find-nth-perfect-number()

Step 1: Understand the Problem

The requirement is to create a function in Swift that will find the nth perfect number. A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. Our task is to create a function that finds the nth perfect number.

var perfectNumbers = [Int]()

Step 2: Writing the Function to Check a Perfect Number

The first thing we'll do is to write a function which checks whether given number is perfect or not. We can do this by creating a for loop from 1 to half of the number (since no divisor can be greater than half of the number), and adding divisor to sum if it divides the number completely (remainder is zero).

func isPerfectNumber(_ n: Int) -> Bool {
    var sum = 0
    for i in 1..<(n / 2) + 1 {
        if n % i == 0 {
            sum += i
        }
    }
    return sum == n
}

Step 3: Collecting the Perfect Numbers

Next, we'll loop through the natural numbers from 1 and for each number, we'll check if it is a perfect number using the function we wrote in step 2. If it is, we'll store it in our array of perfect numbers.

var n = 1
while perfectNumbers.count < 4 {
    if isPerfectNumber(n) {
        perfectNumbers.append(n)
    }
    n += 1
}

Step 4: Returning the nth Perfect Number

Finally, we'll build a function findNthPerfectNumber() that will take an integer as input (n), and return the nth perfect number by returning the nth element from our perfect numbers array.

func findNthPerfectNumber(_ n: Int) -> Int {
    return perfectNumbers[n-1]
}

Conclusion

The solution to our problem involved understanding what a perfect number is, and how to establish whether a number fits this criteria. Once this was established, it was a matter of looping through the natural numbers to locate these perfect numbers and adding them to an array. Finally, to solve our initial problem, we created a function that returned the nth perfect number from our array.

Here is the full implementation:

func isPerfectNumber(_ n: Int) -> Bool {
    var sum = 0
    for i in 1..<(n / 2) + 1 {
        if n % i == 0 {
            sum += i
        }
    }
    return sum == n
}

var perfectNumbers = [Int]()
var n = 1
while perfectNumbers.count < 4 {
    if isPerfectNumber(n) {
        perfectNumbers.append(n)
    }
    n += 1
}

func findNthPerfectNumber(_ n: Int) -> Int {
    return perfectNumbers[n-1]
}