Finding the maximum subarray sum.

Here’s an example of a Java program that finds the maximum subarray sum using the Kadane’s algorithm:

   public class MaximumSubarraySum {

    public static int findMaximumSubarraySum(int[] nums) {

        int maxSoFar = nums[0]; // Initialize the maximum sum as the first element

        int maxEndingHere = nums[0]; // Initialize the maximum sum ending at the first element

        // Traverse the array starting from the second element

        for (int i = 1; i < nums.length; i++) {

            // Calculate the maximum sum ending at the current element

            maxEndingHere = Math.max(nums[i], maxEndingHere + nums[i]);

            // Update the maximum sum so far

            maxSoFar = Math.max(maxSoFar, maxEndingHere);

        }

       return maxSoFar;

    }

    public static void main(String[] args) {

        int[] nums = { -2, 1, -3, 4, -1, 2, 1, -5, 4 };

        int maxSum = findMaximumSubarraySum(nums);

        System.out.println("Maximum subarray sum: " + maxSum);
    }

}

In this program, the `findMaximumSubarraySum` method takes an array of integers as input and returns the maximum subarray sum. It uses two variables, `maxSoFar` and `maxEndingHere`, to keep track of the maximum sum found so far and the maximum sum ending at the current element, respectively.

The program then uses a loop to traverse the array starting from the second element. At each step, it calculates the maximum sum ending at the current element by choosing between starting a new subarray or extending the existing subarray. It updates `maxEndingHere` and `maxSoFar` accordingly.

In the `main` method, we provide an example array `nums` and call the `findMaximumSubarraySum` method to find the maximum subarray sum. Finally, the result is printed to the console.