Abstract
In this paper, we study a new version from Dual-pivot Quicksort algorithm when we have some other number of pivots. Hence, we discuss the idea of picking pivots by random way and splitting the list simultaneously according to these. The modified version generalizes these results for multi process. We show that the average number of swaps done by Multi-pivot Quicksort process and we present a special case. Moreover, we obtain a relationship between the average number of swaps of Multi-pivot Quicksort and Stirling numbers of the first kind.
Highlights
Quicksort studied in many books such as [1] [2] and [3]
We study a new version from Dual-pivot Quicksort algorithm when we have some other number k of pivots
We show that the average number of swaps done by Multi-pivot Quicksort process and we present a special case
Summary
Quicksort studied in many books such as [1] [2] and [3] It is an exhaustively anatomize sorting algorithm and following the idea of divide-and-conquer on an input consisting of n items [4]. Quicksort used a pivot item to divide its input items into two partitions; the items in one sublist seem diminutive or identically tantamount to the pivot; the items in the other sublist seem more sizably voluminous than or equipollent to the pivot, after it uses recursion to order these sublists. Yaroslavskiy’s algorithm replaced the new standard Quicksort algorithm in Oracle’s Java 7 runtime library. This algorithm uses two items as pivots to divide the items. Depending on the results of [1] and [9], we analyze the Multi-pivot Quicksort when we selected k pivots and we study the relationship with Striling numbers of the first kind
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