4. Maximum Absolute Sum of Any Subarray

You are given an integer array nums. The absolute sum of a subarray [numsl, numsl+1, ..., numsr-1, numsr] is abs(numsl + numsl+1 + ... + numsr-1 + numsr).

Return the maximum absolute sum of any (possibly empty) subarray of nums.

Note that abs(x) is defined as follows:

• If x is a negative integer, then abs(x) = -x.

• If x is a non-negative integer, then abs(x) = x.

Example 1:

Input: nums = [1,-3,2,3,-4]
Output: 5
Explanation: The subarray [2,3] has absolute sum = abs(2+3) = abs(5) = 5.

Example 2:

Input: nums = [2,-5,1,-4,3,-2]
Output: 8
Explanation: The subarray [-5,1,-4] has absolute sum = abs(-5+1-4) = abs(-8) = 8.

Solution: (Using Kadane's Algorithm)

Approach: Finding the max Sum possible Finding the min sum possible Checking the max.

class Solution
{
public:
    int maxAbsoluteSum(vector<int> &nums)
    {

        int s = 0;
        int maxSum = INT_MIN;
        int minSum = INT_MAX;

        //Finding the max sum subarray
        for (int i = 0; i < nums.size(); i++)
        {
            s += nums[i];
            if (s > maxSum)
            {
                maxSum = s;
            }

            if (s < 0)
            {
                s = 0;
            }
        }

        //Finding the min sum subarray
        s = 0;
        for (int i = 0; i < nums.size(); i++)
        {
            s += nums[i];
            if (s < minSum)
            {
                minSum = s;
            }

            if (s > 0)
            {
                s = 0;
            }
        }

        return max(maxSum, abs(minSum));
    }
};

Time Complexity: O(n)