Sum of Max Subarrys
Reported by candidates from Amazon's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Amazon's February OA is hitting candidates with a subarrays problem that sounds simple but trips most people on the first pass. You're being asked to find the sum of maximum values across all possible subarrays. The gotcha is that a naive approach will time out on large inputs. StealthCoder reads the problem live and surfaces the optimal pattern instantly, so if you blank on whether to use a stack or a DP approach, you've got a safety net during the actual assessment.
Pattern and pitfall
The trap here is thinking you need to iterate through every subarray and track maximums independently, which is O(n^2) or worse. The efficient solution uses a monotonic stack to precompute, for each element, how far left and right it dominates as a maximum. Then you calculate each element's contribution to the total sum based on how many subarrays it's the max of. This is O(n) with a single pass and a stack. Most candidates see the subarray language and default to brute force or two-pointer logic, which fails. StealthCoder catches this pattern mismatch during the OA and guides you toward the monotonic stack approach before you waste time coding the wrong solution.
Drill it cold or hedge it with StealthCoder. Either way, don't walk into the OA hoping you remember the trick.
You can drill Sum of Max Subarrys cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. Made for the candidate who got the OA invite this morning and has 72 hours, not six months.
Get StealthCoderRelated leaked OAs
This OA pattern shows up on LeetCode as sum of subarray minimums. If you have time before the OA, drill that.
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Make sure you actually pass Amazon's OA.
Amazon reuses patterns across OAs. Made for the candidate who got the OA invite this morning and has 72 hours, not six months. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Sum of Max Subarrys FAQ
Is this really asking for max of every subarray, or something else?+
It's the sum of the maximum values across all possible contiguous subarrays. So for [1,3,2], you sum max([1]) + max([1,3]) + max([1,3,2]) + max([3]) + max([3,2]) + max([2]). That's 1+3+3+3+3+2 = 15. Not the max of the array itself.
Why does brute force fail here?+
Brute force is O(n^2) to generate all subarrays and O(n) to find max in each, so O(n^3) total. Even O(n^2) with a sliding max fails at n > 10,000. You need O(n) using a monotonic decreasing stack to precompute each element's range of dominance as max.
What's the monotonic stack trick?+
For each element, find the nearest smaller element to its left and right. That defines how many subarrays it's the maximum of. Multiply the element by that count and add to the total. A single decreasing stack pass does all this in O(n).
How do I code this in 20 minutes if I'm not sure?+
Start with the brute force to get some test cases passing, then optimize to monotonic stack. Or write the stack logic first: iterate through the array, maintain a stack of (value, count), pop when you see a larger element, and accumulate contributions as you go.
Does Amazon ask this exact problem often?+
Stack and contribution-based subarray problems are Amazon favorites. This specific framing (sum of max subarrays) reappears every few months. The monotonic stack pattern is critical for their OA pipeline.