recursion in java full tutorial how to create recursive methods

certainly! recursion is a powerful programming technique in which a method calls itself to solve a problem. in java, recursion can simplify code for problems that can be broken down into smaller, similar subproblems. below is a comprehensive tutorial on recursion in java.

what is recursion?

recursion occurs when a method calls itself in order to solve a problem. each recursive call makes the problem smaller, eventually reaching a base case that terminates the recursion.

key components of recursion

1. **base case**: the condition under which the recursion stops. every recursive method must have a base case to prevent infinite recursion.
2. **recursive case**: the part of the method where the function calls itself with a modified argument, moving towards the base case.

advantages of recursion

- simplifies code for problems that can be divided into similar subproblems (e.g., tree traversals, factorial calculation).
- often leads to cleaner and more intuitive code.

disadvantages of recursion

- can lead to high memory usage due to the call stack.
- may result in stack overflow if the recursion goes too deep.
- performance can be slower than iterative solutions due to overhead of multiple method calls.

recursive method example: factorial calculation

let's look at a classic example of recursion: calculating the factorial of a number.

factorial definition

- factorial of a non-negative integer \( n \) (denoted as \( n! \)) is the product of all positive integers less than or equal to \( n \).
- base case: \( 0! = 1 \)
- recursive case: \( n! = n \times (n-1)! \)

java implementation

explanation of the code

1. **method declaration**: the method `factorial` takes an integer `n` as an argument.
2. **base case**: if `n` is `0`, return `1`.
3. **recursive case**: if `n` is greater than `0`, return `n` multiplied by the factorial of `(n - 1)`.
4. **main method**: calls the `factorial` function and prints the result.

example output

if you run the program ...

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