find-nth-perfect-number-range()

Step 1: Define the Problem

We are tasked with creating a function in Java that generates the N-th perfect number within a certain range. A perfect number is a positive integer that is equal to the sum of its proper positive divisors, excluding the number itself.

Our function should take two parameters: N, which is the N-th perfect number we're trying to find, and R, which defines the range we're looking for the perfect number in (from 1 to R).

public static int findNthPerfectNumberInRange(int n, int r) {
}

Step 2: Identify Perfect Numbers

Next, we need to identify the perfect numbers within our given range. We can do this by iterating from 1 to R and, for each integer, check if it's a perfect number. We'll create a helper function, isPerfect(), that takes an integer and returns whether it's perfect.

public static boolean isPerfect(int num) {
   int sum = 1;
   for (int i = 2; i * i <= num; i++) {
       if (num % i==0) {if (i * i != num)sum = sum + i + num / i; else sum = sum + i;
   }
}

## Step 3: Collect N Perfect Numbers

With our helper function in place, we can start collecting the perfect numbers within our range. We'll maintain a count of how many perfect numbers we've found so far. Once this count equals N, we know we've found our N-th perfect number and can return it.

```java
public static int findNthPerfectNumberInRange(int n, int r) {
   int count = 0;
   for (int i = 2; i <= r; i++) {
       if(isPerfect(i)) {
           count++;
           if(n == count) return i;
       }
   }
   return -1;
}

Step 4: Handle Edge Cases

In the case where there are less than N perfect numbers within our range, our function currently returns -1. However, we need to make sure this is communicated to the user in a clearer way. We can throw an IllegalArgumentException with a helpful error message.

public static int findNthPerfectNumberInRange(int n, int r) {
   int count = 0;
   for (int i = 2; i <= r; i++) {
       if(isPerfect(i)) {
           count++;
           if(n == count) return i;
       }
   }
   throw new IllegalArgumentException("There are not enough perfect numbers in the given range.");
}

Conclusion

And that's it! We've created a function that efficiently finds the N-th perfect number within a given range. Always remember to test your function with various input to ensure it behaves as expected.