# 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.items()]
            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]