suurballe &srb) :
|
|
_graph(srb._graph), _length(srb._length),
|
|
_flow(*srb._flow), _pi(*srb._potential), _pred(srb._pred),
|
|
_s(srb._s), _t(srb._t), _dist(_graph) {}
|
|
|
|
// Run the algorithm and return true if a path is found
|
|
// from the source node to the target node.
|
|
bool run(int cnt) {
|
|
return cnt == 0 ? startFirst() : start();
|
|
}
|
|
|
|
private:
|
|
|
|
// Execute the algorithm for the first time (the flow and potential
|
|
// functions have to be identically zero).
|
|
bool startFirst() {
|
|
HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
|
|
Heap heap(heap_cross_ref);
|
|
heap.push(_s, 0);
|
|
_pred[_s] = INVALID;
|
|
_proc_nodes.clear();
|
|
|
|
// Process nodes
|
|
while (!heap.empty() && heap.top() != _t) {
|
|
Node u = heap.top(), v;
|
|
Length d = heap.prio(), dn;
|
|
_dist[u] = heap.prio();
|
|
_proc_nodes.push_back(u);
|
|
heap.pop();
|
|
|
|
// Traverse outgoing arcs
|
|
for (OutArcIt e(_graph, u); e != INVALID; ++e) {
|
|
v = _graph.target(e);
|
|
switch(heap.state(v)) {
|
|
case Heap::PRE_HEAP:
|
|
heap.push(v, d + _length[e]);
|
|
_pred[v] = e;
|
|
break;
|
|
case Heap::IN_HEAP:
|
|
dn = d + _length[e];
|
|
if (dn < heap[v]) {
|
|
heap.decrease(v, dn);
|
|
_pred[v] = e;
|
|
}
|
|
break;
|
|
case Heap::POST_HEAP:
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
if (heap.empty()) return false;
|
|
|
|
// Update potentials of processed nodes
|
|
Length t_dist = heap.prio();
|
|
for (int i = 0; i < int(_proc_nodes.size()); ++i)
|
|
_pi[_proc_nodes[i]] = _dist[_proc_nodes[i]] - t_dist;
|
|
return true;
|
|
}
|
|
|
|
// Execute the algorithm.
|
|
bool start() {
|
|
HeapCrossRef heap_cross_ref(_graph, Heap::PRE_HEAP);
|
|
Heap heap(heap_cross_ref);
|
|
heap.push(_s, 0);
|
|
_pred[_s] = INVALID;
|
|
_proc_nodes.clear();
|
|
|
|
// Process nodes
|
|
while (!heap.empty() && heap.top() != _t) {
|
|
Node u = heap.top(), v;
|
|
Length d = heap.prio() + _pi[u], dn;
|
|
_dist[u] = heap.prio();
|
|
_proc_nodes.push_back(u);
|
|
heap.pop();
|
|
|
|
// Traverse outgoing arcs
|
|
for (OutArcIt e(_graph, u); e != INVALID; ++e) {
|
|
if (_flow[e] == 0) {
|
|
v = _graph.target(e);
|
|
switch(heap.state(v)) {
|
|
case Heap::PRE_HEAP:
|
|
heap.push(v, d + _length[e] - _pi[v]);
|
|
_pred[v] = e;
|
|
break;
|
|
case Heap::IN_HEAP:
|
|
dn = d + _length[e] - _pi[v];
|
|
if (dn < heap[v]) {
|
|
heap.decrease(v, dn);
|
|
_pred[v] = e;
|
|
}
|
|
break;
|
|
case Heap::POST_HEAP:
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Traverse incoming arcs
|
|
for (InArcIt e(_graph, u); e != INVALID; ++e) {
|
|
if (_flow[e] == 1) {
|
|
v = _graph.source(e);
|
|
switch(heap.state(v)) {
|
|
case Heap::PRE_HEAP:
|
|
heap.push(v, d - _length[e] - _pi[v]);
|
|
_pred[v] = e;
|
|
break;
|
|
case Heap::IN_HEAP:
|
|
dn = d - _length[e] - _pi[v];
|
|
if (dn < heap[v]) {
|
|
heap.decrease(v, dn);
|
|
_pred[v] = e;
|
|
}
|
|
break;
|
|
case Heap::POST_HEAP:
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (heap.empty()) return false;
|
|
|
|
// Update potentials of processed nodes
|
|
Length t_dist = heap.prio();
|
|
for (int i = 0; i < int(_proc_nodes.size()); ++i)
|
|
_pi[_proc_nodes[i]] += _dist[_proc_nodes[i]] - t_dist;
|
|
return true;
|
|
}
|
|
|
|
}; //class ResidualDijkstra
|
|
|
|
public:
|
|
|
|
/// \name Named Template Parameters
|
|
/// @{
|
|
|
|
template <typename T>
|
|
struct SetFlowMapTraits : public Traits {
|
|
typedef T FlowMap;
|
|
};
|
|
|
|
/// \brief \ref named-templ-param "Named parameter" for setting
|
|
/// \c FlowMap type.
