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Batcher's odd–even mergesort is a generic construction devised by Ken Batcher for sorting networks of size O(''n'' (log ''n'')2) and depth O((log ''n'')2), where ''n'' is the number of items to be sorted. Although it is not asymptotically optimal, Knuth concluded in 1998, with respect to the AKS network that "Batcher's method is much better, unless ''n'' exceeds the total memory capacity of all computers on earth!"〔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.〕 It is popularized by the second ''GPU Gems'' book,〔http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter46.html〕 as an easy way of doing reasonably efficient sorts on graphics-processing hardware. == Example code == The following is an implementation of odd–even mergesort algorithm in Python. The input is a list ''x'' of length a power of 2. The output is a list sorted in ascending order. def oddeven_merge(lo, hi, r): step = r * 2 if step < hi - lo: yield from oddeven_merge(lo, hi, step) yield from oddeven_merge(lo + r, hi, step) yield from (i + r) for i in range(lo + r, hi - r, step) ) else: yield (lo, lo + r) def oddeven_merge_sort_range(lo, hi): """ sort the part of x with indices between lo and hi. Note: endpoints (lo and hi) are included. """ if (hi - lo) >= 1: # if there is more than one element, split the input # down the middle and first sort the first and second # half, followed by merging them. mid = lo + ((hi - lo) // 2) yield from oddeven_merge_sort_range(lo, mid) yield from oddeven_merge_sort_range(mid + 1, hi) yield from oddeven_merge(lo, hi, 1) def oddeven_merge_sort(length): """ "length" is the length of the list to be sorted. Returns a list of pairs of indices starting with 0 """ yield from oddeven_merge_sort_range(0, length - 1) def compare_and_swap(x, a, b): if x() > x(): x(), x() = x(), x() >>> data = (4, 3, 5, 6, 1, 7, 8 ) >>> pairs_to_compare = list(oddeven_merge_sort(len(data))) >>> pairs_to_compare (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) ) >>> for i in pairs_to_compare: compare_and_swap(data, *i) >>> data (2, 3, 4, 5, 6, 7, 8 ) More concise and non-recursive calculation of partner node is possible. Here is a Scala implementation to get the partner of an index at each step:〔(【引用サイトリンク】title=Sorting network from Batcher's Odd-Even merge: partner calculation )〕 def partner(index: Int, merge: Int, step: Int): Int = 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Batcher odd–even mergesort」の詳細全文を読む スポンサード リンク
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