Question

What is direct recursion? What is indirect recursion?

Short answer

Answer: Direct recursion occurs when a function calls itself within its own body to solve a problem by breaking it down into smaller sub-problems. An example of direct recursion is the factorial function: factorial(n): if n == 0: return 1 else: return n * factorial(n-1) Indirect recursion occurs when a function calls another function, which might call the original function either directly or through a sequence of other functions, eventually leading back to the initial function. It involves multiple functions that call each other in a cycle. An example of indirect recursion is the following functions A and B: function A(n): if n <= 0: return 1 else: return n * B(n-1) function B(n): if n == 1: return 1 else: return n * A(n-1)

Step-by-step solution

Direct Recursion Definition

Direct recursion occurs when a function calls itself within its own body, i.e., a function refers to itself to solve a problem by breaking it down into smaller sub-problems. It is the most common type of recursion.

Direct Recursion Example

Consider the following example in which the function "factorial" calculates the factorial of a positive integer n using direct recursion. factorial(n): if n == 0: return 1 else: return n * factorial(n-1) Here, the function "factorial" calls itself within its own body to solve the problem.

Indirect Recursion Definition

Indirect recursion occurs when a function calls another function, which might call the original function either directly or through a sequence of other functions, eventually leading back to the initial function. In other words, indirect recursion involves multiple functions that call each other in a cycle.

Indirect Recursion Example

Consider the following example involving two functions "A" and "B" that illustrate indirect recursion. function A(n): if n <= 0: return 1 else: return n * B(n-1) function B(n): if n == 1: return 1 else: return n * A(n-1 In this example, function A calls function B, which in turn calls function A again, resulting in indirect recursion.