A Worst Case Analysis of Heap-Sort (Classic Reprint)
Book Details
Author(s)
Clyde P. Kruskal
Publisher
Forgotten Books
ISBN / ASIN
133221360X
ISBN-13
9781332213603
Availability
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Sales Rank
#99,999,999
Marketplace
United States 🇺🇸
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Description
Excerpt from A Worst Case Analysis of Heap-Sort
It is interesting to compare various sorting algorithms based on numbers of comparisons and exchanges. This point is emphasized in Knuth [Kn, sec. 5.3.1]: "... a theoretical study of this subject [counting comparisons] gives us a good deal of useful insight into the nature of sorting processes ..."
The most commonly known 0 (n log n) comparison-exchange sorting algorithm not needing external storage is heapsort (sometimes referred to as treesort) [F1], [Wi]. It is relatively easy to calculate the maximum number of exchanges required by heapsort; in this paper, we calculate the maximum number of (key) comparisons required, assuming that the size of the input is one less than a power of two. In addition, we exhibit an algorithm producing input yielding the maximum number of comparisons.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
It is interesting to compare various sorting algorithms based on numbers of comparisons and exchanges. This point is emphasized in Knuth [Kn, sec. 5.3.1]: "... a theoretical study of this subject [counting comparisons] gives us a good deal of useful insight into the nature of sorting processes ..."
The most commonly known 0 (n log n) comparison-exchange sorting algorithm not needing external storage is heapsort (sometimes referred to as treesort) [F1], [Wi]. It is relatively easy to calculate the maximum number of exchanges required by heapsort; in this paper, we calculate the maximum number of (key) comparisons required, assuming that the size of the input is one less than a power of two. In addition, we exhibit an algorithm producing input yielding the maximum number of comparisons.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
