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authorRaymond Hettinger <python@rcn.com>2003-11-08 10:24:38 (GMT)
committerRaymond Hettinger <python@rcn.com>2003-11-08 10:24:38 (GMT)
commitb3af1813eb5cf99766f55a0dfc0d566e9bd7c3c1 (patch)
tree521b04bd610668139d07ee16fbaa3f8ae99b6166 /Lib
parent1021c44b413ebe264a6187322447ac296a0a18a7 (diff)
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Convert heapq.py to a C implementation.
Diffstat (limited to 'Lib')
-rw-r--r--Lib/heapq.py255
-rw-r--r--Lib/test/test___all__.py1
2 files changed, 0 insertions, 256 deletions
diff --git a/Lib/heapq.py b/Lib/heapq.py
deleted file mode 100644
index 2223a97..0000000
--- a/Lib/heapq.py
+++ /dev/null
@@ -1,255 +0,0 @@
-# -*- coding: Latin-1 -*-
-
-"""Heap queue algorithm (a.k.a. priority queue).
-
-Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
-all k, counting elements from 0. For the sake of comparison,
-non-existing elements are considered to be infinite. The interesting
-property of a heap is that a[0] is always its smallest element.
-
-Usage:
-
-heap = [] # creates an empty heap
-heappush(heap, item) # pushes a new item on the heap
-item = heappop(heap) # pops the smallest item from the heap
-item = heap[0] # smallest item on the heap without popping it
-heapify(x) # transforms list into a heap, in-place, in linear time
-item = heapreplace(heap, item) # pops and returns smallest item, and adds
- # new item; the heap size is unchanged
-
-Our API differs from textbook heap algorithms as follows:
-
-- We use 0-based indexing. This makes the relationship between the
- index for a node and the indexes for its children slightly less
- obvious, but is more suitable since Python uses 0-based indexing.
-
-- Our heappop() method returns the smallest item, not the largest.
-
-These two make it possible to view the heap as a regular Python list
-without surprises: heap[0] is the smallest item, and heap.sort()
-maintains the heap invariant!
-"""
-
-# Original code by Kevin O'Connor, augmented by Tim Peters
-
-__about__ = """Heap queues
-
-[explanation by François Pinard]
-
-Heaps are arrays for which a[k] <= a[2*k+1] and a[k] <= a[2*k+2] for
-all k, counting elements from 0. For the sake of comparison,
-non-existing elements are considered to be infinite. The interesting
-property of a heap is that a[0] is always its smallest element.
-
-The strange invariant above is meant to be an efficient memory
-representation for a tournament. The numbers below are `k', not a[k]:
-
- 0
-
- 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
-
-
-In the tree above, each cell `k' is topping `2*k+1' and `2*k+2'. In
-an usual binary tournament we see in sports, each cell is the winner
-over the two cells it tops, and we can trace the winner down the tree
-to see all opponents s/he had. However, in many computer applications
-of such tournaments, we do not need to trace the history of a winner.
-To be more memory efficient, when a winner is promoted, we try to
-replace it by something else at a lower level, and the rule becomes
-that a cell and the two cells it tops contain three different items,
-but the top cell "wins" over the two topped cells.
-
-If this heap invariant is protected at all time, index 0 is clearly
-the overall winner. The simplest algorithmic way to remove it and
-find the "next" winner is to move some loser (let's say cell 30 in the
-diagram above) into the 0 position, and then percolate this new 0 down
-the tree, exchanging values, until the invariant is re-established.
-This is clearly logarithmic on the total number of items in the tree.
-By iterating over all items, you get an O(n ln n) sort.
-
-A nice feature of this sort is that you can efficiently insert new
-items while the sort is going on, provided that the inserted items are
-not "better" than the last 0'th element you extracted. This is
-especially useful in simulation contexts, where the tree holds all
-incoming events, and the "win" condition means the smallest scheduled
-time. When an event schedule other events for execution, they are
-scheduled into the future, so they can easily go into the heap. So, a
-heap is a good structure for implementing schedulers (this is what I
-used for my MIDI sequencer :-).
-
-Various structures for implementing schedulers have been extensively
-studied, and heaps are good for this, as they are reasonably speedy,
-the speed is almost constant, and the worst case is not much different
-than the average case. However, there are other representations which
-are more efficient overall, yet the worst cases might be terrible.
-
-Heaps are also very useful in big disk sorts. You most probably all
-know that a big sort implies producing "runs" (which are pre-sorted
-sequences, which size is usually related to the amount of CPU memory),
-followed by a merging passes for these runs, which merging is often
-very cleverly organised[1]. It is very important that the initial
-sort produces the longest runs possible. Tournaments are a good way
-to that. If, using all the memory available to hold a tournament, you
-replace and percolate items that happen to fit the current run, you'll
-produce runs which are twice the size of the memory for random input,
-and much better for input fuzzily ordered.
