Is Maximum Subarray Sum With Length Divisible by K easy or hard?

The problem is generally rated Medium because the brute-force idea is straightforward but the optimal solution requires recognizing a prefix-sum and modulo pattern. Once the relationship between index remainders and valid subarray lengths is identified, the implementation becomes a linear-time scan.

Maximum Subarray Sum With Length Divisible by K Python/Java solution

Implement the prefix sum + modulo grouping approach. Maintain an array or map storing the minimum prefix sum for each remainder i % k. While iterating through the array, compute the current prefix sum, check the stored minimum for that remainder, update the maximum subarray sum, and refresh the minimum prefix if needed.

How to solve Maximum Subarray Sum With Length Divisible by K in O(n)?

Compute a running prefix sum while iterating through the array. For each index i, calculate r = i % k and maintain the smallest prefix sum previously seen with the same remainder. The candidate subarray sum becomes prefix[i] minus that stored minimum. Updating these values during a single traversal yields an O(n) solution.

What is the best approach for Maximum Subarray Sum With Length Divisible by K?

The most efficient approach uses prefix sums combined with grouping indices by their modulo k value. If two prefix indices share the same remainder i % k, the subarray between them has length divisible by k. By tracking the minimum prefix sum for each remainder, you can compute the maximum subarray sum in O(n) time and O(k) space.

Is Maximum Subarray Sum With Length Divisible by K asked at Google/Amazon/Meta?

Variants of prefix sum and subarray divisibility problems appear frequently in interviews at companies like Google, Amazon, and Meta. Problems involving prefix sums, modulo grouping, and maximum subarray calculations are common because they test pattern recognition and optimization skills.

What data structure is used in Maximum Subarray Sum With Length Divisible by K?

The solution primarily uses a prefix sum array and a structure to track the minimum prefix value for each remainder group. This structure is typically an array of size k or a hash table mapping remainder values to the smallest prefix sum seen so far.

What is the time complexity of Maximum Subarray Sum With Length Divisible by K?

The optimal solution runs in O(n) time using a single pass through the array with prefix sums and remainder tracking. Space complexity is O(k) because the algorithm stores the minimum prefix sum for each modulo class from 0 to k-1.

Description Hints 1 Solution Video 31:35

3381. Maximum Subarray Sum With Length Divisible by K

Medium49.6% acceptance4 companies

You are given an array of integers nums and an integer k.

Return the maximum sum of a subarray of nums, such that the size of the subarray is divisible by k.

Example 1:

Input: nums = [1,2], k = 1

Output: 3

Explanation:

The subarray [1, 2] with sum 3 has length equal to 2 which is divisible by 1.

Example 2:

Input: nums = [-1,-2,-3,-4,-5], k = 4

Output: -10

Explanation:

The maximum sum subarray is [-1, -2, -3, -4] which has length equal to 4 which is divisible by 4.

Example 3:

Input: nums = [-5,1,2,-3,4], k = 2

Output: 4

Explanation:

The maximum sum subarray is [1, 2, -3, 4] which has length equal to 4 which is divisible by 2.

Constraints:

1 <= k <= nums.length <= 2 * 10⁵
-10⁹ <= nums[i] <= 10⁹

Asked at 4 companies

Bloomberg

Google Amazon Meta

Topics

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Hint 1

Maintain minimum prefix sum ending at every possible index%k.

31:35

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3381. Maximum Subarray Sum With Length Divisible by K

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