What is the best approach for Maximize Subarray Sum After Removing All Occurrences of One Element?

The most efficient approach uses a Segment Tree that stores maximum subarray information (sum, prefix, suffix, and max subarray). For each distinct value, temporarily replace its positions with 0, query the tree for the maximum subarray sum, and then revert the changes. This reduces the overall complexity to O(n log n).

Is Maximize Subarray Sum After Removing All Occurrences of One Element asked at Google/Amazon/Meta?

Problems combining maximum subarray logic with structural modifications frequently appear in interviews at companies like Google, Amazon, and Meta. Variants involving Kadane’s algorithm, dynamic programming, and segment trees are common in high‑level algorithm rounds.

What data structure is used in Maximize Subarray Sum After Removing All Occurrences of One Element?

The optimal solution typically uses a Segment Tree to maintain maximum subarray metrics while performing temporary updates. The approach also relies on Kadane-style dynamic programming concepts to reason about maximum subarray sums.

What is the time complexity of Maximize Subarray Sum After Removing All Occurrences of One Element?

The optimized solution runs in O(n log n) time using a segment tree with point updates. Each element may be updated and reverted once, and every update takes O(log n). The brute force alternative can reach O(n^2) in the worst case if the array contains many unique values.

Description Hints 2 Video 57:21

3410. Maximize Subarray Sum After Removing All Occurrences of One Element

Q: Is Maximize Subarray Sum After Removing All Occurrences of One Element easy or hard?

This problem is classified as Hard because it combines multiple ideas: maximum subarray computation, value grouping, and efficient updates using a segment tree or advanced dynamic programming. Handling all possible values efficiently is the main challenge.

Q: Maximize Subarray Sum After Removing All Occurrences of One Element Python/Java solution

Most implementations build a segment tree over the array and group indices by value using a hash map. Each value’s indices are updated to zero, the tree’s max subarray value is queried, and the updates are reverted. The same strategy works consistently in Python, Java, C++, and Go.

Q: How to solve Maximize Subarray Sum After Removing All Occurrences of One Element in O(n)?

A pure O(n) implementation is difficult because the maximum subarray must be recomputed after removing each value type. Most competitive solutions rely on a segment tree or advanced dynamic programming ideas, which lead to an O(n log n) time complexity while still handling large inputs efficiently.

Hard23.0% acceptance2 companies

You are given an integer array nums.

You can do the following operation on the array at most once:

Choose any integer x such that nums remains non-empty on removing all occurrences of x.
Remove all occurrences of x from the array.

Return the maximum subarray sum across all possible resulting arrays.

Example 1:

Input: nums = [-3,2,-2,-1,3,-2,3]

Output: 7

Explanation:

We can have the following arrays after at most one operation:

The original array is nums = [-3, 2, -2, -1, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = -3 results in nums = [2, -2, -1, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = -2 results in nums = [-3, 2, -1, 3, 3]. The maximum subarray sum is 2 + (-1) + 3 + 3 = 7.
Deleting all occurences of x = -1 results in nums = [-3, 2, -2, 3, -2, 3]. The maximum subarray sum is 3 + (-2) + 3 = 4.
Deleting all occurences of x = 3 results in nums = [-3, 2, -2, -1, -2]. The maximum subarray sum is 2.

The output is max(4, 4, 7, 4, 2) = 7.

Example 2:

Input: nums = [1,2,3,4]

Output: 10

Explanation:

It is optimal to not perform any operations.

Constraints:

1 <= nums.length <= 10⁵
-10⁶ <= nums[i] <= 10⁶

Asked at 2 companies

Rubrik

Google

Topics

Hints open one at a time

Hint 1

Use a segment tree data structure to solve the problem.

Hint 2

Each node of the segment tree should store the subarray sum, the maximum subarray sum, the maximum prefix sum, and the maximum suffix sum within the subarray defined by that node.