|
|
///
|
|
/// \ref named-templ-param "Named parameter" for setting
|
|
/// \c FlowMap type.
|
|
template <typename T>
|
|
struct SetFlowMap
|
|
: public Suurballe<GR, LEN, SetFlowMapTraits<T> > {
|
|
typedef Suurballe<GR, LEN, SetFlowMapTraits<T> > Create;
|
|
};
|
|
|
|
template <typename T>
|
|
struct SetPotentialMapTraits : public Traits {
|
|
typedef T PotentialMap;
|
|
};
|
|
|
|
/// \brief \ref named-templ-param "Named parameter" for setting
|
|
/// \c PotentialMap type.
|
|
///
|
|
/// \ref named-templ-param "Named parameter" for setting
|
|
/// \c PotentialMap type.
|
|
template <typename T>
|
|
struct SetPotentialMap
|
|
: public Suurballe<GR, LEN, SetPotentialMapTraits<T> > {
|
|
typedef Suurballe<GR, LEN, SetPotentialMapTraits<T> > Create;
|
|
};
|
|
|
|
template <typename T>
|
|
struct SetPathTraits : public Traits {
|
|
typedef T Path;
|
|
};
|
|
|
|
/// \brief \ref named-templ-param "Named parameter" for setting
|
|
/// \c %Path type.
|
|
///
|
|
/// \ref named-templ-param "Named parameter" for setting \c %Path type.
|
|
/// It must conform to the \ref lemon::concepts::Path "Path" concept
|
|
/// and it must have an \c addBack() function.
|
|
template <typename T>
|
|
struct SetPath
|
|
: public Suurballe<GR, LEN, SetPathTraits<T> > {
|
|
typedef Suurballe<GR, LEN, SetPathTraits<T> > Create;
|
|
};
|
|
|
|
template <typename H, typename CR>
|
|
struct SetHeapTraits : public Traits {
|
|
typedef H Heap;
|
|
typedef CR HeapCrossRef;
|
|
};
|
|
|
|
/// \brief \ref named-templ-param "Named parameter" for setting
|
|
/// \c Heap and \c HeapCrossRef types.
|
|
///
|
|
/// \ref named-templ-param "Named parameter" for setting \c Heap
|
|
/// and \c HeapCrossRef types with automatic allocation.
|
|
/// They will be used for internal Dijkstra computations.
|
|
/// The heap type must conform to the \ref lemon::concepts::Heap "Heap"
|
|
/// concept and its priority type must be \c Length.
|
|
template <typename H,
|
|
typename CR = typename Digraph::template NodeMap<int> >
|
|
struct SetHeap
|
|
: public Suurballe<GR, LEN, SetHeapTraits<H, CR> > {
|
|
typedef Suurballe<GR, LEN, SetHeapTraits<H, CR> > Create;
|
|
};
|
|
|
|
/// @}
|
|
|
|
private:
|
|
|
|
// The digraph the algorithm runs on
|
|
const Digraph &_graph;
|
|
// The length map
|
|
const LengthMap &_length;
|
|
|
|
// Arc map of the current flow
|
|
FlowMap *_flow;
|
|
bool _local_flow;
|
|
// Node map of the current potentials
|
|
PotentialMap *_potential;
|
|
bool _local_potential;
|
|
|
|
// The source node
|
|
Node _s;
|
|
// The target node
|
|
Node _t;
|
|
|
|
// Container to store the found paths
|
|
std::vector<Path> _paths;
|
|
int _path_num;
|
|
|
|
// The pred arc map
|
|
PredMap _pred;
|
|
|
|
// Data for full init
|
|
PotentialMap *_init_dist;
|
|
PredMap *_init_pred;
|
|
bool _full_init;
|
|
|
|
protected:
|
|
|
|
Suurballe() {}
|
|
|
|
public:
|
|
|
|
/// \brief Constructor.
