I Couldn't Optimize Max Sum Min-Product Until I Flipped the Question

This is part of a series where I break down coding concepts I understand when reading about them but struggle to reuse when I actually need them. Not tutorials. Personal learning journeys that break down the "why does this actually work" part. The problem that tripped me up LeetCode 1856: Maximum Subarray Min-Product. The formula is straightforward. For any subarray, multiply the minimum element by the sum of the subarray. Find the maximum across all possible subarrays. I could see the O(n^2) so