Leetcode #2941: Maximum GCD-Sum of a Subarray
In this guide, we solve Leetcode #2941 Maximum GCD-Sum of a Subarray in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Array, Math, Binary Search, Number Theory
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
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.
It can be shown that we can not select any other subarray with a gcd-sum greater than 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
The time complexity is O(log n) or O(n log n). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.