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) solution clearly. Try every subarray, track the running min and running sum, update the max. But dropping to O(n)? That's where I got stuck. Where my intuition went wrong My first instinct was a sliding window approach. Add an element to the range, check if it improves the answer, otherwise store the max and reset. It felt right because you're building ranges and checking them. But here's why it fails: the decision to "keep going or reset" depends on both the sum AND the minimum changing at the same time.…