Maximum Absolute Sum of Any Subarray

Problem Description

You are given an integer array nums. The absolute sum of a subarray [nums_l, nums_{l+1}, ..., nums_{r-1}, nums_r] is abs(nums_l + nums_{l+1} + ... + nums_{r-1} + nums_r). Return the maximum absolute sum of any (possibly empty) subarray of nums.

Key Insights

• The absolute sum of a subarray can be influenced by both positive and negative numbers.
• To find the maximum absolute sum, we can consider both the sum of the subarray elements and their negatives.
• We can utilize a modified version of Kadane's algorithm to track both the maximum and minimum subarray sums.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use Kadane's algorithm, which is an efficient way to find the maximum sum of a contiguous subarray. We will modify this algorithm to also track the minimum subarray sum to account for the absolute values. The key steps are:

1. Initialize two variables to track the current maximum and minimum subarray sums.
2. Iterate through the array, updating these variables based on the current number.
3. Keep track of the overall maximum absolute sum by checking both the maximum and minimum sums encountered.

Code Solutions