package ProjectEuler;

/**
 * The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The
 * square of the sum of the first ten natural numbers is, (1 + 2 + ... + 10)^2 = 552 = 3025 Hence
 * the difference between the sum of the squares of the first ten natural numbers and the square of
 * the sum is 3025 − 385 = 2640. Find the difference between the sum of the squares of the first N
 * natural numbers and the square of the sum.
 *
 * <p>link: https://projecteuler.net/problem=6
 */
public class Problem06 {
  public static void main(String[] args) {
    int[][] testNumbers = {
      {10, 2640},
      {15, 13160},
      {20, 41230},
      {50, 1582700}
    };

    for (int[] testNumber : testNumbers) {
      assert solution1(testNumber[0]) == testNumber[1]
          && solutions2(testNumber[0]) == testNumber[1];
    }
  }

  private static int solution1(int n) {
    int sum1 = 0;
    int sum2 = 0;
    for (int i = 1; i <= n; ++i) {
      sum1 += i * i;
      sum2 += i;
    }
    return sum2 * sum2 - sum1;
  }

  private static int solutions2(int n) {
    int sumOfSquares = n * (n + 1) * (2 * n + 1) / 6;
    int squareOfSum = (int) Math.pow((n * (n + 1) / 2.0), 2);
    return squareOfSum - sumOfSquares;
  }
}