# 1749. 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.

Constraints:

1 <= nums.length <= 105 -104 <= nums\[i] <= 104

## Solutions

1. **dynamic programming**

```cpp
class Solution {
public:
    int maxAbsoluteSum(vector<int>& nums) {
        int mins = 0, maxs = 0, res = 0;
        for (auto n : nums) {
            mins = min(mins + n, min(n, 0));
            maxs = max(maxs + n, max(n, 0));
            res = max(res, max(abs(mins), abs(maxs)));
        }
        return res;
    }
};
```