maximum-alternating-sum-of-squares

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Algorithms

You are given an integer array <code>nums</code>. You may rearrange the elements in any order.

The alternating score of an array <code>arr</code> is defined as:

<ul>
	<li><code>score = arr[0]2 - arr[1]2 + arr[2]2 - arr[3]2 + ...</code></li>
</ul>

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

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [1,2,3]

Output: 12

Explanation:

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

The alternating score is calculated as:

<code>score = 22 - 12 + 32 = 4 - 1 + 9 = 12</code>
</div>

Example 2:

<div class="example-block">
Input: nums = [1,-1,2,-2,3,-3]

Output: 16

Explanation:

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

The alternating score is calculated as:

<code>score = (-3)2 - (-1)2 + (-2)2 - (1)2 + (3)2 - (2)2 = 9 - 1 + 4 - 1 + 9 - 4 = 16</code>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 105</code></li>
	<li><code>-4 * 104 &lt;= nums[i] &lt;= 4 * 104</code></li>
</ul>