Optimizing Divide and Conquer Based Algorithms: the Case of Heapsort

Abstract

The divide and conquer approach is very useful in computer science applications. With this approach a large problem is broken down into small and manageable subproblems and each is solved separately. Then these solutions are combined to give the final solution to the problem. This paper presents a discussion on the divide and conquer based techniques for various sorting algorithm with special emphasis on heap sort. Most divide and conquer approachdividesaproblemintotwosubproblemsrecursively. Thethesisshowsthatternary systems are more promising than the more traditional binary systems used in the divide and conquer approach. In particular, heap on ternary tree does indicate some theoretical advantages over the more established binary systems. The paper also makes an endeavour to present a set of simulations with random numbers for both integers and floating point numbers to support our theoretically proven claim. For doing so, at first algorithm for conventional binary heapsort has been modified for three and four child heapsort. Thereafter, the paper finds out number of comparisons required, number of movements required and time taken for all the three systems. Experimental results clearly state that in most cases three child heasort demonstrates better performance than both binary and four child version of heapsort. The experimental data with graphical representation have also been presented to support the analysis. This experiment can surely be a guide to establish more promising ternary system in applications related to divide and conquer technique with the motivation‘A little advantage in optimization can be proven very useful in implementation of large systems’.