Abstract
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.
Highlights
An algorithm is a set of instructions to specify a solution to the problem in a finite time
As the results demonstrated that difference of coefficients of n and difference of constant terms of two algorithmic functions is nearer so a simpler formula generates the approximate crossover point for algorithmic functions
The relation between terms of algorithmic functions leads to the formula for intersecting point
Summary
An algorithm is a set of instructions to specify a solution to the problem in a finite time. Given the number of algorithms for a problem, it is obligatory that every algorithm differs in the order of complexity. Considering the difference in complexity of algorithms, some algorithms perform better than others in the provided environment. The level of complexity effects in execution time, the memory space acquired and lines of code (LOC) for the algorithms. From the given three metrics of complexity, LOC has no direct impact on algorithm complexity and is not considered a good metric for analysis of algorithm [1]. Execution time and space acquired are metrics for analysis of algorithms. The run-time of the algorithm is measured either by approximate analysis or execution time on the machine. The approximate method follows a virtual computational model. The virtual computational model depends on certain fixed execution times for different programming structures.
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