What is the difference between direct and mutual recursion?

Direct recursion is when a function calls itself, while mutual recursion is when two or more functions call each other in a cycle.

Direct recursion is a concept in computer science where a function, within its definition, calls itself. This is a common technique used in programming to solve problems that can be broken down into smaller, similar problems. For example, the factorial of a number is a classic example of direct recursion. The factorial function calls itself with a smaller argument until it reaches the base case, which is usually a condition where the function can return a result without any further recursion.

On the other hand, mutual recursion involves two or more functions that call each other in a cycle. This means that function A calls function B, function B calls function C, and so on, until the last function calls function A again, forming a cycle. This type of recursion is less common than direct recursion but is still a useful technique in certain situations. For instance, mutual recursion can be used to simulate alternating processes or states.

In both direct and mutual recursion, it's crucial to have one or more base cases to prevent infinite recursion, which would result in a stack overflow error. The base case is a condition that stops the recursion by returning a value without making any more recursive calls.

While both direct and mutual recursion are powerful techniques, they can also be difficult to understand and debug due to their non-linear execution flow. Therefore, it's important to use them judiciously and ensure that the logic of the recursion is clear and correct.