What methods can you use to compare algorithms for the same task?

Time complexity for various level of inputs and various size of inputs will help to understand whether your algorithm is better or not

It refers to the amount of time required so that an algorithm completes its task (relative to the size of the input data). In simpler words, it’s a way to understand how the running time of an algorithm changes when the input size grows. It answers a simple question: What’s the rate of change in time when we change the inputs?

It’s the amount of memory (space) an algorithm uses to complete its task (relative to the size of the input data). Just like with time, we want to understand how much more memory will be required as the input size grows. It answers a simple question: What’s the rate of change in memory (spcae) when we change the inputs?

I believe it's also important to indicate the differences of the use cases of accuracy and correctness. While accuracy is quantitative measure and it is stands for how close your results are regarding to expected results, correctness is a binary measure which it means it is rather correct or not. In sorting algorithms, authentication systems etc. we expect a a specific response like if the user inserts the same password value with the value in our database or if the response of the sorting algorithm successfully sorted the data with the given order. However, since the accuracy is a quantitive value we do not expect to get binary results instead we are expecting a degree of correctness like we practice on classification or regression tasks

One other aspect to consider is how feasible it is to make further improvements and optimizations to the algorithm in the future. One should not only consider how maintainable an algorithm is, but also how improvable it is before deciding which is the appropriate choice. You may find that in a naive implementation of two algorithms, one has better readability and maintainability, but once all of the necessary improvements and optimizations are added the other has better readability. Some algorithms may have improvements that are trivial to implement while others may require a much more significant development time to get the most out of the algorithm.

To compare algorithms for the same task, you can: Time Complexity Analysis: Measure how execution time scales with input size. Space Complexity Analysis: Examine memory usage as input grows. Benchmarking: Run algorithms on actual data and compare performance. Big O Notation: Express algorithm efficiency as a mathematical function. Experimental Analysis: Conduct experiments to observe real-world performance. Each method provides insights into an algorithm's strengths and weaknesses, helping you choose the best one for a specific task.

One also should consider the average case Scenario which aims to show how the algorithm performs in general, everyday situations. It’s a realistic measure of an algorithm’s efficiency in everyday use. It Reflects Real-World Use: Most of the time, algorithms are not running in the best or worst-case scenarios. They’re dealing with everyday, typical inputs. The average-case scenario tells us how the algorithm is likely to perform in these normal conditions. some algorithms might have a poor worst-case performance but a good average-case performance, making them suitable for practical use.