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1262. Greatest Sum Divisible by Three (Medium)

Given an array nums of integers, we need to find 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 * 10^4
• 1 <= nums[i] <= 10^4

Related Topics

[Dynamic Programming]

Hints

Hint 1

Represent the state as DP[pos][mod]: maximum possible sum starting in the position "pos" in the array where the current sum modulo 3 is equal to mod.