-
-Moreover, if you output the 0'th item on disk and get an input which
-may not fit in the current tournament (because the value "wins" over
-the last output value), it cannot fit in the heap, so the size of the
-heap decreases. The freed memory could be cleverly reused immediately
-for progressively building a second heap, which grows at exactly the
-same rate the first heap is melting. When the first heap completely
-vanishes, you switch heaps and start a new run. Clever and quite
-effective!
-
-In a word, heaps are useful memory structures to know. I use them in
-a few applications, and I think it is good to keep a `heap' module
-around. :-)
-
---------------------
-[1] The disk balancing algorithms which are current, nowadays, are
-more annoying than clever, and this is a consequence of the seeking
-capabilities of the disks. On devices which cannot seek, like big
-tape drives, the story was quite different, and one had to be very
-clever to ensure (far in advance) that each tape movement will be the
-most effective possible (that is, will best participate at
-"progressing" the merge). Some tapes were even able to read
-backwards, and this was also used to avoid the rewinding time.
-Believe me, real good tape sorts were quite spectacular to watch!
-From all times, sorting has always been a Great Art! :-)
-"""
-
-__all__ = ['heappush', 'heappop', 'heapify', 'heapreplace']
-
-def heappush(heap, item):
- """Push item onto heap, maintaining the heap invariant."""
- heap.append(item)
- _siftdown(heap, 0, len(heap)-1)
-
-def heappop(heap):
- """Pop the smallest item off the heap, maintaining the heap invariant."""
- lastelt = heap.pop() # raises appropriate IndexError if heap is empty
- if heap:
- returnitem = heap[0]
- heap[0] = lastelt
- _siftup(heap, 0)
- else:
- returnitem = lastelt
- return returnitem
-
-def heapreplace(heap, item):
- """Pop and return the current smallest value, and add the new item.
-
- This is more efficient than heappop() followed by heappush(), and can be
- more appropriate when using a fixed-size heap. Note that the value
- returned may be larger than item! That constrains reasonable uses of
- this routine.
- """
- returnitem = heap[0] # raises appropriate IndexError if heap is empty
- heap[0] = item
- _siftup(heap, 0)
- return returnitem
-
-def heapify(x):
- """Transform list into a heap, in-place, in O(len(heap)) time."""
- n = len(x)
- # Transform bottom-up. The largest index there's any point to looking at
- # is the largest with a child index in-range, so must have 2*i + 1 < n,
- # or i < (n-1)/2. If n is even = 2*j, this is (2*j-1)/2 = j-1/2 so
- # j-1 is the largest, which is n//2 - 1. If n is odd = 2*j+1, this is
- # (2*j+1-1)/2 = j so j-1 is the largest, and that's again n//2-1.
- for i in reversed(xrange(n//2)):
- _siftup(x, i)
-
-# 'heap' is a heap at all indices >= startpos, except possibly for pos. pos
-# is the index of a leaf with a possibly out-of-order value. Restore the
-# heap invariant.
-def _siftdown(heap, startpos, pos):
- newitem = heap[pos]
- # Follow the path to the root, moving parents down until finding a place
- # newitem fits.
- while pos > startpos:
- parentpos = (pos - 1) >> 1
- parent = heap[parentpos]
- if parent <= newitem:
- break
- heap[pos] = parent
- pos = parentpos
- 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 __cmp__ 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
- newitem = heap[pos]
- # Bubble up the smaller child until hitting a leaf.
- childpos = 2*pos + 1 # leftmost child position
- while childpos < endpos:
- # Set childpos to index of smaller child.
- rightpos = childpos + 1
- if rightpos < endpos and heap[rightpos] <= heap[childpos]:
- childpos = rightpos
- # Move the smaller child up.
- heap[pos] = heap[childpos]
- pos = childpos
- childpos = 2*pos + 1
- # The leaf at pos is empty now. Put newitem there, and bubble it up
- # to its final resting place (by sifting its parents down).
- heap[pos] = newitem
- _siftdown(heap, startpos, pos)
-
-if __name__ == "__main__":
- # Simple sanity test
- heap = []
- data = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]
- for item in data:
- heappush(heap, item)
- sort = []
- while heap:
- sort.append(heappop(heap))
- print sort
diff --git a/Lib/test/test___all__.py b/Lib/test/test___all__.py
index 6643a19..99eaa59 100644
--- a/Lib/test/test___all__.py
+++ b/Lib/test/test___all__.py
@@ -100,7 +100,6 @@ class AllTest(unittest.TestCase):
self.check_all("glob")
self.check_all("gopherlib")
self.check_all("gzip")
- self.check_all("heapq")
self.check_all("htmllib")
self.check_all("httplib")
self.check_all("ihooks")