UVA – 11436 – Cubes – EXTREME!!!

Here’s the Solution
X^3-Y^3 = (X-Y)(X^2 + XY + Y^2) = N
Then we should check all factors of N,assume we have a factor i
let X-Y=i,X^2 + XY + Y^2 = N/i
solving those equations together Will give us X and Y.
However the problem here is the bounds.i.e what is the limit for i
for i to be maximum then X-Y must be maximum.
then Y must be zero
at Y = 0
N=(X-Y)*(X^2+XY+Y^2)=X*(X^2)
then i must be <= cubicRoot(N)
Also since Y cannot be zero
then i must be < cubicRoot(N)

import java.util.Scanner;
public class CubesExtreme {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		while (true) {
			long l = in.nextLong();
			if (l == 0)
				break;
			long xx = -1;
			long yy = Integer.MAX_VALUE;
			for (long i = 1; i * i * i < l; i++) {
				if (l % i == 0) {
					// x=i+y
					// (i+y)^2 + (i+y)y + y^2
					// i^2 + 3y^2 + 3iy
					long a = 3;
					long b = 3 * i;
					long c = i * i - (l / i);
					if (b * b >= 4 * a * c) {
						long r1 = (long) ((-b - Math.sqrt(b * b - 4 * a * c)) / (2 * a));
						long r2 = (long) ((-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a));
						if (r1 > 0
								&& (i + r1) * (i + r1) * (i + r1) - r1 * r1
										* r1 == l) {
							if (r1 < yy) {
								xx = i + r1;
								yy = r1;
							}
						}
						if (r2 > 0
								&& (i + r2) * (i + r2) * (i + r2) - r2 * r2
										* r2 == l) {
							if (r2 < yy) {
								xx = i + r2;
								yy = r2;
							}
						}
					}
				}
			}
			if (xx > 0)
				System.out.println(xx + " " + yy);
			else
				System.out.println("No solution");
		}

	}
}