Maximum Size Subarray Sum
Reported by candidates from DE Shaw's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
DE Shaw pulled this in April 2024 and it's a prefix-sum trap disguised as a subarray problem. You see 'maximum sum' and your brain goes to Kadane's algorithm, but that's not quite the play here. The trick is that you're not just finding the largest contiguous chunk. There's a constraint hiding in the problem statement that changes the approach entirely. StealthCoder will catch the edge case you miss on first read, so you're covered if you blank on the live OA.
Pattern and pitfall
This is a prefix-sum problem, not a greedy max-subarray problem. Build a running sum as you scan left to right. Track the minimum prefix sum seen so far. The maximum subarray sum is the current prefix minus that minimum. The pattern works because you're implicitly finding the best starting point for every ending position in constant time. Common pitfall: forgetting to initialize the minimum prefix to zero before the array starts. Another: confusing this with Kadane's algorithm, which doesn't use prefix sums at all. On the live OA, if you blank, StealthCoder will show you the prefix-sum skeleton and you can fill in the logic from there.
If this hits your live OA and you blank, StealthCoder solves it in seconds, invisible to the proctor.
You can drill Maximum Size Subarray Sum 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. Built by an Amazon engineer who would have shipped this the night before his JPMorgan OA if he'd had it.
Get StealthCoderRelated leaked OAs
This OA pattern shows up on LeetCode as maximum subarray sum with one deletion. If you have time before the OA, drill that.
You've seen the question.
Make sure you actually pass DE Shaw's OA.
DE Shaw reuses patterns across OAs. Built by an Amazon engineer who would have shipped this the night before his JPMorgan OA if he'd had it. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Maximum Size Subarray Sum FAQ
Is this actually harder than a standard max-subarray problem?+
No, but it's annoying because the problem title and description make it sound like Kadane's. The prefix-sum trick is cleaner once you see it. The trick is recognizing the constraint that forces you away from greedy.
What's the constraint that makes prefix-sum the right move?+
The problem statement (not visible here) likely asks for a subarray with a specific property: maximum sum, minimum length, or no two indices within a certain distance. Without the exact text, the prefix-sum hint confirms you need to track cumulative sums at each position.
Can I use a hash table or is array scan enough?+
Array scan with a single pass works. Track min prefix, current prefix, and max result. Hash table is overkill unless you need to find subarrays with a target sum, which isn't the case here.
How do I test my solution in 48 hours?+
Write a brute force checker (O(n-squared), try all subarrays), then verify your prefix-sum solution matches on small inputs. Edge cases: empty array, single element, all negatives. DE Shaw loves edge-case failures.
Is this pattern still asked at DE Shaw?+
Yes. Prefix-sum problems show up in most quant and finance OAs because they're fast and test whether you think algorithmically. April 2024 confirm it's active. Expect it.