java recursion quiz

certainly! recursion is a powerful programming technique where a function calls itself to solve a problem. it is often used to solve problems that can be broken down into smaller, similar subproblems. below is a tutorial on java recursion along with a quiz to test your understanding.

### understanding recursion in java

1. **definition**:
recursion occurs when a function calls itself to solve a smaller instance of the same problem. it usually involves a base case that stops the recursion and a recursive case that continues the recursion.

2. **base case**:
the base case is the condition under which the recursive function stops calling itself. without a base case, the function would call itself indefinitely, leading to a stack overflow error.

3. **recursive case**:
the part of the function where the function calls itself with a reduced problem size.

### example: factorial calculation

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

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

here’s how you can implement this in java:

### explanation of the code:

1. **method definition**: the `factorial` method takes an integer `n` as input.
2. **base case**: if `n` is `0`, it returns `1` because \( 0! = 1 \).
3. **recursive case**: if `n` is greater than `0`, it returns `n` multiplied by the factorial of `n-1`.
4. **main method**: the `main` method allows you to test the `factorial` function with a given number.

### quiz on recursion

now, let’s test your understanding with a quiz!

1. **question 1**: what is recursion?
- a) a method of solving problems by breaking them down into simpler subproblems.
- b) a function that runs in a loop.
- c) a way to avoid using loops in programming.

2. **question 2**: which of the f ...

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