Question:

Write a recursive method named factorial that takes an integer parameter n and returns the factorial of that number. The factorial of a non-negative integer n is denoted as n! and is defined as the product of all positive integers less than or equal to n.

For example, factorial(5) should return 120, as 5! = 5 * 4 * 3 * 2 * 1 = 120.

Write the method factorial to accomplish this using recursion.

Provide the Java code for the factorial method, and also provide a step-by-step explanation of how the method works using an example call to factorial(5).

public class RecursiveMethods {
    public static int factorial(int n) {
        // Base case: factorial of 0 is 1
        if (n == 0) {
            return 1;
        } else {
            // Recursive case: n! = n * (n-1)!
            return n * factorial(n - 1);
        }
    }
}

Explanation:

When the factorial method is called with factorial(5), the following steps occur:

1. The method checks if n is equal to 0. Since it's not, it proceeds to the else block.
2. The method calculates the factorial of 5 by multiplying 5 with the return value of factorial(4).
3. Now, in order to calculate factorial(4), it multiplies 4 with the return value of factorial(3).
4. This process repeats until factorial(1) is called, where the base case is triggered and it returns 1.
5. The method keeps returning values up the call stack, calculating the factorial at each level.
6. Finally, factorial(5) returns the result of 5 * 4 * 3 * 2 * 1, which is 120.

This demonstrates how the recursive method factorial works by breaking the original problem into smaller subproblems until reaching the base case, and then combining the results to obtain the final factorial value.