Recursion mechanics

A recursive method calls itself on a smaller input. Two ingredients are mandatory:

1. Base case — an input answered directly, no call.
2. Recursive case — the call moves toward the base case (progress).

public static int factorial(int n) {
    if (n <= 1) {            // base case
        return 1;
    }
    return n * factorial(n - 1);   // progress: n shrinks by 1
}

The call stack makes traces mechanical. For factorial(4):

factorial(4) = 4 * factorial(3)
                 factorial(3) = 3 * factorial(2)
                                 factorial(2) = 2 * factorial(1)
                                                 factorial(1) = 1

Unwind: 1 → 2 → 6 → 24. Write the descent, hit the base, multiply back up.

Exam trace conventions: count calls (factorial(4) makes 4 total), and remember StackOverflowError is the runtime signature of missing progress — an infinite loop's recursive twin.