maximum-alternating-sum-of-squares

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