Absolute Max Algorithm

The Absolute Max Algorithm is a computational method used to determine the maximum value of a function within a specified domain. This algorithm is particularly useful in solving optimization problems, where the goal is to find the highest or lowest value of a function given certain constraints. The Absolute Max Algorithm works by analyzing the function's behavior within the given domain, examining critical points, endpoints, and other points of interest, and determining the maximum and minimum values of the function based on this analysis. To apply the Absolute Max Algorithm, one must first identify the critical points of the function, which are the points where the derivative is equal to zero or does not exist. Next, the function's values at the critical points, the endpoints of the domain, and any other points of interest are evaluated. Once all of these values have been computed, the algorithm compares them to determine which is the largest (or smallest, in the case of minimizing the function) and returns that value as the absolute maximum (or minimum) of the function within the specified domain. This algorithm is widely used in various fields, such as economics, engineering, and physics, where finding the optimal solution or maximizing the efficiency of a given process is crucial for success.
package Maths;

import java.util.Arrays;

/**
 * description:
 * <p>
 * absMax([0, 5, 1, 11]) = 11, absMax([3 , -10, -2]) = -10
 * </p>
 */
public class AbsoluteMax {
    public static void main(String[] args) {
        int[] numbers = new int[]{3, -10, -2};
        System.out.println("absMax(" + Arrays.toString(numbers) + ") = " + absMax(numbers));
    }

    /**
     * get the value, return the absolute max value
     *
     * @param numbers contains elements
     * @return the absolute max value
     */
    public static int absMax(int[] numbers) {
        int absMaxValue = numbers[0];
        for (int i = 1, length = numbers.length; i < length; ++i) {
            if (Math.abs(numbers[i]) > Math.abs(absMaxValue)) {
                absMaxValue = numbers[i];
            }
        }
        return absMaxValue;
    }
}

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