Inventing a new sorting algorithm: A case study

Abstract

Dijkstra�s algorithm for finding the length of the longest upsequence within a given sequence of numbers is used as the basis for a case study in the development of a new sorting algorithm. The case study has pedagogic value for several reasons: the motivation for each step in the development of the algorithm is explained; interesting data structures are introduced; the complexity of the algorithm is analyzed using mathematics familiar to first year computer science students; the appendices provide detailed description of the implementation of the algorithm as well as several interesting examples of its use. The proposed algorithm merits attention since it uses O(nlogn) compares in the worst case (actually less than 2nlogn) and O(n) for both ordered or nearly ordered and reverse ordered or nearly reverse ordered sequences. © 1990, ACM. All rights reserved.