maximum-split-of-positive-even-integers

Maximum Split of Positive Even Integers

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maximumEvenSplit

You are given an integer <code>finalSum</code>. Split it into a sum of a maximum number of unique positive even integers.

<ul>
	<li>For example, given <code>finalSum = 12</code>, the following splits are valid (unique positive even integers summing up to <code>finalSum</code>): <code>(12)</code>, <code>(2 + 10)</code>, <code>(2 + 4 + 6)</code>, and <code>(4 + 8)</code>. Among them, <code>(2 + 4 + 6)</code> contains the maximum number of integers. Note that <code>finalSum</code> cannot be split into <code>(2 + 2 + 4 + 4)</code> as all the numbers should be unique.</li>
</ul>

Return a list of integers that represent a valid split containing a maximum number of integers. If no valid split exists for <code>finalSum</code>, return an empty list. You may return the integers in any order.

&nbsp;
Example 1:

<pre>
Input: finalSum = 12
Output: [2,4,6]
Explanation: The following are valid splits: <code>(12)</code>, <code>(2 + 10)</code>, <code>(2 + 4 + 6)</code>, and <code>(4 + 8)</code>.
(2 + 4 + 6) has the maximum number of integers, which is 3. Thus, we return [2,4,6].
Note that [2,6,4], [6,2,4], etc. are also accepted.
</pre>

Example 2:

<pre>
Input: finalSum = 7
Output: []
Explanation: There are no valid splits for the given finalSum.
Thus, we return an empty array.
</pre>

Example 3:

<pre>
Input: finalSum = 28
Output: [6,8,2,12]
Explanation: The following are valid splits: <code>(2 + 26)</code>, <code>(6 + 8 + 2 + 12)</code>, and <code>(4 + 24)</code>. 
<code>(6 + 8 + 2 + 12)</code> has the maximum number of integers, which is 4. Thus, we return [6,8,2,12].
Note that [10,2,4,12], [6,2,4,16], etc. are also accepted.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= finalSum &lt;= 1010</code></li>
</ul>

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