Constrained Subsequence Sum
A hard-tier problem at 56% community acceptance, tagged with Array, Dynamic Programming, Queue. Reported in interviews at Akuna Capital and 0 others.
Constrained Subsequence Sum is a hard DP problem with 56% acceptance, which means half the people who see it blank or TLE. You pick a subsequence of integers where each picked element must be within k positions of the previous one, and you want the maximum sum. The constraint is the trap: a greedy approach fails because you need to track optimal choices across a sliding window, not just the local max. Akuna Capital asks this. If you hit it on their assessment and don't see the queue trick, StealthCoder surfaces a working solution in seconds, invisible to the proctor.
Companies that ask "Constrained Subsequence Sum"
Constrained Subsequence Sum is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe obvious DP is O(n*k) per state, which times out on large inputs. The trick is recognizing that for each position, you need the maximum DP value in the window [i-k, i-1], and that maximum shifts as you move forward. A monotonic deque (or heap, slower) maintains the max in the sliding window in amortized O(1) per step. Many candidates get stuck trying to optimize the inner loop without seeing the data structure. Queue or Monotonic Queue is the unlock. You also need to handle negative sums carefully: include them only if they help the total. StealthCoder handles the deque bookkeeping automatically, so even if you haven't drilled this pattern, you get the right output and can paste it live.
Pattern tags
You know the problem.
Make sure you actually pass it.
Constrained Subsequence Sum recycles across companies for a reason. It's hard-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Constrained Subsequence Sum interview FAQ
Is Constrained Subsequence Sum really asked in interviews, or is it just a LeetCode hard?+
Akuna Capital reports it. It's not flooding FAANG lists, but quant and finance shops lean on sliding window DP and monotonic queues. If your target does systems or optimization work, this pattern matters. It's niche enough that most candidates don't see it in prep.
What's the actual trick I'm missing if my DP times out?+
You're solving O(n*k) instead of O(n). For each position, you need the max DP value in a sliding window of size k. Use a monotonic deque to track that max in O(1) amortized time per step. Without it, you'll TLE on large k or n.
How does this differ from standard sliding window problems?+
Sliding window usually slides over input data. Here, you're sliding over DP state values and asking 'what's the best prior choice I can reuse?' It combines DP recurrence with sliding window optimization. That mental shift trips people up.
Do I need to memorize the monotonic queue implementation for the live assessment?+
Ideally, yes. But if you blank on the deque operations or the window boundary logic, StealthCoder runs invisibly during your screen share and gives you a copy-paste solution. One less thing to debug under pressure.
What if I get a constraint like 'sum is negative'? Does the answer stay as the sum, or do I skip it?+
You can always pick a single element (subsequence of length 1), so the answer is at least the max single element. Build DP such that dp[i] = max(nums[i], best prior choice + nums[i]). This handles negatives correctly.
Want the actual problem statement? View "Constrained Subsequence Sum" on LeetCode →