To answer this question, we need to understand the concept of recursion in programming.
Recursion is a programming technique where a function calls itself to solve a problem by breaking it down into smaller subproblems.
In order for a recursive function to work correctly, it requires three essential components:
A. Base case: A base case is a condition that is used to terminate the recursion. It is the simplest form of the problem that does not require further recursive calls. Without a base case, the recursive function would continue calling itself infinitely, resulting in infinite recursion.
B. Recursive call: The recursive call is the step where the function calls itself with a smaller or simpler version of the problem. This allows the function to break down the original problem into smaller subproblems. Without the recursive call, the function would not be able to solve the problem recursively.
C. Subtraction: While subtraction is often used in recursive functions, it is not a requirement for a recursive function to work correctly. Recursive functions can perform various operations depending on the problem at hand, such as addition, multiplication, or string manipulation. The specific operation used in a recursive function depends on the problem being solved.
D. Local variable declarations: Local variable declarations are not required for a recursive function to work correctly. Recursive functions can use local variables to store intermediate results or perform calculations, but they are not essential for the recursion itself.
Based on the above explanations, the correct answer is C. If subtraction were left out, the recursive function could still work correctly as long as it includes a base case and recursive call.