<![CDATA[Data sorting is a fundamental step in the computer process that greatly affects the effectiveness of programs and overall system performance. In this study, three sorting algorithms, namely Bubble Sort, Insertion Sort, and Intro Sort, are analyzed and compared using recursive and iterative approaches. Bubble Sort serves as a basic algorithm example to understand the basic idea of element exchange, while Insertion Sort was chosen for its efficiency on small and nearly sorted datasets. Intro Sort, as a combination algorithm that integrates Quick Sort, Heap Sort, and Insertion Sort, was studied to reveal how its adaptive mechanism can provide more optimal results. The testing was conducted by measuring execution speed, sorting stability, and memory usage efficiency. The findings from this study show that Bubble Sort ranks lowest in terms of performance and is less suitable for large data sets. Insertion Sort shows better results on small data sets and those with similar patterns. Intro Sort emerges as the most effective algorithm with stable processing time, high adaptability, and faster and more efficient sorting results for various data sizes. Overall, this study emphasizes the importance of choosing a sorting algorithm that suits the characteristics of the data and the needs of the application. The combination of adaptive strategies such as those in Intro Sort is the best solution for current data processing, which demands high speed and efficiency.]]>
