Maximum GCD-Sum of a Subarray — LeetCode 2941 Python Solution

The problem

You are given an array of integers nums and an integer k. The gcd-sum of an array a is calculated as follows: Let s be the sum of all the elements of a.

Example

Input

nums = [2,1,4,4,4,2], k = 2

Output

48

Explanation

We take the subarray [4,4,4], the gcd-sum of this array is 4 * (4 + 4 + 4) = 48.

Python solution

class Solution:
    def maxGcdSum(self, nums: List[int], k: int) -> int:
        s = list(accumulate(nums, initial=0))
        f = []
        ans = 0
        for i, v in enumerate(nums):
            g = []
            for j, x in f:
                y = gcd(x, v)
                if not g or g[-1][1] != y:
                    g.append((j, y))
            f = g
            f.append((i, v))
            for j, x in f:
                if i - j + 1 >= k:
                    ans = max(ans, (s[i + 1] - s[j]) * x)
        return ans

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 2941. Maximum GCD-Sum of a Subarray is filed here because the reference solution below belongs to the algorithm family this hub collects, even though its LeetCode tags point elsewhere.

The monotonic stack guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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