Maximum Sum of 3 Non-Overlapping Subarrays

HardDynamic Programmingprefix sum

Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

Given an array of positive integers nums and a window length k, choose three subarrays, each of length exactly k, that do not overlap and whose combined sum is as large as possible. Return the three starting indices in increasing order. If several choices reach the maximum sum, return the lexicographically smallest list of indices (compare the first index, then the second, then the third). Aim for O(n) time.

Examples

Input: nums = [1,2,1,2,6,7,5,1], k = 2
Output: [0, 3, 5]
Windows starting at 0, 3 and 5 are [1,2], [2,6] and [7,5], summing to 23. Starting at 1, 3, 5 also gives 23, but [0,3,5] is lexicographically smaller.
Input: nums = [1,2,1,2,1,2,1,2,1], k = 2
Output: [0, 2, 4]
Every window sums to 3, so the earliest valid choice [0,2,4] wins.

Constraints

  • 1 <= nums.length <= 2 * 10^4
  • 1 <= nums[i] < 2^16
  • 1 <= k <= floor(nums.length / 3)

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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