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Dijkstra's algorithm in Python +info:https://jariasf.wordpress.com/2012/03/19/camino-mas-corto-algoritmo-de-dijkstra/
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# Dijkstra's algorithm for shortest paths | |
# David Eppstein, UC Irvine, 4 April 2002 | |
# http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/117228 | |
from priodict import priorityDictionary | |
def Dijkstra(G,start,end=None): | |
D = {} # dictionary of final distances | |
P = {} # dictionary of predecessors | |
Q = priorityDictionary() # est.dist. of non-final vert. | |
Q[start] = 0 | |
for v in Q: | |
D[v] = Q[v] | |
if v == end: break | |
for w in G[v]: | |
vwLength = D[v] + G[v][w] | |
if w in D: | |
if vwLength < D[w]: | |
raise ValueError, "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 shortestPath(G,start,end): | |
D,P = Dijkstra(G,start,end) | |
Path = [] | |
while 1: | |
Path.append(end) | |
if end == start: break | |
end = P[end] | |
Path.reverse() | |
return Path |
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# Priority dictionary using binary heaps | |
# David Eppstein, UC Irvine, 8 Mar 2002 | |
from __future__ import generators | |
class priorityDictionary(dict): | |
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 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 grows | |
too 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.iteritems()] | |
self.__heap.sort() # builtin sort likely faster than O(n) heapify | |
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 call our customized __setitem__.''' | |
if key not in self: | |
self[key] = val | |
return self[key] |
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método Dijkstra(Grafo,origen): | |
2 creamos una cola de prioridad Q | |
3 agregamos origen a la cola de prioridad Q | |
4 mientras Q no este vacío: | |
5 sacamos un elemento de la cola Q llamado u | |
6 si u ya fue visitado continuo sacando elementos de Q | |
7 marcamos como visitado u | |
8 para cada vértice v adyacente a u en el Grafo: | |
9 sea w el peso entre vértices ( u , v ) | |
10 si v no ah sido visitado: | |
11 Relajacion( u , v , w ) | |
1 método Relajacion( actual , adyacente , peso ): | |
2 si distancia[ actual ] + peso < distancia[ adyacente ] | |
3 distancia[ adyacente ] = distancia[ actual ] + peso | |
4 agregamos adyacente a la cola de prioridad Q |
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