Question

What is direct recursion? What is indirect recursion?

Short answer

Answer: Direct recursion occurs when a function calls itself within its own definition, usually to solve problems that can be broken down into smaller, similar subproblems. An example of direct recursion is the calculation of the factorial of a number (n!) using the function Factorial(n). In contrast, indirect recursion happens when a function calls another function, which then calls the original function, creating a cycle of function calls. An example of indirect recursion is the calculation of the odd and even sequence for a number using two alternating functions, odd(n) and even(n).

Step-by-step solution

Definition of Direct Recursion

Direct recursion occurs when a function calls itself within its own definition. This means that the function will keep calling itself until a base case or stopping condition is met. This is a common technique used in programming when solving problems that can be easily broken down into smaller, similar subproblems.

Example of Direct Recursion

A simple example of direct recursion is the calculation of the factorial of a number. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. In mathematical terms, using direct recursion: Factorial(n) = 1, if n = 0 Factorial(n) = n * Factorial(n-1), if n > 0

Definition of Indirect Recursion

Indirect recursion occurs when a function calls another function, which in turn calls the original function, creating a cycle of function calls. In other words, the original function indirectly calls itself through a series of other function calls. This can be achieved through multiple functions working together to reach the stopping condition.

Example of Indirect Recursion

A simple example of indirect recursion is the calculation of the odd and even sequence for a number. We will use two functions, one for odd numbers (odd(n)) and one for even numbers (even(n)), to demonstrate this: 1. odd(n): - returns true if n is 0 - else, calls even(n-1) 2. even(n): - returns false if n is 0 - else, calls odd(n-1) With indirect recursion, the function calls alternate between odd(n) and even(n) depending on the input value until the base case is met (when n==0), determining whether the given number is odd or even.