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(). | |

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 | |

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.

**Parameters:**-
g The digraph the algorithm runs on. length The length map used by the algorithm.

Dijkstra& processedMap | ( | ProcessedMap & | m | ) | ` [inline]` |

Dijkstra& heap | ( | Heap & | hp, |

HeapCrossRef & | cr |
||

) | ` [inline]` |

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]` |

Value dist | ( | Node | v | ) | const` [inline]` |

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().

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().

const DistMap& distMap | ( | ) | const` [inline]` |

const PredMap& predMap | ( | ) | const` [inline]` |

bool reached | ( | Node | v | ) | const` [inline]` |

bool processed | ( | Node | v | ) | const` [inline]` |

Generated on Wed Nov 9 2011 11:44:23 by 1.7.3