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altgraph.GraphAlgo - Graph algorithms
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=====================================
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é )Ú
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GraphErrorNc
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C s° i }i }t }d||< |D ]}|| ||< ||kr6 q¨| |¡D ]d}| ||¡}|| | |¡ } ||kr| || k r¤tdq@||ks| || k r@| ||< |||< q@q||fS )a`
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Dijkstra's algorithm for shortest paths
|
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`David Eppstein, UC Irvine, 4 April 2002
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<http://www.ics.uci.edu/~eppstein/161/python/>`_
|
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`Python Cookbook Recipe
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<http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/119466>`_
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Find shortest paths from the start node to all nodes nearer than or
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equal to the end node.
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Dijkstra's algorithm is only guaranteed to work correctly when all edge
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lengths are positive. This code does not verify this property for all
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edges (only the edges examined until the end vertex is reached), but will
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correctly compute shortest paths even for some graphs with negative edges,
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and will raise an exception if it discovers that a negative edge has
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caused it to make a mistake.
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Adapted to altgraph by Istvan Albert, Pennsylvania State University -
|
June, 9 2004
|
r z3Dijkstra: found better path to already-final vertex)Ú_priorityDictionaryZout_nbrsZ edge_by_nodeZ edge_datar )
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ÚgraphÚstartÚendÚDÚPÚQÚvÚwZedge_idZvwLength© r úId:\z\workplace\vscode\pyvenv\venv\Lib\site-packages\altgraph/GraphAlgo.pyÚdijkstra s( ÿ r c C s> t | ||\}}g }| |¡ ||kr(q2|| }q| ¡ |S )a
|
Find a single shortest path from the *start* node to the *end* node.
|
The input has the same conventions as dijkstra(). The output is a list of
|
the nodes in order along the shortest path.
|
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**Note that the distances must be stored in the edge data as numeric data**
|
)r ÚappendÚreverse)r r r r r ÚPathr r r Ú shortest_path8 s
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r c @ s8 e Zd ZdZdd Zdd Zdd Zdd Zd
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d Zd S ) r a¶
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Priority dictionary using binary heaps (internal use only)
|
|
David Eppstein, UC Irvine, 8 Mar 2002
|
|
Implements a data structure that acts almost like a dictionary, with
|
two modifications:
|
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1. D.smallest() returns the value x minimizing D[x]. For this to
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work correctly, all values D[x] stored in the dictionary must be
|
comparable.
|
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2. iterating "for x in D" finds and removes the items from D in sorted
|
order. Each item is not removed until the next item is requested,
|
so D[x] will still return a useful value until the next iteration
|
of the for-loop. Each operation takes logarithmic amortized time.
|
c C s g | _ t | ¡ dS )a
|
Initialize priorityDictionary by creating binary heap of pairs
|
(value,key). Note that changing or removing a dict entry will not
|
remove the old pair from the heap until it is found by smallest()
|
or until the heap is rebuilt.
|
N)Ú_priorityDictionary__heapÚdictÚ__init__©Úselfr r r r b s z _priorityDictionary.__init__c C sÌ t | dkrtd| j}|d d | ksF| |d d |d d krÀ| ¡ }d}d| d }|d t |k r|| ||d kr|d7 }|t |ks¢||| kr¬|||< q|| ||< |}qRq|d d S )zU
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Find smallest item after removing deleted items from front of heap.
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r z$smallest of empty priorityDictionaryé é )ÚlenÚ
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IndexErrorr Úpop)r ÚheapZlastItemÚinsertionPointZ
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smallChildr r r Úsmallestl s$ , ÿþ z _priorityDictionary.smallestc s fdd}| S )zK
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Create destructive sorted iterator of priorityDictionary.
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c 3 s& t dkr" ¡ } | V | = q d S )Nr )r r )Úxr r r Úiterfn s z,_priorityDictionary.__iter__.<locals>.iterfnr )r r! r r r Ú__iter__ s z _priorityDictionary.__iter__c C s¬ t | ||¡ | j}t|dt| krHdd | ¡ D | _| j ¡ n`||f}t|}| d¡ |dkr |||d d k r ||d d ||< |d d }qb|||< dS )z½
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Change value stored in dictionary and add corresponding pair to heap.
|
Rebuilds the heap if the number of deleted items gets large, to avoid
|
memory leakage.
|
r c S s g | ]\}}||fqS r r )Ú.0Úkr
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r r r Ú
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<listcomp> s z3_priorityDictionary.__setitem__.<locals>.<listcomp>Nr r )r Ú __setitem__r r ÚitemsÚsortr )r ÚkeyÚvalr ZnewPairr r r r r& s
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z _priorityDictionary.__setitem__c C s || kr|| |< | | S )zT
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Reimplement setdefault to pass through our customized __setitem__.
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r )r r) r* r r r Ú
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setdefault¥ s z _priorityDictionary.setdefaultN) Ú__name__Ú
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__module__Ú __qualname__Ú__doc__r r r" r& r+ r r r r r O s
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