Is Maximum Sum Score of Array easy or hard?

Maximum Sum Score of Array is considered a medium difficulty problem. The logic is straightforward once you recognize that suffix sums can be derived from the total sum, but identifying this prefix-sum optimization is the key challenge.

Maximum Sum Score of Array Python/Java solution

Most implementations compute the total sum first, then iterate while maintaining a running prefix sum. At each index, calculate the suffix using the total and update the maximum score. The same logic works across Python, Java, C++, Go, TypeScript, Rust, and JavaScript.

How to solve Maximum Sum Score of Array in O(n)?

First compute the total sum of the array. Iterate through the array while maintaining a running prefix sum. At each index i, compute the suffix as total minus the prefix sum before i, then evaluate max(prefix, suffix). Track the maximum value seen during the traversal.

What is the best approach for Maximum Sum Score of Array?

The best approach uses a running prefix sum combined with the total array sum. At each index, compute the prefix sum and derive the suffix sum using total minus the previous prefix. The score is max(prefix, suffix). This method runs in O(n) time and uses O(1) extra space.

Is Maximum Sum Score of Array asked at Google/Amazon/Meta?

Problems based on prefix sums and array scoring patterns frequently appear in interviews at companies like Amazon, Google, and Meta. While this exact problem may not always appear, the prefix–suffix sum technique tested here is a common interview pattern.

What data structure is used in Maximum Sum Score of Array?

The problem primarily uses arrays and the prefix sum technique. No advanced data structures are required. The optimal implementation only keeps a few integer variables to track the running prefix sum and total sum.

What is the time complexity of Maximum Sum Score of Array?

The optimal solution runs in O(n) time because the array is scanned a constant number of times. A brute force method that recomputes prefix and suffix sums for every index takes O(n²) time. Space complexity can be reduced to O(1) using a running prefix sum.

Description Hints 2 Solution Video 4:48

2219. Maximum Sum Score of Array

Medium62.6% acceptance1 companyPremium elsewhere, free here

You are given a 0-indexed integer array nums of length n.

The sum score of nums at an index i where 0 <= i < n is the maximum of:

The sum of the first i + 1 elements of nums.
The sum of the last n - i elements of nums.

Return the maximum sum score of nums at any index.

Example 1:

Input: nums = [4,3,-2,5]
Output: 10
Explanation:
The sum score at index 0 is max(4, 4 + 3 + -2 + 5) = max(4, 10) = 10.
The sum score at index 1 is max(4 + 3, 3 + -2 + 5) = max(7, 6) = 7.
The sum score at index 2 is max(4 + 3 + -2, -2 + 5) = max(5, 3) = 5.
The sum score at index 3 is max(4 + 3 + -2 + 5, 5) = max(10, 5) = 10.
The maximum sum score of nums is 10.

Example 2:

Input: nums = [-3,-5]
Output: -3
Explanation:
The sum score at index 0 is max(-3, -3 + -5) = max(-3, -8) = -3.
The sum score at index 1 is max(-3 + -5, -5) = max(-8, -5) = -5.
The maximum sum score of nums is -3.

Constraints:

n == nums.length
1 <= n <= 10⁵
-10⁵ <= nums[i] <= 10⁵

Asked at 1 company

Amazon

Topics

Array Prefix Sum

Hints open one at a time

Hint 1

How can we use precalculation to efficiently calculate the average difference at an index?

Hint 2

Create a prefix and/or suffix sum array.

4:48

Still stuck?Read the written solution, or watch a walkthrough.

Open solution