Question

What is direct recursion? What is indirect recursion?

Short answer

Direct recursion is defined as a function that calls itself directly within its body, such as the factorial function. Indirect recursion occurs when a function calls another function, and that second function calls the first function, creating a recursive loop between the two functions, as seen in the calculation of the nth number in the Fibonacci sequence using two functions, fibonacci_even and fibonacci_odd.

Step-by-step solution

Direct recursion definition

Direct recursion occurs when a function calls itself directly within its body. It is a simple form of recursion, where the function can solve a base case easily, and for more complex cases, it calls itself with a reduced version of the input.

Indirect recursion definition

Indirect recursion occurs when a function calls another function, and that second function calls the first function. This creates a recursive loop between the two functions, leading back to the original function. This type of recursion requires multiple functions working together to achieve the desired output.

Direct recursion example

An example of direct recursion in Python is the calculation of a factorial of a number, n. The factorial function directly calls itself, reducing n by 1 each time, and multiplying n by the factorial function called with n-1, until it reaches the base case (0 or 1). ```python def factorial_direct(n): if n == 0 or n == 1: return 1 else: return n * factorial_direct(n - 1) ```

Indirect recursion example

An example of indirect recursion in Python is the calculation of the nth number in the Fibonacci sequence. Two functions (fibonacci_even and fibonacci_odd) alternately call each other, depending on whether n is even or odd, until the base case is reached. ```python def fibonacci_even(n): if n == 0: return 0 else: return fibonacci_odd(n - 1) def fibonacci_odd(n): if n == 1: return 1 else: return fibonacci_even(n - 1) + fibonacci_odd(n - 2) ``` In conclusion, direct recursion is when a function directly calls itself to solve a problem, while indirect recursion involves multiple functions calling each other to achieve the desired result.