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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]
```