An Effective Approach to Analyze Algorithms with Linear O(n) Worst-Case Asymptotic Complexity

A theoretical approach of asymptote analyzes the algorithms for approximate time complexity. The worst-case asymptotic complexity classifies an algorithm to a certain class. The asymptotic complexity for algorithms returns the degree variable of the algorithmic function while ignores the lower terms. In perspective of programming, asymptote only considers the number of iterations in a loop ignoring inside and outside statements. However, every statement must have some execution time. This paper provides an effective approach to analyze the algorithms belonging to the same class of asymptotes. The theoretical analysis of algorithmic functions shows that the difference between theoretical outputs of two algorithmic functions depends upon the difference between their coefficient of ‘n’ and the constant term. The said difference marks the point for the behavioral change of algorithms. This theoretic analysis approach is applied to algorithms with linear asymptotic complexity. Two algorithms are considered having a different number of statements outside and inside the loop. The results positively indicated the effectiveness of the proposed approach as the tables and graphs validates the results of the derived formula.

@article{Yousaf2019,
  title     = {An Effective Approach to Analyze Algorithms with Linear O(n) Worst-Case Asymptotic Complexity},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {10},
  number    = {3},
  year      = {2019},
  publisher = {The Science and Information Organization},
  author    = {Qazi Haseeb Yousaf and Muhammad Arif Shah and Rashid Naseem and Karzan Wakil and Ghufran Ullah},
  doi       = {10.14569/IJACSA.2019.0100344},
  url       = {https://doi.org/10.14569/IJACSA.2019.0100344}
}