1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
|
# 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]
|