Dijkstra< GR, LEN, TR > Class Template Reference

Detailed Description

template<typename GR, typename LEN, typename TR>
class lemon::Dijkstra< GR, LEN, TR >

This class provides an efficient implementation of the Dijkstra algorithm.

The Dijkstra algorithm solves the single-source shortest path problem when all arc lengths are non-negative. If there are negative lengths, the BellmanFord algorithm should be used instead.

The arc lengths are passed to the algorithm using a ReadMap, so it is easy to change it to any kind of length. The type of the length is determined by the Value of the length map. It is also possible to change the underlying priority heap.

There is also a function-type interface for the Dijkstra algorithm, which is convenient in the simplier cases and it can be used easier.

Template Parameters

GR	The type of the digraph the algorithm runs on. The default type is ListDigraph.
LEN	A readable arc map that specifies the lengths of the arcs. It is read once for each arc, so the map may involve in relatively time consuming process to compute the arc lengths if it is necessary. The default map type is GR::ArcMap<int>.
TR	The traits class that defines various types used by the algorithm. By default, it is DijkstraDefaultTraits<GR, LEN>. In most cases, this parameter should not be set directly, consider to use the named template parameters instead.

#include <lemon/dijkstra.h>

Classes
struct	SetDistMap
	Named parameter for setting DistMap type. More...
struct	SetHeap
	Named parameter for setting heap and cross reference types More...
struct	SetOperationTraits
	Named parameter for setting OperationTraits type More...
struct	SetPredMap
	Named parameter for setting PredMap type. More...
struct	SetProcessedMap
	Named parameter for setting ProcessedMap type. More...
struct	SetStandardHeap
	Named parameter for setting heap and cross reference types with automatic allocation More...
struct	SetStandardProcessedMap
	Named parameter for setting ProcessedMap type to be Digraph::NodeMap<bool>. More...

Public Types
typedef TR::Digraph	Digraph
	The type of the digraph the algorithm runs on.
typedef TR::Value	Value
	The type of the arc lengths.
typedef TR::LengthMap	LengthMap
	The type of the map that stores the arc lengths.
typedef TR::PredMap	PredMap
	The type of the map that stores the predecessor arcs of the shortest paths.
typedef TR::DistMap	DistMap
	The type of the map that stores the distances of the nodes.
typedef TR::ProcessedMap	ProcessedMap
	The type of the map that indicates which nodes are processed.
typedef PredMapPath< Digraph, PredMap >	Path
	The type of the paths.
typedef TR::HeapCrossRef	HeapCrossRef
	The cross reference type used for the current heap.
typedef TR::Heap	Heap
	The heap type used by the algorithm.
typedef TR::OperationTraits	OperationTraits
	The operation traits class of the algorithm.
typedef TR	Traits
	The traits class of the algorithm.

Public Member Functions
	Dijkstra (const Digraph &g, const LengthMap &length)
	Constructor.
	~Dijkstra ()
	Destructor.
Dijkstra &	lengthMap (const LengthMap &m)
	Sets the length map.
Dijkstra &	predMap (PredMap &m)
	Sets the map that stores the predecessor arcs.
Dijkstra &	processedMap (ProcessedMap &m)
	Sets the map that indicates which nodes are processed.
Dijkstra &	distMap (DistMap &m)
	Sets the map that stores the distances of the nodes.
Dijkstra &	heap (Heap &hp, HeapCrossRef &cr)
	Sets the heap and the cross reference used by algorithm.
Execution Control
The simplest way to execute the Dijkstra algorithm is to use one of the member functions called run(). If you need better control on the execution, you have to call init() first, then you can add several source nodes with addSource(). Finally the actual path computation can be performed with one of the start() functions.
void	init ()
void	addSource (Node s, Value dst=OperationTraits::zero())
	Adds a new source node.
Node	processNextNode ()
	Processes the next node in the priority heap.
Node	nextNode () const
	The next node to be processed.
bool	emptyQueue () const
	Returns false if there are nodes to be processed.
int	queueSize () const
	Returns the number of the nodes to be processed.
void	start ()
	Executes the algorithm.
void	start (Node t)
	Executes the algorithm until the given target node is processed.
template<class NodeBoolMap >
Node	start (const NodeBoolMap &nm)
	Executes the algorithm until a condition is met.
void	run (Node s)
	Runs the algorithm from the given source node.
bool	run (Node s, Node t)
	Finds the shortest path between s and t.
Query Functions
The results of the Dijkstra algorithm can be obtained using these functions. Either run() or init() should be called before using them.
Path	path (Node t) const
	The shortest path to the given node.
Value	dist (Node v) const
	The distance of the given node from the root(s).
Arc	predArc (Node v) const
	Returns the 'previous arc' of the shortest path tree for the given node.
Node	predNode (Node v) const
	Returns the 'previous node' of the shortest path tree for the given node.
const DistMap &	distMap () const
	Returns a const reference to the node map that stores the distances of the nodes.
const PredMap &	predMap () const
	Returns a const reference to the node map that stores the predecessor arcs.
bool	reached (Node v) const
	Checks if the given node is reached from the root(s).
bool	processed (Node v) const
	Checks if a node is processed.
Value	currentDist (Node v) const
	The current distance of the given node from the root(s).

Constructor & Destructor Documentation

Dijkstra ( const Digraph &  g, const LengthMap &  length  )

inline

Constructor.

Parameters

g	The digraph the algorithm runs on.
length	The length map used by the algorithm.

Member Function Documentation

Dijkstra& lengthMap ( const LengthMap &  m )

inline

Sets the length map.

