A Worst Case Analysis of Heap-Sort (Classic Reprint)

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.

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