Single.java

package control;

public class Single {
  /**
   * This method is used to calculate the sum of the first n natural numbers.
   * n exclusive
   *
   * @param n The number of natural numbers to sum.
   * @return The sum of the first n natural numbers.
   */
  public static int sumRange(int n) {
    // Direct calculation using the formula for the sum of the first n natural numbers
    return (n * (n - 1)) / 2;
  }

  /**
   * This method calculates the maximum value in an array of integers.
   *
   * @param arr The array of integers.
   * @return The maximum value in the array.
   */
  public static int maxArray(int[] arr) {
    if (arr == null || arr.length == 0) {
      return 0; // Handle empty or null array
    }
    int max = arr[0];
    for (int i = 1; i < arr.length; i++) {
      if (arr[i] > max) {
        max = arr[i];
      }
    }
    return max;
  }

  /**
   * This method calculates the sum of the first n natural numbers, modulo m.
   *
   * @param n The number of natural numbers to sum.
   * @param m The modulus.
   */
  public static int sumModulus(int n, int m) {
    int k = (n - 1) / m; // Calculate the number of multiples of m
    return m * (k * (k + 1)) / 2; // Sum of multiples of m using the formula, more efficient
  }
}