Sorting and Order Statistics

We will analyze the number of comparisons needed to solve the problem of sorting n distinct items into ascending order, and the related problem of selecting the kth smallest item from an unsorted list of n items. Section 1 examines mergesort, an algorithm with excellent worst case performance, and Section 2 examines quicksort, an algorithm with excellent average case performance. Section 3 contains some decision tree lower bounds on the number of comparisons used by any comparison-based sorting algorithm in the worst and average cases. Section 4 contains two linear-time selection algorithms, one average case and one worst case, and a lower bound based on the adversary method.