Question

What is direct recursion? What is indirect recursion?

Short answer

Answer: Direct recursion occurs when a function directly calls itself within its own function body, such as the factorial function. Indirect recursion occurs when a function A calls another function B, which then calls the original function A, as in the case of mutually recursive functions like even and odd.

Step-by-step solution

Definition of Direct Recursion

Direct recursion occurs when a function directly calls itself within its own function body. This means that the function performs some actions, and then calls itself again with new arguments, which eventually leads to a base case that ends the recursion.

Example of Direct Recursion

An example of a direct recursion function is the factorial function in mathematics. Here's a simple implementation of the factorial function using direct recursion: ``` def factorial(n): if n == 0: return 1 else: return n * factorial(n-1) ``` In this case, the function `factorial` directly calls itself within the function body.

Definition of Indirect Recursion

Indirect recursion occurs when a function A calls another function B, which then calls the original function A. This means that there is a cycle of function calls between two or more functions, with each function playing a role in the recursive process.

Example of Indirect Recursion

An example of indirect recursion can be found in a pair of mutually recursive functions. Here's a simple implementation of the even and odd functions using indirect recursion: ``` def is_even(n): if n == 0: return True else: return is_odd(n-1) def is_odd(n): if n == 0: return False else: return is_even(n-1) ``` In this case, the function `is_even` calls `is_odd`, which in turn calls `is_even` again. This cycle continues until the base case is reached, ending the recursion.