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| {{Infobox Algorithm
| | Hi there! :) My name is Antoine, I'm a student studying Industrial and Labor Relations from Zurich, Switzerland.<br><br>my webpage: [http://www.golfidence.nl/userinfo.php?uid=49211 Fifa 15 Coin Generator] |
| |class=[[Sorting algorithm]]
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| |image=[[File:Batcher Odd-Even Mergesort for eight inputs.svg|Visualization of the odd–even mergesort network with eight inputs]]
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| |caption=Visualization of the odd–even mergesort network with eight inputs
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| |data=[[Array data structure|Array]]
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| |best-time= <math>O(\log^2(n))</math> parallel time
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| |average-time= <math>O(\log^2(n))</math> parallel time
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| |time=<math>O(\log^2(n))</math> parallel time
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| |space=<math>O(n\log^2(n))</math> comparators
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| |optimal=No
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| }}
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| '''Batcher's odd–even mergesort''' is a generic construction devised by [[Ken Batcher]] for [[sorting network]]s of size O(''n'' (log ''n'')<sup>2</sup>) and depth O((log ''n'')<sup>2</sup>), where ''n'' is the number of items to be sorted. Although it is not asymptotically optimal, [[Donald Knuth|Knuth]] concluded in 1998, with respect to the [[Sorting_network#Optimal_sorting|AKS network]] that "Batcher's method is much better, unless ''n'' exceeds the total memory capacity of all computers on earth!"<ref>[[Donald Knuth|D.E. Knuth]]. ''[[The Art of Computer Programming]]'', Volume 3: ''Sorting and Searching'', Third Edition. Addison-Wesley, 1998. ISBN 0-201-89685-0. Section 5.3.4: Networks for Sorting, pp. 219–247.</ref>
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| It is popularized by the second ''[[GPU Gems]]'' book,<ref>http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter46.html</ref> as an easy way of doing reasonably efficient sorts on graphics-processing hardware.
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| == Example code ==
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| The following is an implementation of odd–even mergesort algorithm in [[Python (programming language)|Python]]. The input is a list ''x'' of length a power of 2. The output is a list sorted in ascending order.
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| <source lang="python">
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| def oddeven_merge(lo, hi, r):
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| step = r * 2
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| if step < hi - lo:
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| yield from oddeven_merge(lo, hi, step)
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| yield from oddeven_merge(lo + r, hi, step)
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| yield from [(i, i + r) for i in range(lo + r, hi - r, step)]
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| else:
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| yield (lo, lo + r)
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| def oddeven_merge_sort_range(lo, hi):
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| """ sort the part of x with indices between lo and hi.
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| Note: endpoints (lo and hi) are included.
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| """
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| if (hi - lo) >= 1:
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| # if there is more than one element, split the input
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| # down the middle and first sort the first and second
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| # half, followed by merging them.
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| mid = lo + ((hi - lo) // 2)
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| yield from oddeven_merge_sort_range(lo, mid)
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| yield from oddeven_merge_sort_range(mid + 1, hi)
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| yield from oddeven_merge(lo, hi, 1)
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| def oddeven_merge_sort(length):
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| """ "length" is the length of the list to be sorted.
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| Returns a list of pairs of indices starting with 0 """
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| yield from oddeven_merge_sort_range(0, length - 1)
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| def compare_and_swap(x, a, b):
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| if x[a] > x[b]:
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| x[a], x[b] = x[b], x[a]
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| </source> | |
| <source lang="pycon"> | |
| >>> data = [2, 4, 3, 5, 6, 1, 7, 8]
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| >>> pairs_to_compare = list(oddeven_merge_sort(len(data)))
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| >>> pairs_to_compare
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| [(0, 1), (2, 3), (0, 2), (1, 3), (1, 2), (4, 5), (6, 7), (4, 6), (5, 7), (5, 6), (0, 4), (2, 6), (2, 4), (1, 5), (3, 7), (3, 5), (1, 2), (3, 4), (5, 6)]
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| >>> for i in pairs_to_compare: compare_and_swap(data, *i)
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| >>> data
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| [1, 2, 3, 4, 5, 6, 7, 8]
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| </source>
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| ==See also==
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| * [[Bitonic sorter]]
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| == References ==
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| {{reflist}}
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| ==External links==
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| *[http://www.iti.fh-flensburg.de/lang/algorithmen/sortieren/networks/oemen.htm Odd–even mergesort] at fh-flensburg.de
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| {{sorting}}
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| {{DEFAULTSORT:Batcher odd-even mergesort}}
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| [[Category:Sorting algorithms]]
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| {{algorithm-stub}}
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Hi there! :) My name is Antoine, I'm a student studying Industrial and Labor Relations from Zurich, Switzerland.
my webpage: Fifa 15 Coin Generator