My first instinct was to brute-force every subarray and track min/max as I expanded, which works but I spent too long second-guessing whether there was a smarter O(n) trick.
First, clarify the problem and edge cases. Then, discuss a brute-force approach and its time complexity. Finally, propose an optimized solution using a monotonic stack to find for each element the nearest greater and smaller elements, and compute the maximum sum of min and max over all subarrays of length at least 2.
Pro tip: Mention that the subarray must have at least two elements, so handle cases where the optimal subarray might be of length 2. Also, note that the sum of min and max can be maximized by considering pairs of elements that are the min and max of the subarray, and using monotonic stacks to efficiently find the largest subarray where they are the min and max.
Restate the problem in your own words and ask clarifying questions about input size, constraints, and expected output. Confirm that the subarray must be contiguous and have at least two elements.
Explain that a naive solution would check all subarrays of length >=2, compute min and max for each, and track the maximum sum. Analyze the time complexity as O(n^3) or O(n^2) with optimization, which may be too slow for large inputs.
Describe using monotonic stacks to find, for each element, the nearest greater and smaller elements to determine the range where it is the min or max. Then, for each possible pair of min and max, compute the maximum sum over subarrays where they are the min and max, ensuring length >=2.
State that the optimized solution runs in O(n) time and O(n) space. Discuss edge cases such as arrays of length 2, all elements equal, and strictly increasing/decreasing arrays.
Walk through a small example to verify the approach, such as [1,3,2,4] where the subarray [3,2,4] has min=2, max=4, sum=6, which is the maximum.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.