Ebook: Probabilistic analysis of some searching and sorting algorithms

We use binary trees to analyze two algorithms, insertion sort and multiple quckselect. In each case, we consider the number of comparisons consumed as a measure of performance. We assume that the ranks of the n data values being searched or sorted form a random permutation of the integers {l,...,n}. For insertion sort, we consider the limiting distribution of the number of comparisons consumed in the process of sorting the n keys. We present an average-case analysis of the number of comparisons multiple qukkselect (MQS) requires for simultaneously finding several order statistics in the data set.