What is the purpose of big O notation?

Big O notation is a mathematical concept used to describe the performance or complexity of an algorithm in terms of its time or space requirements as the input size grows. It provides a high-level understanding of how the algorithm behaves in relation to the size of the input, allowing developers and computer scientists to predict the efficiency and scalability of algorithms when working with large datasets.

This notation abstracts away constants and lower-order terms to focus on the most impactful factors influencing an algorithm's performance. For example, if an algorithm runs in O(n) time, it indicates that the time it takes to complete the algorithm will increase linearly with the size of the input n. Understanding how different algorithms compare in their complexity is crucial when selecting the most efficient algorithm for a given problem.

While the other options touch on important aspects of computing, they do not directly relate to the core function of big O notation. For instance, describing the speed of a computer pertains more to hardware than algorithm complexity, and measuring memory usage could involve other metrics beyond big O notation. Analyzing data security involves different considerations altogether, focusing on the safety and protection of information rather than performance efficiency.