## DEV Community

Abhishek Chaudhary

Posted on

# 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`

SOLUTION:

``````class Solution:
def maximumEvenSplit(self, finalSum: int) -> List[int]:
res = []
if finalSum & 1:
return res
i = 1
while i * (i + 1) <= finalSum:
res.append(2 * i)
i += 1
if i * (i + 1) > finalSum:
res.pop()
res.append(finalSum - (i - 1) * (i - 2))
return res
``````