Greatest Sum Divisible by Three — LeetCode 1262 Python Solution

The problem

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

Example

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).

Python solution

class Solution:
    def maxSumDivThree(self, nums: List[int]) -> int:
        n = len(nums)
        f = [[-inf] * 3 for _ in range(n + 1)]
        f[0][0] = 0
        for i, x in enumerate(nums, 1):
            for j in range(3):
                f[i][j] = max(f[i - 1][j], f[i - 1][(j - x) % 3] + x)
        return f[n][0]

Complexity

Pattern: Greedy

Take the locally best option every time — when you can prove that never costs you later. LeetCode 1262. Greatest Sum Divisible by Three is filed here because LeetCode tags it Greedy, which is the vocabulary this hub collects.

The greedy guide has the Python template for the pattern and the 346 LeetCode problems that use it.

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