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Journal ArticleDOI

Comparisons in Hoare's Find Algorithm

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TLDR
Using trivariate generating functions, an explicit expression is obtained for the variance of the number of comparisons, if the authors search for the jth element in a random permutation of n elements, under the assumption that j is proportional to n.
Abstract
We study the number of comparisons in Hoare's Find algorithm. Using trivariate generating functions, we get an explicit expression for the variance of the number of comparisons, if we search for the jth element in a random permutation of n elements. The variance is also asymptotically evaluated under the assumption that j is proportional to n. Similar results for the number of passes (recursive calls) are given, too.

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Citations
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Journal ArticleDOI

The contraction method for recursive algorithms

TL;DR: A new quite general model for branching dynamical systems is introduced and the contraction method can be applied in this model and this model includes many classical examples of random trees and gives a general frame for further applications.
Journal ArticleDOI

Optimal Sampling Strategies in Quicksort and Quickselect

TL;DR: The optimal sample size to minimize the average total cost of quicksort, as a function of the size n of the current subarray size, is a, which depends on the selection algorithm and the costs of elementary comparisons and exchanges.
Journal ArticleDOI

Quickselect and the Dickman Function

TL;DR: In this article, it was shown that the Dickman function is the limiting distribution of the number of comparisons used by Hoare's quickselect algorithm when given a random permutation of n elements for finding the mth-smallest element, where m = o(n).

Quickselect and Dickman function

TL;DR: In this article, it was shown that the Dickman function is the limiting distribution of the number of comparisons used by Hoare's quickselect algorithm when given a random permutation of n elements for nding the m-th smallest element, where m = o(n).
Journal ArticleDOI

Cost Decision Support in Product Design

TL;DR: In this paper, a functional architecture for costing data support during product design, as well as a corresponding data structure are presented, which can be used to support cost data support in decision making processes.
References
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Book

The Art of Computer Programming

TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.