Question

How do we generally after the perameter to get to the base case

Answer 1

To reach the base case in a recursive function, we generally decrease or change the parameter value with each recursive call until it reaches a point where the base case condition is satisfied.

Here is a typical approach to design a recursive function with the base case:

1. Identify the problem and the desired solution.
2. Define the base case(s), which represents the simplest form of the problem where no further recursive calls are required. It should be a specific condition that can be easily checked.
3. Determine how to break down the problem into smaller subproblems. This usually involves modifying the parameter(s) in some way.
4. Make the recursive call(s) with the modified parameter(s), bringing the problem closer to the base case.
5. Combine the results of the recursive call(s) to obtain the final solution.

Here's an example implementation of a recursive function to calculate the factorial of a number:

```python
def factorial(n):
# Base case: factorial of 0 or 1 is 1
if n == 0 or n == 1:
return 1

# Recursive call: reducing the problem size by 1
return n * factorial(n - 1)
```

In this example, the base case is when `n` is equal to 0 or 1. The recursive call reduces the problem size by subtracting 1 from `n` until it reaches the base case.

It's important to ensure that the recursive call eventually reaches the base case to avoid infinite recursion.