LeetCode 2178. Maximum Split of Positive Even Integers

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

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

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

Example 1:

Input: finalSum = 12

Output: [2,4,6]

Explanation:

The following are valid splits: (12), (2 + 10), (2 + 4 + 6), and (4 + 8). (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.

Example 2:

Input: finalSum = 7

Output: []

Explanation: 

There are no valid splits for the given finalSum. Thus, we return an empty array.

Example 3:

Input: finalSum = 28

Output: [6,8,2,12]

Explanation: 

The following are valid splits: (2 + 26), (6 + 8 + 2 + 12), and (4 + 24). (6 + 8 + 2 + 12) 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.

Constraints:

• 1 <= finalSum <= 1010

这里面主要是判断最后的数字的情况，如果finalsum可以被i跟i+2联系分解的话，那么就继续进行分解，直到小于i+i+2的时候，这时候将后面剩下的数字全部添加到list中就行，

下面是代码：

Runtime: 14 ms, faster than 60.44% of Java online submissions for Maximum Split of Positive Even Integers.

Memory Usage: 55.3 MB, less than 83.11% of Java online submissions for Maximum Split of Positive Even Integers.