Breaking Down Heap Sort: A Deep Dive into Algorithmic Efficiency

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The better algorithm to sort the array of elements is heap sort.

Big-O of Heapsort

The big-o notation for heap sort is 0(n log n) = 0(log n!). To heapify elements whose subtrees already have max heads, one needs to keep comparing the elements with its right and left child’s and continue driving it downwards until the children are smaller than it. Heap sort has the worst time of (O(nlogn)) as one has to keep exchanging the root and last element up to the last stage.

Big-O of Mergesort

The time complexity of the best, average and worst cases of a heap sort is O(n * log(n)). According to (Chivers 360), the merge sort adopts a divide and conquer algorithm that subdivides the midpoint of each sub-array. The entire input is iterated at a frequency of O(log(n)) times. The iteration of n items log(n) times gives the result O(n log(n)).

Reasons for choosing Heap Sort

It requires less space as compared to merge sort. Since we have limited memory, using an algorithm that is less memory sensitive will make one wait for a long time for a program to be executed.

The slow random access performance will make other algorithms to perform poorly. The extra space required by a merge sort will continue to affect the performance of the computer thus making other resources to be unavailable.

Benefits of Heap Sort

1. One of the benefits heap sorts would have is that it has minimal memory usage.

2. The second benefit is that it can be used as an internal sorting algorithm.

3. Another benefit is it is more efficient.

Importance of RAM

RAM is a big concern in today’s world. It determines the speed and performance of a computer. As a programmer, one will spend more time executing codes when writing programs. The higher the RAM in a computer the more the speed and performance thus one will spend less time running and executing programs during coding. Also, considering that applications such as Android Studio and local servers such as WAMP and XAMP are memory sensitive, the more RAM a computer has the better the programs will perform.

The areas where RAM may come to play is in the installation and running of computer programs. In the most application that is used in programming, they consume a lot of resources and having a computer with less RAM will be a challenge to a programmer. The applications will take a lot of time to start up and in executing programs that one will end up spending more time doing simple tasks. Therefore, RAM is essential for a programmer and one should always choose a computer with more RAM.

Work Cited

Chivers, Ian, and Jane Sleightholme. "An Introduction to Algorithms and the Big O Notation." Introduction to Programming with Fortran. Springer, Cham, 2015. 359-364.

September 11, 2023
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