When you write an algorithm, you want it to be efficient, correct, and easy to understand. But how do you know if your algorithm is better than another one that solves the same task? In this article, you will learn about some methods that you can use to compare algorithms and evaluate their performance.
One of the most common ways to compare algorithms is to measure their time complexity, or how fast they run as the input size grows. Time complexity is usually expressed using the big O notation, which describes the upper bound of the worst-case scenario. For example, if an algorithm has a time complexity of O(n^2), it means that its running time increases quadratically with the input size. You can use time complexity to compare algorithms by finding the one with the lowest big O value for a given 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?
Another way to compare algorithms is to measure their space complexity, or how much memory they use as the input size grows. Space complexity is also expressed using the big O notation, but it refers to the amount of extra space that an algorithm allocates or uses during its execution. For example, if an algorithm has a space complexity of O(n), it means that it needs linear space proportional to the input size. You can use space complexity to compare algorithms by finding the one with the lowest big O value for a given task.
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?
A third way to compare algorithms is to measure their accuracy and correctness, or how well they produce the expected output for a given input. Accuracy and correctness are especially important for algorithms that deal with numerical, probabilistic, or approximate problems. You can use accuracy and correctness to compare algorithms by testing them on different inputs and checking their outputs against a reference solution or a predefined criterion. For example, if an algorithm is supposed to sort a list of numbers, you can compare its output with a sorted list and count the number of errors or deviations.
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
A fourth way to compare algorithms is to measure their readability and maintainability, or how easy they are to understand and modify by humans. Readability and maintainability are important for algorithms that are complex, long, or involve multiple steps or components. You can use readability and maintainability to compare algorithms by applying some coding standards and best practices, such as using meaningful names, comments, indentation, modularity, and documentation. For example, if an algorithm is written in pseudocode, you can compare its readability and maintainability with an algorithm written in a specific programming language.
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.
A fifth way to compare algorithms is to consider the trade-offs and context, or how well they balance the different aspects of performance and suitability for a given task. Trade-offs and context are important for algorithms that have different advantages and disadvantages depending on the input, output, or environment. You can use trade-offs and context to compare algorithms by weighing the pros and cons of each algorithm and choosing the one that best fits your needs and goals. For example, if an algorithm is fast but uses a lot of memory, you can compare it with an algorithm that is slower but uses less memory, and decide which one is more appropriate for your situation.
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.