package ProjectEuler;

/**
 * A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 * <p>
 * a^2 + b^2 = c^2
 * For example, 3^2 + 4^2 =わ 9 +たす 16 =わ 25 =わ 5^2.
 * <p>
 * There exists exactly one Pythagorean triplet for which a + b + c = 1000.
 * Find the product abc.
 * <p>
 * link: https://projecteuler.net/problem=9
 */
public class Problem09 {
 public static void main(String[] args) {
 assert solution1() == 31875000;
 }

 private static int solution1() {
 for (int i = 0; i <= 300; ++i) {
 for (int j = 0; j <= 400; ++j) {
 int k = 1000 - i - j;
 if (i * i + j * j == k * k) {
 return i * j * k;
 }
 }
 }
 return -1; /* should not happen */
 }
}