|
|
///
|
|
/// Constructor.
|
|
///
|
|
/// \param graph The digraph the algorithm runs on.
|
|
/// \param length The length (cost) values of the arcs.
|
|
Suurballe( const Digraph &graph,
|
|
const LengthMap &length ) :
|
|
_graph(graph), _length(length), _flow(0), _local_flow(false),
|
|
_potential(0), _local_potential(false), _pred(graph),
|
|
_init_dist(0), _init_pred(0)
|
|
{}
|
|
|
|
/// Destructor.
|
|
~Suurballe() {
|
|
if (_local_flow) delete _flow;
|
|
if (_local_potential) delete _potential;
|
|
delete _init_dist;
|
|
delete _init_pred;
|
|
}
|
|
|
|
/// \brief Set the flow map.
|
|
///
|
|
/// This function sets the flow map.
|
|
/// If it is not used before calling \ref run() or \ref init(),
|
|
/// an instance will be allocated automatically. The destructor
|
|
/// deallocates this automatically allocated map, of course.
|
|
///
|
|
/// The found flow contains only 0 and 1 values, since it is the
|
|
/// union of the found arc-disjoint paths.
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
Suurballe& flowMap(FlowMap &map) {
|
|
if (_local_flow) {
|
|
delete _flow;
|
|
_local_flow = false;
|
|
}
|
|
_flow = ↦
|
|
return *this;
|
|
}
|
|
|
|
/// \brief Set the potential map.
|
|
///
|
|
/// This function sets the potential map.
|
|
/// If it is not used before calling \ref run() or \ref init(),
|
|
/// an instance will be allocated automatically. The destructor
|
|
/// deallocates this automatically allocated map, of course.
|
|
///
|
|
/// The node potentials provide the dual solution of the underlying
|
|
/// \ref min_cost_flow "minimum cost flow problem".
|
|
///
|
|
/// \return <tt>(*this)</tt>
|
|
Suurballe& potentialMap(PotentialMap &map) {
|
|
if (_local_potential) {
|
|
delete _potential;
|
|
_local_potential = false;
|
|
}
|
|
_potential = ↦
|
|
return *this;
|
|
}
|
|
|
|
/// \name Execution Control
|
|
/// The simplest way to execute the algorithm is to call the run()
|
|
/// function.\n
|
|
/// If you need to execute the algorithm many times using the same
|
|
/// source node, then you may call fullInit() once and start()
|
|
/// for each target node.\n
|
|
/// If you only need the flow that is the union of the found
|
|
/// arc-disjoint paths, then you may call findFlow() instead of
|
|
/// start().
|
|
|
|
/// @{
|
|
|
|
/// \brief Run the algorithm.
|
|
///
|
|
/// This function runs the algorithm.
|
|
///
|
|
/// \param s The source node.
|
|
/// \param t The target node.
|
|
/// \param k The number of paths to be found.
|
|
///
|
|
/// \return \c k if there are at least \c k arc-disjoint paths from
|
|
/// \c s to \c t in the digraph. Otherwise it returns the number of
|
|
/// arc-disjoint paths found.
|
|
///
|
|
/// \note Apart from the return value, <tt>s.run(s, t, k)</tt> is
|
|
/// just a shortcut of the following code.
|
|
/// \code
|
|
/// s.init(s);
|
|
/// s.start(t, k);
|
|
/// \endcode
|
|
int run(const Node& s, const Node& t, int k = 2) {
|
|
init(s);
|
|
start(t, k);
|
|
return _path_num;
|
|
}
|
|
|
|
/// \brief Initialize the algorithm.
|
|
///
|
|
/// This function initializes the algorithm with the given source node.
|
|
///
|
|
/// \param s The source node.
|
|
void init(const Node& s) {
|
|
_s = s;
|
|
|
|
// Initialize maps
|
|
if (!_flow) {
|
|
_flow = new FlowMap(_graph);
|
|
_local_flow = true;
|
|
}
|
|
if (!_potential) {
|
|
_potential = new PotentialMap(_graph);
|
|
_local_potential = true;
|
|
}
|
|
_full_init = false;
|
|
}
|
|
|
|
/// \brief Initialize the algorithm and perform Dijkstra.
|
|
///
|
|
/// This function initializes the algorithm and performs a full
|
|
/// Dijkstra search from the given source node. It makes consecutive
|
|
/// executions of \ref start() "start(t, k)" faster, since they
|
|
/// have to perform %Dijkstra only k-1 times.
