# Priority dictionary using binary heaps
# 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.

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 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.iteritems()]
            self.__heap.sort()  # builtin sort probably faster than O(n)-time 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 pass through our customized __setitem__.'''
        if key not in self:
            self[key] = val
        return self[key]