Comparative Analysis of Sorting Algorithms: Time Complexity and Practical Applications

In the field of computer science, sorting algorithms are crucial because they facilitate the effective processing and arrangement of data in a variety of scenarios, including data analysis, searching, and optimal system operation. The objective of this study is to look at and compare different sorting algorithms to see how well they work and how useful they are in different situations. The study tests popular sorting algorithms like Quick Sort, Merge Sort, and Bubble Sort on different input sizes, types of data (sorted, reversed, and random), and how they are implemented in the C++ programming language. The study shows how they work in terms of time complexity, resource use, and real applications through a systematic analysis. The most important results show that algorithms work differently depending on the inputs. For example, Quick Sort does better in most situations, while Merge Sort stays stable in the worst ones. This work also finds situations where simpler algorithms, like Bubble Sort, are good for small data sets. This paper is unique because it gives real-life cases, suggestions for choosing the best algorithm based on specific needs, and suggestions for how to do that. The goal of these results is to help programmers, teachers, and experts pick the right sorting algorithms for their computer tasks.