Maximum Absolute Sum of Any Subarray

class Solution {
public:
    int calculateMaxAbsoluteSum(vector<int>& arr) {
        int minSum = 0, maxSum = 0;
        int currentSum = 0;
        for (int num : arr) {
            currentSum += num;
            minSum = min(minSum, currentSum);
            maxSum = max(maxSum, currentSum);
        }
        return maxSum - minSum;
    }
};

This solution in C++ effectively calculates the maximum absolute sum of any subarray in a given integer array. The function calculateMaxAbsoluteSum receives a vector of integers and utilizes the Kadane's algorithm variant to find the maximum absolute sum. Here's a breakdown of the method:

• Initialize variables minSum and maxSum to zero. These variables will keep track of the minimum and maximum cumulative sums encountered as the array is traversed, respectively.
• A currentSum variable is used to store the running total of elements as the array is iterated through.
• Iterate through each number in the array:
  • Add the current number to currentSum.
  • Update minSum with the smaller of minSum or currentSum.
  • Update maxSum with the larger of maxSum or currentSum.
• After completing the iteration, the function returns the difference between maxSum and minSum, which represents the maximum absolute sum of any subarray within the provided array.

This approach ensures that you get the correct maximum absolute sum with optimal performance and minimal additional space usage.

class Solution {

    public int maximumAbsoluteSum(int[] data) {
        int lowestSum = 0, highestSum = 0;
        int cumulativeSum = 0;

        for (int num : data) {
            cumulativeSum += num;

            lowestSum = Math.min(lowestSum, cumulativeSum);
            highestSum = Math.max(highestSum, cumulativeSum);
        }

        return highestSum - lowestSum;
    }
}

The Java function maximumAbsoluteSum calculates the maximum absolute sum of any subarray from a given array of integers. The function operates by maintaining a cumulative sum of values iterated through the array, using this running total to determine the minimum and maximum sums encountered.

Here's a concise breakdown of the algorithm:

• Initialize lowestSum and highestSum to 0. These variables track the smallest and largest values of the cumulative sum respectively as the array is processed.
• Initialize cumulativeSum to 0 to begin summing array elements.
• Iterate over each element in the array data:
  • Add the current element to cumulativeSum.
  • Update lowestSum to be the smaller of lowestSum or cumulativeSum.
  • Update highestSum to be the larger of highestSum or cumulativeSum.
• After completing the iteration over the array, compute the difference between highestSum and lowestSum, which gives the maximum absolute sum of any subarray.

This difference is then returned as the result, representing the maximum possible absolute sum of the subarray differences within the array. The approach efficiently calculates this value in a single pass through the array, ensuring optimal performance.

class Solution:
    def maximumAbsoluteSum(self, values):
        smallest_prefix = 0
        largest_prefix = 0
        cumulative_sum = 0

        for value in values:
            cumulative_sum += value

            smallest_prefix = min(smallest_prefix, cumulative_sum)
            largest_prefix = max(largest_prefix, cumulative_sum)

        return largest_prefix - smallest_prefix

This Python function solves the problem of finding the maximum absolute sum of any subarray by keeping track of the smallest and largest prefix sums encountered during a single iteration over the values list. The solution method is efficient, employing a running cumulative sum to update the smallest and largest encountered prefix sums.

• Calculate the cumulative sum of elements in the input array while iterating.
• Track the smallest and largest cumulative sum observed up to each point in the array.
• Subtract the smallest prefix sum from the largest prefix sum to derive the maximum absolute sum of any subarray.

The output returns this difference, which represents the solution. This implementation provides an optimal approach given its linear time complexity, O(n), where n is the number of elements in the input array.