Abstract

We present three variations of the following new sorting theme: Throughout the sort, the arrayismaintained in piles of sorted elements. Ateach step, the piles are split into two parts, so that the elements of the left piles are smaller than #or equal to# the elements of the right piles. Then, the two parts are each sorted, recursively. The theme, then, is a combination of Hoare's Quicksort idea, and the Pick algorithm, by Blum, et al., for linear selection. The variations arise from the possible choices of splitting method. Twovariations attempt to minimize the average number of comparisons. The better of these has an average performance of 1:075n lg n comparisons. The third variation sacri#ces the average case for a worst-case performance of 1:756n lg n, which is better than Heapsort. They all require minimal extra space and about as manydatamoves as comparisons. 1 Introduction The sorting problem is: Given an array a 1 ;a 2 ; ###;a n of elements, rearrange them so t...

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