1262. Greatest Sum Divisible by Three

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

class Solution {
    public int maxSumDivThree(int[] nums) {
        int res = 0, leftOne = 20000, leftTwo = 20000;
        for(int n:nums){
            res+=n;
            if(n%3==1){
                leftTwo = Math.min(leftTwo,leftOne+n);
                leftOne = Math.min(leftOne,n);
            }
            if(n%3==2) {
                leftOne = Math.min(leftOne,leftTwo+n);
                leftTwo = Math.min(leftTwo,n);
            }
        }
        if(res%3==0) return res;
        if(res%3==1) return res-leftOne;
        return res - leftTwo;
        
    }
}

https://leetcode.com/problems/greatest-sum-divisible-by-three/discuss/431108/Java-O(N)-solution-Simple-Math-O(1)-space

牛逼的方法，持續追蹤除3余1和余2最小的數，最后總和整除就返回，余1就減去余1最小的數，余2同理。

注意無論余1還是余2都要持續更新另外一個，因為可能出現[2, 6, 2, 2, 7]這種情況，此時如果只追蹤1或2，答案會是12而非15，因為2+2%3是1，7%3也是1，減的是7.

所以每次要更新兩者。