find-happy-numbers-range()

Step 1: Understanding Happy Numbers

A happy number is defined by the process of taking a number, replacing it with the sum of the squares of its digits, and repeating the process until the number might be replaced by 1, or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1, they are happy numbers.

In Swift, we can first start implementing a helper function that can check if a single number is a happy number or not.

func isHappy(_ n: Int) -> Bool {
    var slow: Int = n
    var fast: Int = n
    repeat {
        slow = findSquareSum(slow)
        fast = findSquareSum(findSquareSum(fast))
    } while slow != fast
    return slow == 1
}
func findSquareSum(_ num: Int) -> Int {
    var _num = num
    var sum = 0
    while _num > 0 {
        let digit = _num % 10
        sum += digit * digit
        _num /= 10
    }
    return sum
}```

## Step 2: Implement the Range Function

Now, let's implement our function to find happy numbers in a given range. 

```swift
func findHappyNumbersRange(_ start: Int,_ end: Int) -> [Int] {
    var happyNumbers: [Int] = []
    for number in start...end {
        if isHappy(number) {
            happyNumbers.append(number)
        }
    }
    return happyNumbers
}

This function initializes an empty array to store happy numbers. It then loops through numbers from start to end (both inclusive), and for each number, it checks if the number is a happy number by calling the helper function we defined earlier. If the number is a happy number, it adds the number to the array. Finally, it returns the array of happy numbers.

Step 3: Testing the Function

Now you can test this function by calling it with different ranges, for example:

print(findHappyNumbersRange(1, 100))

Conclusion

To solve this problem, we first defined a helper function to determine if a single number is a happy number or not. Then we implemented the main function which iterates over all numbers in a given range, and checks if they are happy or not by calling the helper function, and adds the happy numbers to a result array. This solution works in O(n) time, where n is the size of the range.