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Diffstat (limited to 'lib/python2.7/heapq.py')
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diff --git a/lib/python2.7/heapq.py b/lib/python2.7/heapq.py deleted file mode 100644 index ca79db1..0000000 --- a/lib/python2.7/heapq.py +++ /dev/null @@ -1,480 +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 and Raymond Hettinger - -__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', 'merge', - 'nlargest', 'nsmallest', 'heappushpop'] - -from itertools import islice, count, imap, izip, tee, chain -from operator import itemgetter - -def cmp_lt(x, y): - # Use __lt__ if available; otherwise, try __le__. - # In Py3.x, only __lt__ will be called. - return (x < y) if hasattr(x, '__lt__') else (not y <= x) - -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 unless written as part of a conditional replacement: - - if item > heap[0]: - item = heapreplace(heap, item) - """ - returnitem = heap[0] # raises appropriate IndexError if heap is empty - heap[0] = item - _siftup(heap, 0) - return returnitem - -def heappushpop(heap, item): - """Fast version of a heappush followed by a heappop.""" - if heap and cmp_lt(heap[0], item): - item, heap[0] = heap[0], item - _siftup(heap, 0) - return item - -def heapify(x): - """Transform list into a heap, in-place, in O(len(x)) 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) - -def _heappushpop_max(heap, item): - """Maxheap version of a heappush followed by a heappop.""" - if heap and cmp_lt(item, heap[0]): - item, heap[0] = heap[0], item - _siftup_max(heap, 0) - return item - -def _heapify_max(x): - """Transform list into a maxheap, in-place, in O(len(x)) time.""" - n = len(x) - for i in reversed(range(n//2)): - _siftup_max(x, i) - -def nlargest(n, iterable): - """Find the n largest elements in a dataset. - - Equivalent to: sorted(iterable, reverse=True)[:n] - """ - if n < 0: - return [] - it = iter(iterable) - result = list(islice(it, n)) - if not result: - return result - heapify(result) - _heappushpop = heappushpop - for elem in it: - _heappushpop(result, elem) - result.sort(reverse=True) - return result - -def nsmallest(n, iterable): - """Find the n smallest elements in a dataset. - - Equivalent to: sorted(iterable)[:n] - """ - if n < 0: - return [] - it = iter(iterable) - result = list(islice(it, n)) - if not result: - return result - _heapify_max(result) - _heappushpop = _heappushpop_max - for elem in it: - _heappushpop(result, elem) - result.sort() - return result - -# '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 cmp_lt(newitem, parent): - heap[pos] = parent - pos = parentpos - continue - 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 __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 not cmp_lt(heap[childpos], heap[rightpos]): - 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) - -def _siftdown_max(heap, startpos, pos): - 'Maxheap variant of _siftdown' - 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 cmp_lt(parent, newitem): - heap[pos] = parent - pos = parentpos - continue - break - heap[pos] = newitem - -def _siftup_max(heap, pos): - 'Maxheap variant of _siftup' - endpos = len(heap) - startpos = pos - newitem = heap[pos] - # Bubble up the larger child until hitting a leaf. - childpos = 2*pos + 1 # leftmost child position - while childpos < endpos: - # Set childpos to index of larger child. - rightpos = childpos + 1 - if rightpos < endpos and not cmp_lt(heap[rightpos], heap[childpos]): - childpos = rightpos - # Move the larger 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_max(heap, startpos, pos) - -# If available, use C implementation -try: - from _heapq import * -except ImportError: - pass - -def merge(*iterables): - '''Merge multiple sorted inputs into a single sorted output. - - Similar to sorted(itertools.chain(*iterables)) but returns a generator, - does not pull the data into memory all at once, and assumes that each of - the input streams is already sorted (smallest to largest). - - >>> list(merge([1,3,5,7], [0,2,4,8], [5,10,15,20], [], [25])) - [0, 1, 2, 3, 4, 5, 5, 7, 8, 10, 15, 20, 25] - - ''' - _heappop, _heapreplace, _StopIteration = heappop, heapreplace, StopIteration - - h = [] - h_append = h.append - for itnum, it in enumerate(map(iter, iterables)): - try: - next = it.next - h_append([next(), itnum, next]) - except _StopIteration: - pass - heapify(h) - - while 1: - try: - while 1: - v, itnum, next = s = h[0] # raises IndexError when h is empty - yield v - s[0] = next() # raises StopIteration when exhausted - _heapreplace(h, s) # restore heap condition - except _StopIteration: - _heappop(h) # remove empty iterator - except IndexError: - return - -# Extend the implementations of nsmallest and nlargest to use a key= argument -_nsmallest = nsmallest -def nsmallest(n, iterable, key=None): - """Find the n smallest elements in a dataset. - - Equivalent to: sorted(iterable, key=key)[:n] - """ - # Short-cut for n==1 is to use min() when len(iterable)>0 - if n == 1: - it = iter(iterable) - head = list(islice(it, 1)) - if not head: - return [] - if key is None: - return [min(chain(head, it))] - return [min(chain(head, it), key=key)] - - # When n>=size, it's faster to use sorted() - try: - size = len(iterable) - except (TypeError, AttributeError): - pass - else: - if n >= size: - return sorted(iterable, key=key)[:n] - - # When key is none, use simpler decoration - if key is None: - it = izip(iterable, count()) # decorate - result = _nsmallest(n, it) - return map(itemgetter(0), result) # undecorate - - # General case, slowest method - in1, in2 = tee(iterable) - it = izip(imap(key, in1), count(), in2) # decorate - result = _nsmallest(n, it) - return map(itemgetter(2), result) # undecorate - -_nlargest = nlargest -def nlargest(n, iterable, key=None): - """Find the n largest elements in a dataset. - - Equivalent to: sorted(iterable, key=key, reverse=True)[:n] - """ - - # Short-cut for n==1 is to use max() when len(iterable)>0 - if n == 1: - it = iter(iterable) - head = list(islice(it, 1)) - if not head: - return [] - if key is None: - return [max(chain(head, it))] - return [max(chain(head, it), key=key)] - - # When n>=size, it's faster to use sorted() - try: - size = len(iterable) - except (TypeError, AttributeError): - pass - else: - if n >= size: - return sorted(iterable, key=key, reverse=True)[:n] - - # When key is none, use simpler decoration - if key is None: - it = izip(iterable, count(0,-1)) # decorate - result = _nlargest(n, it) - return map(itemgetter(0), result) # undecorate - - # General case, slowest method - in1, in2 = tee(iterable) - it = izip(imap(key, in1), count(0,-1), in2) # decorate - result = _nlargest(n, it) - return map(itemgetter(2), result) # undecorate - -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 - - import doctest - doctest.testmod() |