|
|
///
|
|
/// This initialization is usually worth using instead of \ref init()
|
|
/// if the algorithm is executed many times using the same source node.
|
|
///
|
|
/// \param s The source node.
|
|
void fullInit(const Node& s) {
|
|
// Initialize maps
|
|
init(s);
|
|
if (!_init_dist) {
|
|
_init_dist = new PotentialMap(_graph);
|
|
}
|
|
if (!_init_pred) {
|
|
_init_pred = new PredMap(_graph);
|
|
}
|
|
|
|
// Run a full Dijkstra
|
|
typename Dijkstra<Digraph, LengthMap>
|
|
::template SetStandardHeap<Heap>
|
|
::template SetDistMap<PotentialMap>
|
|
::template SetPredMap<PredMap>
|
|
::Create dijk(_graph, _length);
|
|
dijk.distMap(*_init_dist).predMap(*_init_pred);
|
|
dijk.run(s);
|
|
|
|
_full_init = true;
|
|
}
|
|
|
|
/// \brief Execute the algorithm.
|
|
///
|
|
/// This function executes the algorithm.
|
|
///
|
|
/// \param t The target node.
|
|
/// \param k The number of paths to be found.
|
|
///
|
|
/// \return \c k if there are at least \c k arc-disjoint paths from
|
|
/// \c s to \c t in the digraph. Otherwise it returns the number of
|
|
/// arc-disjoint paths found.
|
|
///
|
|
/// \note Apart from the return value, <tt>s.start(t, k)</tt> is
|
|
/// just a shortcut of the following code.
|
|
/// \code
|
|
/// s.findFlow(t, k);
|
|
/// s.findPaths();
|
|
/// \endcode
|
|
int start(const Node& t, int k = 2) {
|
|
findFlow(t, k);
|
|
findPaths();
|
|
return _path_num;
|
|
}
|
|
|
|
/// \brief Execute the algorithm to find an optimal flow.
|
|
///
|
|
/// This function executes the successive shortest path algorithm to
|
|
/// find a minimum cost flow, which is the union of \c k (or less)
|
|
/// arc-disjoint paths.
|
|
///
|
|
/// \param t The target node.
|
|
/// \param k The number of paths to be found.
|
|
///
|
|
/// \return \c k if there are at least \c k arc-disjoint paths from
|
|
/// the source node to the given node \c t in the digraph.
|
|
/// Otherwise it returns the number of arc-disjoint paths found.
|
|
///
|
|
/// \pre \ref init() must be called before using this function.
|
|
int findFlow(const Node& t, int k = 2) {
|
|
_t = t;
|
|
ResidualDijkstra dijkstra(*this);
|
|
|
|
// Initialization
|
|
for (ArcIt e(_graph); e != INVALID; ++e) {
|
|
(*_flow)[e] = 0;
|
|
}
|
|
if (_full_init) {
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
(*_potential)[n] = (*_init_dist)[n];
|
|
}
|
|
Node u = _t;
|
|
Arc e;
|
|
while ((e = (*_init_pred)[u]) != INVALID) {
|
|
(*_flow)[e] = 1;
|
|
u = _graph.source(e);
|
|
}
|
|
_path_num = 1;
|
|
} else {
|
|
for (NodeIt n(_graph); n != INVALID; ++n) {
|
|
(*_potential)[n] = 0;
|
|
}
|
|
_path_num = 0;
|
|
}
|
|
|
|
// Find shortest paths
|
|
while (_path_num < k) {
|
|
// Run Dijkstra
|
|
if (!dijkstra.run(_path_num)) break;
|
|
++_path_num;
|
|
|
|
// Set the flow along the found shortest path
|
|
Node u = _t;
|
|
Arc e;
|
|
while ((e = _pred[u]) != INVALID) {
|
|
if (u == _graph.target(e)) {
|
|
(*_flow)[e] = 1;
|
|
u = _graph.source(e);
|
|
} else {
|
|
(*_flow)[e] = 0;
|
|
u = _graph.target(e);
|
|
}
|
|
}
|
|
}
|
|
return _path_num;
|
|
}
|
|
|
|
/// \brief Compute the paths from the flow.
|
|
///
|
|
/// This function computes arc-disjoint paths from the found minimum
|
|
/// cost flow, which is the union of them.
|
|
///
|
|
/// \pre \ref init() and \ref findFlow() must be called before using
|
|
/// this function.
