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 tofinalSum
):(12)
,(2 + 10)
,(2 + 4 + 6)
, and(4 + 8)
. Among them,(2 + 4 + 6)
contains the maximum number of integers. Note thatfinalSum
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
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