# Empirical Analysis

Empirical analysis in algorithm analysis involves the experimental evaluation of an algorithm’s performance using actual data or simulations. This involves running the algorithm multiple times on different input sizes or datasets and measuring its running time and memory usage.

Empirical analysis can help identify the actual running time of an algorithm, which may differ from the theoretical analysis. In addition, empirical analysis can help identify the worst-case and best-case scenarios for an algorithm, which can provide insights into the algorithm’s performance in different situations.

To perform empirical analysis, one needs to define the input size, generate random or real-world data, and measure the algorithm’s running time and memory usage. The results can be plotted on a graph to visualize the algorithm’s performance and identify trends.

Empirical analysis can be used to compare the performance of different algorithms for the same problem and help in choosing the most efficient algorithm for a particular use case.

### Example

Let’s take the example of sorting algorithms to explain empirical analysis in algorithm analysis.

Suppose we have two sorting algorithmsSelection Sort and Quick Sort, and we want to compare their performance in terms of running time and memory usage. The theoretical analysis suggests that Quick Sort has an average case time complexity of O(nlogn), while Selection Sort has a time complexity of O(n^2).

To perform empirical analysis, we can create an array of random integers of different sizes, say from 1000 to 10000, and run each algorithm multiple times on these arrays. We can measure the running time of each algorithm and the memory usage required by each algorithm to sort the arrays.

Once we have collected the data, we can plot the results on a graph to visualize the performance of each algorithm. The graph may show that Quick Sort is faster than Selection Sort, especially for larger arrays. We can also observe that the memory usage of Quick Sort is more than Selection Sort.

By performing empirical analysis, we can conclude that Quick Sort is a better choice for sorting large datasets in terms of running time, while Selection Sort may be suitable for smaller datasets where memory usage is a constraint.

Overall, empirical analysis provides a practical approach to evaluate the performance of algorithms, and helps in choosing the most efficient algorithm for a specific use case.

We hope this article helped you to understand about Concept of Empirical Analysis in a very detailed way.

Online Web Tutor invites you to try Skillshike! Learn CakePHP, Laravel, CodeIgniter, Node Js, MySQL, Authentication, RESTful Web Services, etc into a depth level. Master the Coding Skills to Become an Expert in PHP Web Development. So, Search your favourite course and enroll now.