1031. Maximum Sum of Two Non-Overlapping Subarrays (Subarray Sum => Prefix Sum !) 20.6.16 Medium

Given an array A of non-negative integers, 
return the maximum sum of elements in two non-overlapping (contiguous) subarrays, 
which have lengths L and M.  (For clarification, the L-length subarray could occur before or after the M-length subarray.)

Formally, return the largest V for which V = (A[i] + A[i+1] + ... + A[i+L-1]) + (A[j] + A[j+1] + ... + A[j+M-1]) and either:

0 <= i < i + L - 1 < j < j + M - 1 < A.length, or
0 <= j < j + M - 1 < i < i + L - 1 < A.length.
 

Example 1:

Input: A = [0,6,5,2,2,5,1,9,4], L = 1, M = 2
Output: 20
Explanation: One choice of subarrays is [9] with length 1, and [6,5] with length 2.
Example 2:

Input: A = [3,8,1,3,2,1,8,9,0], L = 3, M = 2
Output: 29
Explanation: One choice of subarrays is [3,8,1] with length 3, and [8,9] with length 2.
Example 3:

Input: A = [2,1,5,6,0,9,5,0,3,8], L = 4, M = 3
Output: 31
Explanation: One choice of subarrays is [5,6,0,9] with length 4, and [3,8] with length 3.
 

Note:

L >= 1
M >= 1
L + M <= A.length <= 1000
0 <= A[i] <= 1000


Solution: O(n) T and O(1) S
class Solution(object):
    def maxSumTwoNoOverlap(self, A, L, M):
        """
        :type A: List[int]
        :type L: int
        :type M: int
        :rtype: int
        """
        for i in range(1, len(A)):
            A[i] += A[i - 1]
        res, L_max, M_max = A[L + M - 1], A[L - 1], A[M - 1]
        # window  | --- L --- | --- M --- |
        for i in range(L + M, len(A)):
            L_max = max(L_max, A[i - M] - A[i - L - M])
            res = max(res, A[i] - A[i - M] + L_max)
        # window  | --- M --- | --- L --- |
        for i in range(L + M, len(A)):
            M_max = max(M_max, A[i - L] - A[i - L - M])
            res = max(res, A[i] - A[i - L] + M_max)
        return res