Is Maximum Good Subarray Sum easy or hard?

Maximum Good Subarray Sum is rated Medium difficulty. The challenge lies in recognizing that the condition on the first and last elements can be converted into hash lookups combined with prefix sum subtraction.

Maximum Good Subarray Sum Python/Java solution

Python and Java solutions typically maintain a running prefix sum and a HashMap or dictionary mapping numbers to the smallest prefix sum seen before them. During iteration, the algorithm checks for values differing by k and updates the maximum subarray sum accordingly.

How to solve Maximum Good Subarray Sum in O(n)?

Maintain a running prefix sum while iterating through the array. For each element x, check if x - k or x + k appeared earlier using a hash map that stores the smallest prefix sum before those values. Subtracting that stored prefix from the current prefix gives the subarray sum candidate in constant time.

What is the best approach for Maximum Good Subarray Sum?

The most efficient approach uses a prefix sum combined with a hash map. While iterating through the array, store the minimum prefix sum seen for each value and check if values differing by k exist. This allows computing candidate subarray sums in constant time, producing an overall O(n) time complexity.

Is Maximum Good Subarray Sum asked at Google/Amazon/Meta?

Problems involving prefix sums, hash maps, and subarray optimization frequently appear in interviews at companies like Amazon, Google, and Meta. Variants of this problem test the ability to transform subarray conditions into prefix sum lookups.

What data structure is used in Maximum Good Subarray Sum?

The key data structures are a hash map for constant-time value lookup and a prefix sum array or running prefix variable for quick subarray sum computation. This combination allows evaluating candidate subarrays without nested loops.

What is the time complexity of Maximum Good Subarray Sum?

The optimal algorithm runs in O(n) time because the array is scanned once and each lookup in the hash map takes constant time on average. The space complexity is O(n) to store prefix sums or value mappings.

Description Hints 3 Solution Video 25:33

3026. Maximum Good Subarray Sum

Medium22.7% acceptance5 companies

You are given an array nums of length n and a positive integer k.

A subarray of nums is called good if the absolute difference between its first and last element is exactly k, in other words, the subarray nums[i..j] is good if |nums[i] - nums[j]| == k.

Return the maximum sum of a good subarray of nums. If there are no good subarrays, return 0.

Example 1:

Input: nums = [1,2,3,4,5,6], k = 1
Output: 11
Explanation: The absolute difference between the first and last element must be 1 for a good subarray. All the good subarrays are: [1,2], [2,3], [3,4], [4,5], and [5,6]. The maximum subarray sum is 11 for the subarray [5,6].

Example 2:

Input: nums = [-1,3,2,4,5], k = 3
Output: 11
Explanation: The absolute difference between the first and last element must be 3 for a good subarray. All the good subarrays are: [-1,3,2], and [2,4,5]. The maximum subarray sum is 11 for the subarray [2,4,5].

Example 3:

Input: nums = [-1,-2,-3,-4], k = 2
Output: -6
Explanation: The absolute difference between the first and last element must be 2 for a good subarray. All the good subarrays are: [-1,-2,-3], and [-2,-3,-4]. The maximum subarray sum is -6 for the subarray [-1,-2,-3].

Constraints: