diff --git a/python/heapq.py b/python/heapq.py index 48432a8e..855ae53c 100644 --- a/python/heapq.py +++ b/python/heapq.py @@ -1,8 +1,4 @@ # Heap queue algorithm (a.k.a. priority queue) - -__all__ = ['heappush', 'heappop', 'heapify', 'heapreplace', 'merge', - 'nlargest', 'nsmallest', 'heappushpop'] - def heappush(heap, item): """Push item onto heap, maintaining the heap invariant.""" heap.append(item) @@ -69,45 +65,6 @@ def _siftdown(heap, startpos, pos): break heap[pos] = newitem -# The child indices of heap index pos are already heaps, and we want to make -# a heap at index pos too. We do this by bubbling the smaller child of -# pos up (and so on with that child's children, etc) until hitting a leaf, -# then using _siftdown to move the oddball originally at index pos into place. -# -# We *could* break out of the loop as soon as we find a pos where newitem <= -# both its children, but turns out that's not a good idea, and despite that -# many books write the algorithm that way. During a heap pop, the last array -# element is sifted in, and that tends to be large, so that comparing it -# against values starting from the root usually doesn't pay (= usually doesn't -# get us out of the loop early). See Knuth, Volume 3, where this is -# explained and quantified in an exercise. -# -# Cutting the # of comparisons is important, since these routines have no -# way to extract "the priority" from an array element, so that intelligence -# is likely to be hiding in custom comparison methods, or in array elements -# storing (priority, record) tuples. Comparisons are thus potentially -# expensive. -# -# On random arrays of length 1000, making this change cut the number of -# comparisons made by heapify() a little, and those made by exhaustive -# heappop() a lot, in accord with theory. Here are typical results from 3 -# runs (3 just to demonstrate how small the variance is): -# -# Compares needed by heapify Compares needed by 1000 heappops -# -------------------------- -------------------------------- -# 1837 cut to 1663 14996 cut to 8680 -# 1855 cut to 1659 14966 cut to 8678 -# 1847 cut to 1660 15024 cut to 8703 -# -# Building the heap by using heappush() 1000 times instead required -# 2198, 2148, and 2219 compares: heapify() is more efficient, when -# you can use it. -# -# The total compares needed by list.sort() on the same lists were 8627, -# 8627, and 8632 (this should be compared to the sum of heapify() and -# heappop() compares): list.sort() is (unsurprisingly!) more efficient -# for sorting. - def _siftup(heap, pos): endpos = len(heap) startpos = pos