Maximum Subarray Sum with One Deletion — LeetCode 1186 Python Solution

The problem

Given an array of integers, return the maximum sum for a non-empty subarray (contiguous elements) with at most one element deletion. In other words, you want to choose a subarray and optionally delete one element from it so that there is still at least one element left and the sum of the remaining elements is maximum possible.

Example

Input

arr = [1,-2,0,3]

Output

4

Explanation

Because we can choose [1, -2, 0, 3] and drop -2, thus the subarray [1, 0, 3] becomes the maximum value.

Python solution

class Solution:
    def maximumSum(self, arr: List[int]) -> int:
        n = len(arr)
        left = [0] * n
        right = [0] * n
        s = 0
        for i, x in enumerate(arr):
            s = max(s, 0) + x
            left[i] = s
        s = 0
        for i in range(n - 1, -1, -1):
            s = max(s, 0) + arr[i]
            right[i] = s
        ans = max(left)
        for i in range(1, n - 1):
            ans = max(ans, left[i - 1] + right[i + 1])
        return ans

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1186. Maximum Subarray Sum with One Deletion is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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