findHappyNumbersRange()

Step 1: Understand the Problem

First, we need to understand the problem we are trying to solve and the requirements. A ‘Happy number’ is defined by following a process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlesssly in a cycle. Our task is to write a Java function that finds all happy numbers in a given range.

Java code:

Step 2: Start to Write The Function

Start by writing the skeleton of the function. Let's name it findHappyNumbersInRange. The start and end integers will be provided as arguments since we're finding happy numbers within a specific range.

Java code:

public static List<Integer> findHappyNumbersInRange(int start, int end) {
}

Step 3: Implement The Happy Check Function

Next, let's implement a helper function named isHappy. This function takes an integer as an input and returns boolean depending on whether the number is happy or not.

Java code:

public static boolean isHappy(int num) {
}

Step 4: Build The isHappy Method

Inside the isHappy method, use a while loop to perform the operation of replacing the number with the sum of squares of its digits until it becomes 1 or when it starts to repeat.

Java code:

public static boolean isHappy(int num) {
    int slow = num, fast = num;
    do {
        slow = calculateSumOfSquares(slow);
        fast = calculateSumOfSquares(calculateSumOfSquares(fast));
    } while (slow != fast);
    return slow == 1;
}

Step 5: Finish The Happy Numbers Function

Now, we can use the isHappy function inside our findHappyNumbersInRange to find and add happy numbers to our result list.

Java code:

public static List<Integer> findHappyNumbersInRange(int start, int end) {
    List<Integer> result = new ArrayList<>();

    for (int i = start; i <= end; i++) {
        if (isHappy(i)) {
            result.add(i);
        }
    }

    return result; 
}

Conclusion

This Java function successfully calculates and returns all happy numbers within a given range. As a programmer, understanding the process of breaking down tasks into smaller, more manageable tasks – such as creating helper functions – is essential, and this function exemplifies that methodology.