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"""
altgraph.GraphAlgo - Graph algorithms
=====================================
"""
from altgraph import GraphError
def dijkstra(graph, start, end=None):
"""
Dijkstra's algorithm for shortest paths
`David Eppstein, UC Irvine, 4 April 2002
<http://www.ics.uci.edu/~eppstein/161/python/>`_
`Python Cookbook Recipe
<http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/119466>`_
Find shortest paths from the start node to all nodes nearer than or
equal to the end node.
Dijkstra's algorithm is only guaranteed to work correctly when all edge
lengths are positive. This code does not verify this property for all
edges (only the edges examined until the end vertex is reached), but will
correctly compute shortest paths even for some graphs with negative edges,
and will raise an exception if it discovers that a negative edge has
caused it to make a mistake.
Adapted to altgraph by Istvan Albert, Pennsylvania State University -
June, 9 2004
"""
D = {} # dictionary of final distances
P = {} # dictionary of predecessors
Q = _priorityDictionary() # estimated distances of non-final vertices
Q[start] = 0
for v in Q:
D[v] = Q[v]
if v == end:
break
for w in graph.out_nbrs(v):
edge_id = graph.edge_by_node(v, w)
vwLength = D[v] + graph.edge_data(edge_id)
if w in D:
if vwLength < D[w]:
raise GraphError(
"Dijkstra: found better path to already-final vertex"
)
elif w not in Q or vwLength < Q[w]:
Q[w] = vwLength
P[w] = v
return (D, P)
def shortest_path(graph, start, end):
"""
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.
**Note that the distances must be stored in the edge data as numeric data**
"""
D, P = dijkstra(graph, start, end)
Path = []
while 1:
Path.append(end)
if end == start:
break
end = P[end]
Path.reverse()
return Path
#
# Utility classes and functions
#
class _priorityDictionary(dict):
"""
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:
1. D.smallest() returns the value x minimizing D[x]. For this to
work correctly, all values D[x] stored in the dictionary must be
comparable.
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.
"""
def __init__(self):
"""
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.
"""
self.__heap = []
dict.__init__(self)
def smallest(self):
"""
Find smallest item after removing deleted items from front of heap.
"""
if len(self) == 0:
raise IndexError("smallest of empty priorityDictionary")
heap = self.__heap
while heap[0][1] not in self or self[heap[0][1]] != heap[0][0]:
lastItem = heap.pop()
insertionPoint = 0
while 1:
smallChild = 2 * insertionPoint + 1
if (
smallChild + 1 < len(heap)
and heap[smallChild] > heap[smallChild + 1]
):
smallChild += 1
if smallChild >= len(heap) or lastItem <= heap[smallChild]:
heap[insertionPoint] = lastItem
break
heap[insertionPoint] = heap[smallChild]
insertionPoint = smallChild
return heap[0][1]
def __iter__(self):
"""
Create destructive sorted iterator of priorityDictionary.
"""
def iterfn():
while len(self) > 0:
x = self.smallest()
yield x
del self[x]
return iterfn()
def __setitem__(self, key, val):
"""
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.
"""
dict.__setitem__(self, key, val)
heap = self.__heap
if len(heap) > 2 * len(self):
self.__heap = [(v, k) for k, v in self.items()]
self.__heap.sort()
else:
newPair = (val, key)
insertionPoint = len(heap)
heap.append(None)
while insertionPoint > 0 and newPair < heap[(insertionPoint - 1) // 2]:
heap[insertionPoint] = heap[(insertionPoint - 1) // 2]
insertionPoint = (insertionPoint - 1) // 2
heap[insertionPoint] = newPair
def setdefault(self, key, val):
"""
Reimplement setdefault to pass through our customized __setitem__.
"""
if key not in self:
self[key] = val
return self[key]
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