## Algorithm

Problem Name: 1262. Greatest Sum Divisible by Three

Given an integer array `nums`, return the maximum possible sum of elements of the array such that it is divisible by three.

Example 1:

```Input: nums = [3,6,5,1,8]
Output: 18
Explanation: Pick numbers 3, 6, 1 and 8 their sum is 18 (maximum sum divisible by 3).```

Example 2:

```Input: nums = [4]
Output: 0
Explanation: Since 4 is not divisible by 3, do not pick any number.
```

Example 3:

```Input: nums = [1,2,3,4,4]
Output: 12
Explanation: Pick numbers 1, 3, 4 and 4 their sum is 12 (maximum sum divisible by 3).
```

Constraints:

• `1 <= nums.length <= 4 * 104`
• `1 <= nums[i] <= 104`

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const maxSumDivThree = function (nums) {
const n = nums.length
let dp = [0, -Infinity, -Infinity]
for (let i = n - 1; i >= 0; i--) {
const nextDp = []
for (let j = 0; j  <  3; j++) {
const nextRemain = nums[i] % 3
nextDp[j] = Math.max(nums[i] + dp[(nextRemain + j) % 3], dp[j])
}
dp = nextDp
}
return dp[0]
}
``````
Copy The Code &

Input

cmd
nums = [3,6,5,1,8]

Output

cmd
18

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def maxSumDivThree(
self, nums: List[int], dp: list = [0, -float("inf"), -float("inf")]
) -> int:
for num in nums:
dp = [max(dp[i], dp[(i - num) % 3] + num) for i in range(3)]
return dp[0]
``````
Copy The Code &

Input

cmd
nums = [3,6,5,1,8]

Output

cmd
18