The Function Signature

In many interview problems, you will encounter a well-defined function signature. This signature specifies the function's name, the input parameters it expects, and the type of output it should produce. It serves as a contract that defines how the function should be used and what it should return. By following the function signature, you ensure that your implementation meets the problem's requirements.

function fibonacci(num) {
  // Function implementation
}

In this case, the function name is fibonacci, and it expects a single input parameter called num. As you know, the purpose of the fibonacci function is to calculate the Fibonacci sequence for the given num. The function signature does not specify the return type because JavaScript is a dynamically typed language. However, in statically typed languages, you might see something like function fibonacci(num: number): number, which indicates that the function accepts a number as input and returns a number.

Helper Functions

Now, let's discuss the concept of using a helper function in recursive problems. Recursive solutions often require additional values or arguments to be passed down through each recursive call. However, you should avoid modifying the given function signature unless you have discussed it with the interviewer. In such cases, you can introduce a helper function that accepts the required additional arguments.

For instance, if we want to introduce a cache to optimize the Fibonacci function, we can use a helper function.

Here's an example:

function fibonacci(num) {
  return fibonacciHelper(num, {});
}

function fibonacciHelper(num, cache) {
  // Define the base case and recursive case
}

In this case, the fibonacci function serves as a wrapper that calls the actual recursive implementation fibonacciHelper. The fibonacciHelper function takes two parameters: num represents the current number for which we want to calculate the Fibonacci value, and cache represents a cache object that can store previously calculated Fibonacci values to avoid redundant computations.

Using a helper function, you can extend the number of arguments or values passed down to recursive calls without changing the original function signature. It provides a way to incorporate additional information or optimizations required for an efficient recursive solution.

When dealing with recursive algorithms, certain subproblems may be repeatedly solved with the same input, leading to duplicated efforts and increased computational overhead. Using a cache in these problems is important because it helps avoid redundant calculations and improves the function's efficiency. This optimization method is called Dynamic Programming, which we'll learn about in a later lesson.

Remember, the function signature should remain consistent with the problem requirements, and the helper function can provide the necessary flexibility and extensibility in your recursive implementation.