#3487

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Maximum Unique Subarray Sum After Deletion

Maximize the sum of a subarray after performing deletions, ensuring elements remain unique.

Problem Statement

Given an integer array nums, you can delete any number of elements from it, but the array cannot be empty. Your goal is to select a subarray from the remaining elements such that the sum of the subarray is maximized, and all elements in the subarray are unique.

Return the maximum possible sum of a subarray that satisfies these conditions. You are allowed to delete any elements, and the sum should be computed from the subarray formed by the remaining unique elements.

Examples

Example 1

Input: nums = [1,2,3,4,5]

Output: 15

Select the entire array without deleting any element to obtain the maximum sum.

Example 2

Input: nums = [1,1,0,1,1]

Output: 1

Delete the element nums[0] == 1 , nums[1] == 1 , nums[2] == 0 , and nums[3] == 1 . Select the entire array [1] to obtain the maximum sum.

Example 3

Input: nums = [1,2,-1,-2,1,0,-1]

Output: 3

Delete the elements nums[2] == -1 and nums[3] == -2 , and select the subarray [2, 1] from [1, 2, 1, 0, -1] to obtain the maximum sum.

Constraints

1 <= nums.length <= 100
-100 <= nums[i] <= 100

Solution Approach

Array Scanning with Hash Lookup

Iterate through the array, keeping track of the elements in a hash set. If a duplicate element is found, adjust the subarray by removing the leftmost element to maintain uniqueness. Update the sum accordingly.

Sliding Window Technique

Use the sliding window approach to dynamically expand and contract the subarray. As new unique elements are encountered, include them in the sum. For duplicates, adjust the left boundary of the window and re-calculate the sum.

Maximizing Subarray Sum

While maintaining uniqueness, calculate the sum of the subarray at each step. Keep track of the highest sum encountered, and ensure that no element repeats within the current subarray.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity of this approach is O(n), where n is the length of the array. This is because each element is processed once. The space complexity is O(n), as the hash set stores at most n unique elements during the scan of the array.

What Interviewers Usually Probe

The candidate should identify the importance of handling duplicates efficiently with a hash table.
A strong answer will demonstrate how to apply a sliding window and adjust the sum dynamically.
Watch for understanding of edge cases like arrays with all negative elements or arrays with only duplicates.

Common Pitfalls or Variants

Common pitfalls

Failing to handle edge cases like arrays with only one element or all elements being the same.
Not optimizing for space by relying too heavily on brute-force methods to check for uniqueness.
Overcomplicating the problem by trying to delete elements arbitrarily instead of using efficient window adjustments.

Follow-up variants

Change the deletion rule, allowing only one deletion per subarray.
Introduce additional constraints, such as a minimum subarray size.
Allow a fixed number of deletions and find the maximum sum after performing those deletions.

FAQ

How do I approach the "Maximum Unique Subarray Sum After Deletion" problem?

Start by scanning the array and using a hash set to track unique elements. Adjust the subarray when encountering duplicates and maximize the sum accordingly.

What is the main pattern used in "Maximum Unique Subarray Sum After Deletion"?

The problem uses array scanning combined with hash lookups to manage uniqueness, along with a sliding window technique to maximize the sum of the subarray.

What is the time complexity of solving the "Maximum Unique Subarray Sum After Deletion" problem?

The time complexity is O(n), where n is the length of the array, as each element is processed only once.

Can the "Maximum Unique Subarray Sum After Deletion" problem be solved with brute force?

While brute force is possible, it would be inefficient. The optimal solution leverages hash sets and sliding windows for O(n) performance.

How do I handle duplicates in "Maximum Unique Subarray Sum After Deletion"?

Duplicates are handled by adjusting the left boundary of the window and removing elements from the subarray to ensure uniqueness.

terminal

Solution

Solution 1: Greedy + Hash Table

We first find the maximum value $\textit{mx}$ in the array. If $\textit{mx} \leq 0$, then all elements in the array are less than or equal to 0. Since we need to select a non-empty subarray with the maximum element sum, the maximum element sum would be $\textit{mx}$.

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class Solution:
    def maxSum(self, nums: List[int]) -> int:
        mx = max(nums)
        if mx <= 0:
            return mx
        ans = 0
        s = set()
        for x in nums:
            if x < 0 or x in s:
                continue
            ans += x
            s.add(x)
        return ans

Continue Practicing

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