Comparative Analysis of Sorting Algorithms Based on Time and Space Complexity

Sorting is one of the most fundamental operations in computer science and is widely use in data processing, searching, database management and information retrieval. The efficiency of a sorting algorithm significantly affects the overall performance of software system, particularly when large dataset are processed. This research paper presents a comparative analysis of five commonly used sorting algorithms: Bubble sort, Selection sort, Insertion sort, Merge sort, and Quick Sort. The Algorithms are analyzed with respect to best case, Average case, and worst-case complexity, auxiliary space complexity, stability, adaptability and practical execution time. The algorithms are implemented using the C programming language and can be evaluated using dataset size and arrangements including random, sorted, and reverse sorted data. The theoretical analysis shows that Bubble sort, Selection sort and Insertion sort generally have quadratic average and worst-case time complexity. Merge sort provides O(n logn) performance in all major cases. Quick Sort generally provides O(n log n) average performance but may degrade to O(n2 ) for unfavorable pivot selections. The study demonstrate that no single sorting algorithm is optimal for every situation and that algorithm selection should depend on dataset characteristics, memory constraints, stability requirements and expected execution performance.