Revisiting calculation of moments of number of comparisons used by the randomized quick sort algorithm

TL;DR

This paper revisits a method for calculating the moments of comparisons in randomized quicksort, highlighting its computational efficiency and its applicability to binary search trees, providing a refined analytical approach.

Contribution

It demonstrates that the Kirschenhofer, Prodinger, and Tichy method simplifies the calculation of moments for quicksort comparisons and extends to binary search tree analysis.

Findings

The method reduces computational effort in calculating moments.

It confirms the method's applicability to binary search tree path length.

Provides more efficient analytical tools for randomized algorithms.

Abstract

We revisit the method of Kirschenhofer, Prodinger and Tichy to calculate the moments of comparisons used by the quick sort algorithm. We reemphasize that this approach helps in calculating these quantities with less computation. We also point out that as observed by Knuth this method also gives moments for total path length of a binary search tree built over a random set of n keys.