1031 Maximum Sum of Two Non-Overlapping Subarrays.py

Author: rajeevranjancom

1031 Maximum Sum of Two Non-Overlapping Subarrays.py

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+#!/usr/bin/python3
+"""
+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
+"""
+from typing import List
+
+
+class Solution:
+    def maxSumTwoNoOverlap(self, A: List[int], L: int, M: int) -> int:
+        """
+        Prefix sum + Brute force O(N^2)
+        two pointer i, j
+        """
+        n = len(A)
+        F = [0 for _ in range(n + 1)]
+        for i, a in enumerate(A):
+            F[i+1] = F[i] + a
+
+        ret = -float("inf")
+        for l, m in ((L, M), (M, L)):
+            for i in range(n + 1 - l):
+                for j in range(i + l, n + 1 - m):  # upper needs +1 here 
+                    cur = F[i + l] - F[i] + F[j + m] - F[j]
+                    ret = max(ret, cur)
+
+        return ret
+
+
+if __name__ == "__main__":
+    assert Solution().maxSumTwoNoOverlap([0,6,5,2,2,5,1,9,4], 1, 2) == 20