|
|
void findPaths() {
|
|
FlowMap res_flow(_graph);
|
|
for(ArcIt a(_graph); a != INVALID; ++a) res_flow[a] = (*_flow)[a];
|
|
|
|
_paths.clear();
|
|
_paths.resize(_path_num);
|
|
for (int i = 0; i < _path_num; ++i) {
|
|
Node n = _s;
|
|
while (n != _t) {
|
|
OutArcIt e(_graph, n);
|
|
for ( ; res_flow[e] == 0; ++e) ;
|
|
n = _graph.target(e);
|
|
_paths[i].addBack(e);
|
|
res_flow[e] = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
/// @}
|
|
|
|
/// \name Query Functions
|
|
/// The results of the algorithm can be obtained using these
|
|
/// functions.
|
|
/// \n The algorithm should be executed before using them.
|
|
|
|
/// @{
|
|
|
|
/// \brief Return the total length of the found paths.
|
|
///
|
|
/// This function returns the total length of the found paths, i.e.
|
|
/// the total cost of the found flow.
|
|
/// The complexity of the function is O(m).
|
|
///
|
|
/// \pre \ref run() or \ref findFlow() must be called before using
|
|
/// this function.
|
|
Length totalLength() const {
|
|
Length c = 0;
|
|
for (ArcIt e(_graph); e != INVALID; ++e)
|
|
c += (*_flow)[e] * _length[e];
|
|
return c;
|
|
}
|
|
|
|
/// \brief Return the flow value on the given arc.
|
|
///
|
|
/// This function returns the flow value on the given arc.
|
|
/// It is \c 1 if the arc is involved in one of the found arc-disjoint
|
|
/// paths, otherwise it is \c 0.
|
|
///
|
|
/// \pre \ref run() or \ref findFlow() must be called before using
|
|
/// this function.
|
|
int flow(const Arc& arc) const {
|
|
return (*_flow)[arc];
|
|
}
|
|
|
|
/// \brief Return a const reference to an arc map storing the
|
|
/// found flow.
|
|
///
|
|
/// This function returns a const reference to an arc map storing
|
|
/// the flow that is the union of the found arc-disjoint paths.
|
|
///
|
|
/// \pre \ref run() or \ref findFlow() must be called before using
|
|
/// this function.
|
|
const FlowMap& flowMap() const {
|
|
return *_flow;
|
|
}
|
|
|
|
/// \brief Return the potential of the given node.
|
|
///
|
|
/// This function returns the potential of the given node.
|
|
/// The node potentials provide the dual solution of the
|
|
/// underlying \ref min_cost_flow "minimum cost flow problem".
|
|
///
|
|
/// \pre \ref run() or \ref findFlow() must be called before using
|
|
/// this function.
|
|
Length potential(const Node& node) const {
|
|
return (*_potential)[node];
|
|
}
|
|
|
|
/// \brief Return a const reference to a node map storing the
|
|
/// found potentials (the dual solution).
|
|
///
|
|
/// This function returns a const reference to a node map storing
|
|
/// the found potentials that provide the dual solution of the
|
|
/// underlying \ref min_cost_flow "minimum cost flow problem".
|
|
///
|
|
/// \pre \ref run() or \ref findFlow() must be called before using
|
|
/// this function.
|
|
const PotentialMap& potentialMap() const {
|
|
return *_potential;
|
|
}
|
|
|
|
/// \brief Return the number of the found paths.
|
|
///
|
|
/// This function returns the number of the found paths.
|
|
///
|
|
/// \pre \ref run() or \ref findFlow() must be called before using
|
|
/// this function.
|
|
int pathNum() const {
|
|
return _path_num;
|
|
}
|
|
|
|
/// \brief Return a const reference to the specified path.
|
|
///
|
|
/// This function returns a const reference to the specified path.
|
|
///
|
|
/// \param i The function returns the <tt>i</tt>-th path.
|
|
/// \c i must be between \c 0 and <tt>%pathNum()-1</tt>.
|
|
///
|
|
/// \pre \ref run() or \ref findPaths() must be called before using
|
|
/// this function.
|
|
const Path& path(int i) const {
|
|
return _paths[i];
|
|
}
|
|
|
|
/// @}
|
|
|
|
}; //class Suurballe
|
|
|
|
///@}
|
|
|
|
} //namespace lemon
|
|
|
|
#endif //LEMON_SUURBALLE_H
|