Evaluation Theoretical Efficiency Selection Sort By Big O Notation Analysis

Abstract

Algorithm complexity analysis is a fundamental aspect in computer science education and research, providing a critical framework for evaluating computational efficiency. This study presents a comprehensive theoretical evaluation of the Selection Sort algorithm using Big-O notation analysis to determine formal complexity bounds. The research aims to rigorously assess the time complexity of Selection Sort across best-case, average-case, and worst-case scenarios through asymptotic analysis methodology. The theoretical framework employs Big-O, Big-Theta, and Big-Omega notations alongside mathematical proof techniques including summation analysis and formal verification methods. A systematic operation-counting methodology is applied to derive precise complexity characterizations for each algorithmic phase. The analysis shows that Selection Sort exhibits uniform quadratic time complexity under all input conditions, unlike other sorting algorithms whose performance varies based on input characteristics. Mathematical evidence confirms that the algorithm performs exactly  comparisons regardless of the initial data arrangement, thereby establishing a strict boundary for theoretical complexity. These findings provide a complete mathematical basis for evaluating Selection Sort complexity, making a significant contribution to algorithm analysis literature and educational methodologies. Despite its consistent performance predictability, the quadratic complexity limits its scalability for large datasets. This theoretical evaluation serves as a comprehensive reference for algorithm selection decisions and complexity analysis instruction.