A framework proposal for algorithm animation systems

The learning and analysis of algorithms and algorithm concepts are challenging to students due to the abstract and conceptual nature of algorithms. Algorithm animation is a form of technological support tool which encourages algorithm comprehension by visualising algorithms in execution. Algorithm animation can potentially be utilised to support students while learning algorithms. Despite widespread acknowledgement for the usefulness of algorithm animation in algorithm courses at tertiary institutions, no recognised framework exists upon which algorithm animation systems can be effectively modelled. This dissertation consequently focuses on the design of an extensible algorithm animation framework to support the generation of interactive algorithm animations. A literature and extant system review forms the basis for the framework design process. The result of the review is a list of requirements for a pedagogically effective algorithm animation system. The proposed framework supports the pedagogic requirements by utilising an independent layer structure to support the generation and display of algorithm animations. The effectiveness of the framework is evaluated through the implementation of a prototype algorithm animation system using sorting algorithms as a case study. This dissertation is successful in proposing a framework to support the development of algorithm animations. The prototype developed will enable the integration of algorithm animations into the Nelson Mandela Metropolitan University’s teaching model, thereby permitting the university to conduct future research relating to the usefulness of algorithm animation in algorithm courses

Abstract On the Adaptiveness of Quicksort

variants have been developed, the best of which are among the fastest generic sorting algorithms available, as testified by the choice of Quicksort as the default sorting algorithm in most programming libraries. Some sorting algorithms are adaptive, i.e. they have a complexity analysis which is better for inputs which are nearly sorted, according to some specified measure of presortedness. Quicksort is not among these, as it uses Ω(n log n) comparisons even when the input is already sorted. However, in this paper we demonstrate empirically that the actual running time of Quicksort is adaptive with respect to the presortedness measure Inv. Differences close to a factor of two are observed between instances with low and high Inv value. We then show that for the randomized version of Quicksort, the number of element swaps performed is provably adaptive with respect to the measure Inv. More precisely, we prove that randomized Quicksort performs expected O(n(1 + log(1 + Inv/n))) element swaps, where Inv denotes the number of inversions in the input sequence. This result provides a theoretical explanation for the observed behavior, and gives new insights on the behavior of the Quicksort algorithm. We also give some empirical results on the adaptive behavior of Heapsort and Mergesort.

G.: On the adaptiveness of quicksort

Quicksort was first introduced in 1961 by Hoare. Many variants have been developed, the best of which are among the fastest generic sorting algorithms available, as testified by the choice of Quicksort as the default sorting algorithm in most programming libraries. Some sorting algorithms are adaptive, i.e. they have a complexity analysis which is better for inputs which are nearly sorted, according to some specified measure of presortedness. Quicksort is not among these, as it uses Ω(n log n) comparisons even when the input is already sorted. However, in this paper we demonstrate empirically that the actual running time of Quicksort is adaptive with respect to the presortedness measure Inv. Differences close to a factor of two are observed between instances with low and high Inv value. We then show that for the randomized version of Quicksort, the number of element swaps performed is provably adaptive with respect to the measure Inv. More precisely, we prove that randomized Quicksort performs expected O(n(1 + log(1 + Inv/n))) element swaps, where Inv denotes the number of inversions in the input sequence. This result provides a theoretical explanation for the observed behavior, and gives new insights on the behavior of the Quicksort algorithm. We also give some empirical results on the adaptive behavior of Heapsort and Mergesort.