Balancing Performance Trade-offs in Modern Sorting Methodologies

Abstract

The study of sorting algorithms has always been a key topic. This paper thoroughly explains and investigates the time complexity of six classic sorting algorithms through theoretical analysis and experimental comparison. We implemented insertion sort, selection sort, bubble sort, shell sort, quicksort, and heapsort. By controlling data scale and distribution, we systematically tested the performance of different algorithms under various scenarios. The results show that there are significant efficiency differences between algorithms on small-scale data, and the advantages of quicksort and heapsort become more obvious as data size increases. Through extensive comparative experiments, this paper identifies the application scenarios of each algorithm, providing a theoretical basis for algorithm design and selection.