I stared at this for a bit before realizing the answer is just pick any single element and you get 2x that element's value.
Clarify the problem and constraints, then propose an efficient algorithm. A monotonic stack approach can find for each element the nearest smaller and larger elements to determine valid subarrays where it is the min or max, but a simpler O(n^2) brute force may be acceptable for small inputs. Discuss trade-offs and optimize if needed.
Pro tip: Always start by asking about input size and constraints; this shows you care about efficiency and helps you choose the right approach. Also, consider edge cases like all negative numbers or duplicates.
Ask about input size, value ranges, and whether the subarray must be non-empty. Confirm that min and max refer to the minimum and maximum values within the subarray.
Consider brute force O(n^2) by checking all subarrays, and more efficient methods using monotonic stacks or divide-and-conquer. Discuss time and space complexity.
For an efficient solution, use monotonic stacks to find for each element the range where it is the minimum and the range where it is the maximum. Then, for each element, consider subarrays where it is the min or max, and compute the sum with the other extreme.
Test with arrays of size 1, all equal elements, strictly increasing/decreasing, and negative numbers. Ensure the algorithm returns the correct maximum sum.
State the time and space complexity of your solution. For the monotonic stack approach, aim for O(n) time and O(n) space.
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