Batcher odd–even mergesort
Visualization of the odd–even mergesort network with eight inputs
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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!"
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 compare_and_swap(x, a, b): if x[a] > x[b]: x[a], x[b] = x[b], x[a] def oddeven_merge(x, lo, hi, r): step = r * 2 if step < hi - lo: oddeven_merge(x, lo, hi, step) oddeven_merge(x, lo + r, hi, step) for i in range(lo + r, hi - r, step): compare_and_swap(x, i, i + r) else: compare_and_swap(x, lo, lo + r) def oddeven_merge_sort_range(x, 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) oddeven_merge_sort_range(x, lo, mid) oddeven_merge_sort_range(x, mid + 1, hi) oddeven_merge(x, lo, hi, 1) def oddeven_merge_sort(x): oddeven_merge_sort_range(x, 0, len(x)-1)
>>> data = [2, 4, 3, 5, 6, 1, 7, 8] >>> oddeven_merge_sort(data) >>> data [1, 2, 3, 4, 5, 6, 7, 8]
- 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.
- Odd–even mergesort at fh-flensburg.de
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