Returns

(*this)

Dijkstra& predMap ( PredMap &  m )

inline

Sets the map that stores the predecessor arcs. If you don't use this function before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated map, of course.

Returns

(*this)

Dijkstra& processedMap ( ProcessedMap &  m )

inline

Sets the map that indicates which nodes are processed. If you don't use this function before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated map, of course.

Returns

(*this)

Dijkstra& distMap ( DistMap &  m )

inline

Sets the map that stores the distances of the nodes calculated by the algorithm. If you don't use this function before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated map, of course.

Returns

(*this)

Dijkstra& heap ( Heap &  hp, HeapCrossRef &  cr  )

inline

Sets the heap and the cross reference used by algorithm. If you don't use this function before calling run() or init(), heap and cross reference instances will be allocated automatically. The destructor deallocates these automatically allocated objects, of course.

Returns

(*this)

void init ( )

inline

Initializes the internal data structures.

void addSource ( Node  s, Value  dst = OperationTraits::zero()  )

inline

Adds a new source node to the priority heap. The optional second parameter is the initial distance of the node.

The function checks if the node has already been added to the heap and it is pushed to the heap only if either it was not in the heap or the shortest path found till then is shorter than dst.

Node processNextNode ( )

inline

Processes the next node in the priority heap.

Returns

The processed node.

Warning

The priority heap must not be empty.

Node nextNode ( ) const

inline

Returns the next node to be processed or INVALID if the priority heap is empty.

bool emptyQueue ( ) const

inline

Returns false if there are nodes to be processed in the priority heap.

int queueSize ( ) const

inline

Returns the number of the nodes to be processed in the priority heap.

void start ( )

inline

Executes the algorithm.

This method runs the Dijkstra algorithm from the root node(s) in order to compute the shortest path to each node.

The algorithm computes

• the shortest path tree (forest),
• the distance of each node from the root(s).

Precondition

init() must be called and at least one root node should be added with addSource() before using this function.

Note

d.start() is just a shortcut of the following code.

while ( !d.emptyQueue() ) {
  d.processNextNode();
}

void start ( Node  t )

inline

Executes the algorithm until the given target node is processed.

This method runs the Dijkstra algorithm from the root node(s) in order to compute the shortest path to t.

The algorithm computes

• the shortest path to t,
• the distance of t from the root(s).

Precondition

init() must be called and at least one root node should be added with addSource() before using this function.

Node start ( const NodeBoolMap &  nm )

inline

Executes the algorithm until a condition is met.

This method runs the Dijkstra algorithm from the root node(s) in order to compute the shortest path to a node v with nm[v] true, if such a node can be found.

Parameters

nm	A bool (or convertible) node map. The algorithm will stop when it reaches a node v with nm[v] true.

Returns

The reached node v with nm[v] true or INVALID if no such node was found.

Precondition

init() must be called and at least one root node should be added with addSource() before using this function.

void run ( Node  s )

inline

This method runs the Dijkstra algorithm from node s in order to compute the shortest path to each node.

The algorithm computes

• the shortest path tree,
• the distance of each node from the root.

Note

d.run(s) is just a shortcut of the following code.

d.init();
d.addSource(s);
d.start();

bool run ( Node  s, Node  t  )

inline

This method runs the Dijkstra algorithm from node s in order to compute the shortest path to node t (it stops searching when t is processed).

Returns

true if t is reachable form s.

Note

Apart from the return value, d.run(s,t) is just a shortcut of the following code.

d.init();
d.addSource(s);
d.start(t);

Path path ( Node  t ) const

inline

Returns the shortest path to the given node from the root(s).

Warning

t should be reached from the root(s).

Precondition

Either run() or init() must be called before using this function.

Value dist ( Node  v ) const

inline

Returns the distance of the given node from the root(s).

Warning

If node v is not reached from the root(s), then the return value of this function is undefined.

Precondition

Either run() or init() must be called before using this function.

Arc predArc ( Node  v ) const

inline

This function returns the 'previous arc' of the shortest path tree for the node v, i.e. it returns the last arc of a shortest path from a root to v. It is INVALID if v is not reached from the root(s) or if v is a root.

The shortest path tree used here is equal to the shortest path tree used in predNode() and predMap().

Precondition

Either run() or init() must be called before using this function.

Node predNode ( Node  v ) const

inline

This function returns the 'previous node' of the shortest path tree for the node v, i.e. it returns the last but one node of a shortest path from a root to v. It is INVALID if v is not reached from the root(s) or if v is a root.

The shortest path tree used here is equal to the shortest path tree used in predArc() and predMap().

Precondition

Either run() or init() must be called before using this function.

const DistMap& distMap ( ) const

inline

Returns a const reference to the node map that stores the distances of the nodes calculated by the algorithm.

Precondition

Either run() or init() must be called before using this function.

const PredMap& predMap ( ) const

inline

Returns a const reference to the node map that stores the predecessor arcs, which form the shortest path tree (forest).

Precondition

Either run() or init() must be called before using this function.

bool reached ( Node  v ) const

inline

Returns true if v is reached from the root(s).

Precondition

Either run() or init() must be called before using this function.

bool processed ( Node  v ) const

inline

Returns true if v is processed, i.e. the shortest path to v has already found.

Precondition

Either run() or init() must be called before using this function.

Value currentDist ( Node  v ) const

inline

Returns the current distance of the given node from the root(s). It may be decreased in the following processes.

Precondition

Either run() or init() must be called before using this function and node v must be reached but not necessarily processed.