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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 = []

    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
                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.'''
        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
            newPair = (val,key)
            insertionPoint = len(heap)
            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]