Which of the following is a common use case for recursion in programming?

Recursion is a powerful technique often employed in programming, particularly for tasks that can be broken down into smaller, similar subproblems. One prevalent use case for recursion is traversing a directory structure. This is because a directory can contain subdirectories, each of which can contain further subdirectories, creating a hierarchical tree-like structure.

When using recursion to traverse a directory, a function can call itself to navigate through each subdirectory. This allows the program to explore all levels of the directory structure seamlessly. The base case for this recursive function is typically when the program reaches a file or an empty directory, at which point it can return to the previous level of the hierarchy. This method is elegant and effective, as it simplifies the code and maintains clarity when managing nested structures.

Other options listed, such as sorting an array, typically involve iterative algorithms or use of other techniques (like quicksort or mergesort, which can also be recursive but are not exclusively reliant on recursion). Creating graphical user interfaces often involves event-driven programming rather than recursion. Optimizing performance usually deals with algorithm efficiency and structure rather than recursive techniques. Thus, the choice pertaining to traversing a directory structure stands out as the most common and suitable application of recursion in programming.