# 2178. Maximum Split of Positive Even Integers

## Description

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

## Solutions

• class Solution {
public List<Long> maximumEvenSplit(long finalSum) {
List<Long> ans = new ArrayList<>();
if (finalSum % 2 == 1) {
return ans;
}
for (long i = 2; i <= finalSum; i += 2) {
finalSum -= i;
}
return ans;
}
}

• class Solution {
public:
vector<long long> maximumEvenSplit(long long finalSum) {
vector<long long> ans;
if (finalSum % 2) return ans;
for (long long i = 2; i <= finalSum; i += 2) {
ans.push_back(i);
finalSum -= i;
}
ans.back() += finalSum;
return ans;
}
};

• class Solution:
def maximumEvenSplit(self, finalSum: int) -> List[int]:
if finalSum % 2:
return []
i = 2
ans = []
while i <= finalSum:
ans.append(i)
finalSum -= i
i += 2
ans[-1] += finalSum
return ans


• func maximumEvenSplit(finalSum int64) (ans []int64) {
if finalSum%2 == 1 {
return
}
for i := int64(2); i <= finalSum; i += 2 {
ans = append(ans, i)
finalSum -= i
}
ans[len(ans)-1] += finalSum
return
}

• function maximumEvenSplit(finalSum: number): number[] {
const ans: number[] = [];
if (finalSum % 2 === 1) {
return ans;
}
for (let i = 2; i <= finalSum; i += 2) {
ans.push(i);
finalSum -= i;
}
ans[ans.length - 1] += finalSum;
return ans;
}


• public class Solution {
public IList<long> MaximumEvenSplit(long finalSum) {
IList<long> ans = new List<long>();
if (finalSum % 2 == 1) {
return ans;
}
for (long i = 2; i <= finalSum; i += 2) {