Maximum absolute difference between sum of two contiguous sub-arrays

Given an array of integers, find two non-overlapping contiguous sub-arrays such that the absolute difference between the sum of two sub-arrays is maximum.

• Time : O(n)
• Space : O(n)

c++

int findMaxAbsDiff(vector<int> A) {
    int n = A.size();
    vector<int> midp(n), madp(n);
    midp[n-1] = madp[n-1] = A[n-1];
    for(int i = n - 2, mi = A[n-1], ma = A[n-1]; i >= 0; i--) {
        mi = min(A[i], mi + A[i]);
        ma = max(A[i], ma + A[i]);
        midp[i] = mi;
        madp[i] = ma;
    }
    int res = 0;
    for(int i = 0, mi = 0, ma = 0; i < n - 1; i++) {
        mi = min(A[i], mi + A[i]);
        ma = max(A[i], ma + A[i]);
        res = max({res,
            abs(mi - midp[i+1]),
            abs(mi - madp[i+1]),
            abs(ma - midp[i+1]),
            abs(ma - madp[i+1])
        });
    }
    return res;
}