Question

What is direct recursion? What is indirect recursion?

Short answer

Question: Define direct recursion and indirect recursion and provide examples for each. Answer: Direct recursion occurs when a function calls itself within its own function definition, such as calculating the factorial of a number using the formula n * factorial(n - 1). Indirect recursion is when a function calls another function, which eventually calls the first function back, such as two functions A and B, where function A calls function B, and function B calls function A back.

Step-by-step solution

Direct Recursion

Direct recursion occurs when a function calls itself within its own function definition. It is a common programming technique used to solve problems by breaking them down into smaller, more manageable subproblems. Example: A simple example of direct recursion is the calculation of the factorial of a number. Factorial is denoted by n! and is the product of all the positive integers less than or equal to n. The programming logic for finding the factorial of a number `n` using direct recursion is: 1. If n is 0 or 1, the factorial of n is 1. 2. Otherwise, the factorial of n is n * factorial(n - 1). Here, the function calls itself.

Indirect Recursion

Indirect recursion is when a function calls another function which then eventually calls the first function. Similar to direct recursion, indirect recursion also helps in solving complex problems by dividing them into smaller subproblems. Example: Consider two functions A and B. Function A calls function B, and function B calls function A back. In this case, both functions are indirectly recursive. Factorial computation using indirect recursion: Function A(n): 1. If n is 0 or 1, return 1. 2. Otherwise, call function B(n - 1). Function B(n): 1. Call function A(n - 1) and multiply the result with n. In this example, function A calls function B, which in turn calls function A back.