How do you solve Maximum Alternating Sum of Squares on LeetCode?

Maximum Alternating Sum of Squares (LeetCode #3727) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Even indices should have larger squares.

What is the time complexity of Maximum Alternating Sum of Squares?

The optimal solution for Maximum Alternating Sum of Squares runs in O(n log n) time and uses O(1) space. Sorting the array takes O(n log n), and calculating the score takes O(n), leading to O(n log n) overall.

What is the brute force solution for Maximum Alternating Sum of Squares?

The brute force approach for Maximum Alternating Sum of Squares is Brute Force, with O(n²) time complexity and O(1) space complexity. Try all possible arrangements of the array and compute the alternating score for each. This guarantees finding the maximum score but is inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Alternating Sum of Squares?

Maximum Alternating Sum of Squares uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximum Alternating Sum of Squares?

Explain your thought process clearly. Discuss edge cases like all negative numbers. Practice sorting and array manipulation problems.

What are common mistakes when solving Maximum Alternating Sum of Squares?

Not considering negative numbers properly. Forgetting to square the values.

#3727

Maximum Alternating Sum of Squares

Medium

ArrayGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

💡

Intuition

Time O(n log n)Space O(1)

To maximize the alternating score, place the largest squares at even indices and the smallest squares at odd indices. This ensures the highest positive contributions and lowest negative contributions.

⚙️

Algorithm

3 steps

1Step 1: Sort the array in descending order.
2Step 2: Calculate the score using the sorted array by adding squares at even indices and subtracting squares at odd indices.
3Step 3: Return the calculated score.

solution.py4 lines

1def maxAlternatingSum(nums):
2    nums.sort(reverse=True)
3    score = sum(nums[i] ** 2 if i % 2 == 0 else -nums[i] ** 2 for i in range(len(nums)))
4    return score

ℹ

Complexity note: Sorting the array takes O(n log n), and calculating the score takes O(n), leading to O(n log n) overall.

1Even indices should have larger squares.
2Sorting helps maximize positive contributions.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.