Optimizing Divide and Conquer Based Algorithms: the Case of Heapsort

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 sub problems 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 approach divides a problem into two sub problems recursively. The research shows that ternary 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.