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3727. Maximum Alternating Sum of Squares

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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
ArrayGreedySorting

Hints

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.