Exam Question:

Consider the following Java method that calculates the sum of numbers from 1 to n, where n is a positive integer:

public static int sumNumbers(int n) {
    if (n == 1) {
        return 1;
    } else {
        return n + sumNumbers(n - 1);
    }
}

Explain what the base case(s) are in this method and why they are important.

Answer and Explanation:

The base case in this method is when n is equal to 1. This is important because it provides a stopping condition for the recursive calls and ensures that the method eventually terminates.

When n is equal to 1, the method returns the value 1, which signifies the sum of numbers from 1 to 1 is simply 1.

When n is greater than 1, the method makes a recursive call to sumNumbers(n - 1). This recursive call breaks down the original problem of summing numbers from 1 to n into a smaller subproblem of summing numbers from 1 to n - 1. This process continues recursively until the base case is reached, at which point the method starts returning values from the recursive calls and unwinds the call stack to calculate the final result.

Without the base case, the recursive calls would continue infinitely, causing a stack overflow error and preventing the method from producing the correct result. Therefore, the base case is crucial in providing the necessary condition to terminate the recursion and ensure the method functions correctly.