Answer
A recursive function is a function that calls itself in its definition. Recursive functions are used to solve problems that can be broken down into smaller, similar sub-problems. They are particularly useful when dealing with recursive data structures, such as trees and linked lists.
Work Step by Step
Here are some key characteristics of recursive functions:
Base case: A recursive function must have a base case that defines when to stop the recursion. This is the condition that terminates the recursion and returns a value.
Recursive case: A recursive function must have a recursive case that defines how to reduce the problem to a smaller sub-problem and call the function again.
Function calls: A recursive function makes one or more calls to itself in its definition. Each call results in a smaller instance of the same problem, until the base case is reached.
Stack: Each function call creates a new activation record or stack frame, which is added to a stack of function calls. When the base case is reached and the function returns, the stack is unwound and the return values are combined to give the final result.
Tail recursion: A recursive function is said to be tail-recursive if the recursive call is the last thing that the function does. Tail-recursive functions can be optimized by compilers to avoid building up the call stack.
Infinite recursion: If a recursive function does not have a well-defined base case or if the base case is not reached, the function will go into an infinite loop and result in a stack overflow error.
In summary, recursive functions are powerful and elegant, but they can also be difficult to understand and debug. They require careful design and implementation, and should be used only when appropriate.
