Is Maximum Sum of 3 Non-Overlapping Subarrays easy or hard?

The problem is classified as Hard because it requires combining multiple techniques: sliding windows, prefix sums, and optimal substructure reasoning. The key challenge is realizing you can precompute the best left and right windows to reduce the search space to a linear scan.

Maximum Sum of 3 Non-Overlapping Subarrays Python/Java solution

Implementations typically compute window sums using a sliding window and then maintain best-left and best-right arrays. The same logic translates directly across Python, Java, C++, C#, and JavaScript because it relies only on array traversal and prefix calculations.

How to solve Maximum Sum of 3 Non-Overlapping Subarrays in O(n)?

First compute the sum of every k-length subarray using a sliding window. Build two arrays: one storing the best window from the left up to each index and another storing the best window from the right. Iterate through each possible middle window and combine it with the best left and right windows to maximize the total sum.

What is the best approach for Maximum Sum of 3 Non-Overlapping Subarrays?

The most efficient approach uses prefix sums with a sliding window and helper arrays to track the best left and right subarrays. It computes all k-length window sums and evaluates each possible middle window while referencing optimal windows on both sides. This produces the result in O(n) time with O(n) extra space.

Is Maximum Sum of 3 Non-Overlapping Subarrays asked at Google/Amazon/Meta?

This problem appears in interviews at large tech companies because it combines sliding window optimization with dynamic programming ideas. Variants of the problem have been reported in interviews at companies like Google, Amazon, and Meta where candidates must optimize subarray selection under constraints.

What data structure is used in Maximum Sum of 3 Non-Overlapping Subarrays?

The solution mainly uses arrays along with prefix sums and sliding window calculations. Helper arrays store the best subarray index seen so far from the left and from the right, enabling constant-time lookup when evaluating candidate combinations.

What is the time complexity of Maximum Sum of 3 Non-Overlapping Subarrays?

The optimal solution runs in O(n) time because each element is processed a constant number of times while building window sums and scanning for the best combination. Space complexity is O(n) due to prefix sums and helper arrays that store best left and right window indices.

Description Solution Video 21:17

689. Maximum Sum of 3 Non-Overlapping Subarrays

Hard59.8% acceptance6 companies

Given an integer array nums and an integer k, find three non-overlapping subarrays of length k with maximum sum and return them.

Return the result as a list of indices representing the starting position of each interval (0-indexed). If there are multiple answers, return the lexicographically smallest one.

Example 1:

Input: nums = [1,2,1,2,6,7,5,1], k = 2
Output: [0,3,5]
Explanation: Subarrays [1, 2], [2, 6], [7, 5] correspond to the starting indices [0, 3, 5].
We could have also taken [2, 1], but an answer of [1, 3, 5] would be lexicographically smaller.

Example 2:

Input: nums = [1,2,1,2,1,2,1,2,1], k = 2
Output: [0,2,4]

Constraints:

1 <= nums.length <= 2 * 10⁴
1 <= nums[i] < 2¹⁶
1 <= k <= floor(nums.length / 3)

Asked at 6 companies

General Motors Meta

Google Amazon Microsoft Bloomberg

Topics

Array Dynamic Programming

21:17

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689. Maximum Sum of 3 Non-Overlapping Subarrays

Asked at 6 companies

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