AP Computer Science Exam Question:

Write a base case for a recursive function sumDigits(int n) that takes an integer n as input and returns the sum of its digits.

Answer:

The base case for the recursive function sumDigits(int n) can be defined as follows:

public static int sumDigits(int n) {
    if (n == 0) { // Base case: If the integer is 0
        return 0; // Return 0 as the sum of its digits
    }
}

Explanation:

1. The base case for the sumDigits(int n) function is checked using the conditional statement if (n == 0).
2. Inside the base case, when the input integer n is equal to 0, the function immediately returns 0 as the sum of its digits.
   • This is because when n is 0, it means there are no remaining digits to sum, so the sum is 0.
   • Returning 0 satisfies the base case requirement and allows the recursion to terminate.
3. The base case handles the simplest or smallest possible input for the sumDigits function.
   • In this case, when n is 0, the function returns 0 and stops further recursion.
   • For any positive number, n will eventually be reduced to 0 through the recursive steps.
4. Following the base case, further recursive steps are required to handle larger inputs of n and calculate the sum of their digits.