What are the base case and recursive case in a recursive algorithm?

The base case is the terminating scenario in recursion, while the recursive case is the problem that's divided into smaller sub-problems.

In a recursive algorithm, the base case and the recursive case are two fundamental components. The base case is the simplest form of the problem that can be solved directly without further recursion. It's the condition that allows the recursion to stop, preventing it from going on indefinitely. Without a base case, a recursive algorithm would keep making recursive calls forever, leading to a stack overflow error. The base case is usually a known solution to the problem and is used to gradually simplify the larger problem.

On the other hand, the recursive case is the part of the algorithm where the function calls itself, breaking down the larger problem into smaller, more manageable sub-problems. The recursive case is designed in such a way that each time it's invoked, it brings the algorithm closer to the base case. This is done by changing the parameters in a way that the problem size decreases with each recursive call.

For example, in a factorial function, the base case is when the input number is 0 or 1, both of which return 1 as the factorial. The recursive case is when the input number is greater than 1, in which case the function calls itself with the input number minus one. This continues until the base case is reached.

Understanding the base case and the recursive case is crucial to designing and implementing recursive algorithms. The base case provides the stopping point and the known solution, while the recursive case ensures that the algorithm progresses towards the base case with each recursive call. Together, they form the foundation of any recursive algorithm.