Is Maximum Alternating Sum of Squares easy or hard?

Maximum Alternating Sum of Squares is generally considered a Medium-level problem. The implementation is straightforward once you recognize the greedy insight that larger squares should appear in positive positions. Identifying that ordering determines the optimal result is the main challenge.

Maximum Alternating Sum of Squares Python/Java solution

The typical implementation sorts the input array, then iterates through it while alternating between adding and subtracting squared values. This logic translates directly to Python, Java, C++, Go, or TypeScript with built-in sorting functions and a simple loop.

How to solve Maximum Alternating Sum of Squares in O(n)?

A strict O(n) solution generally is not used because the algorithm relies on ordering elements by magnitude. Determining which elements should occupy positive versus negative positions requires sorting, leading to O(n log n) complexity. Once sorted, the alternating sum can be computed in O(n).

What is the best approach for Maximum Alternating Sum of Squares?

The most effective solution uses a greedy strategy with sorting. Sort the array and place the largest values in positions contributing positively to the alternating expression while assigning the smallest values to negative positions. This maximizes the difference between added and subtracted squared values and runs in O(n log n) time with O(1) extra space.

Is Maximum Alternating Sum of Squares asked at Google/Amazon/Meta?

Problems involving rearranging arrays to maximize expressions appear frequently in interviews at companies like Amazon, Google, and Meta. While the exact problem name may vary, the underlying pattern—sorting combined with greedy placement—is a common interview topic.

What data structure is used in Maximum Alternating Sum of Squares?

The main data structure is a simple array. The algorithm relies on sorting the array and iterating through it to compute the alternating sum of squared values. No additional complex structures such as hash maps or trees are required.

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

The optimal approach runs in O(n log n) time due to sorting the array. After sorting, computing the alternating sum of squares requires a single linear scan, which is O(n). Space complexity is O(1) if sorting is done in place.

Description Hints 2 Solution Video 6:54

3727. Maximum Alternating Sum of Squares

Medium75.7% acceptance

You are given an integer array nums. You may rearrange the elements in any order.

The alternating score of an array arr is defined as:

score = arr[0]² - arr[1]² + arr[2]² - arr[3]² + ...

Return an integer denoting the maximum possible alternating score of nums after rearranging its elements.

Example 1:

Input: nums = [1,2,3]

Output: 12

Explanation:

A possible rearrangement for nums is [2,1,3], which gives the maximum alternating score among all possible rearrangements.

The alternating score is calculated as:

score = 2² - 1² + 3² = 4 - 1 + 9 = 12

Example 2:

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

Output: 16

Explanation:

A possible rearrangement for nums is [-3,-1,-2,1,3,2], which gives the maximum alternating score among all possible rearrangements.

The alternating score is calculated as:

score = (-3)² - (-1)² + (-2)² - (1)² + (3)² - (2)² = 9 - 1 + 4 - 1 + 9 - 4 = 16

Constraints:

1 <= nums.length <= 10⁵
-4 * 10⁴ <= nums[i] <= 4 * 10⁴

Topics

Hints open one at a time

Hint 1

The score uses squares of values. The original signs of nums don't affect the squared terms.

Hint 2

In the alternating sum, even indices contribute positively and odd indices negatively.

6:54

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1class Solution:
2    def maxAlternatingSum(self, nums: List[int]) -> int:
3        

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Examples

Case 1Case 2

Input

[1,2,3]

Input

[1,-1,2,-2,3,-3]

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