Why is a base case necessary in a recursive algorithm?

• A. It slows down the algorithm
• B. It makes recursion impossible
• C. It provides a stopping condition to prevent infinite recursion
• D. It ensures memory usage remains constant

Answer: (C)

In a recursive algorithm, the essential idea is to break the problem into smaller instances of the same problem and solve those until you reach something you can answer directly. The base case is that simplest situation where you can return a result without making further recursive calls. This stops the chain of calls and prevents infinite recursion, ensuring the algorithm terminates with a correct answer. Without a base case, each call would keep spawning more calls forever, eventually exhausting the call stack.

The other statements don’t fit. A base case isn’t about slowing the algorithm down; it’s about providing a guaranteed stopping point. It doesn’t make recursion impossible—quite the opposite, it enables recursion by giving a concrete ending condition. And it doesn’t guarantee constant memory usage—memory depends on how deep the recursion goes, which is controlled by the depth to reach the base case, not by the base case itself.