🔗 Determining an Integer Square Root

For any positive integer n, we want to determine whether n is the square of some positive integer x.

Complete the function that returns the square of x + 1 if n is the square of a positive integer x, or returns -1 if n is not the square of a positive integer.

• n is a positive integer between 1 and 50000000000000, inclusive.

Input/Output Example #1

Since 121 is the square of the positive integer 11, it returns 144, the square of (11+1).

Input/Output Example #2

Since 3 is not the square of a positive integer, it returns -1.

An algorithm that checks whether n is the square of some number, and if so, returns the square of (that number's square root + 1).

If it is a perfect square, return $(\sqrt{n} + 1)^2$.

To check whether n is a perfect square, check whether Math.sqrt(n) matches its integer part.

If this check confirms that n is the square of some number, return the value of $(\sqrt{n} + 1)^2$.

If not, return -1.

JAVA
/**
 * Determining an Integer Square Root class
 *
 * @author RWB
 * @since 2021.12.13 Mon 19:15:59
 */
class Solution
{
	/**
	 * Method that returns the answer
	 *
	 * @param n: [long] integer
	 *
	 * @return [long] answer
	 */
	public long solution(long n)
	{
		double sqrt = Math.sqrt(n);
		
		long num = (long) sqrt;
		
		return sqrt == num ? (long) Math.pow(sqrt + 1, 2) : -1;
	}
}