What is the main purpose of recursion in programming?

Recursion is a programming technique where a function calls itself in order to solve a problem. The main purpose of recursion is to break down complex problems into smaller, more manageable instances of the same problem. This allows programmers to tackle problems by defining a base case (the simplest instance) and an inductive case (where the function calls itself with a modified argument).

For example, in calculating the factorial of a number, the factorial function can be defined in terms of factorials of smaller numbers, ultimately leading down to the simplest case, which is factorial of 0 (or 1). Each recursive call handles a smaller portion of the problem until the base case is reached, thus facilitating a clean and often elegant solution to problems such as those involving nested structures, tree traversals, or combinatorial problems.

The other choices address different programming concepts. Sorting data reflects a specific operation that can be done through various algorithms, while iterating through arrays typically involves using loops rather than recursive calls. Generating random numbers is a completely different function that does not inherently involve recursion. Thus, recursion's primary strength and purpose lie in its ability to simplify problem solving through the reduction of complexity by dividing tasks into smaller, recursive instances.