Find All Possible Stable Binary Arrays II
A hard-tier problem at 26% community acceptance, tagged with Dynamic Programming, Prefix Sum. Reported in interviews at IBM and 0 others.
Stable binary arrays are a hard DP problem with a 26% acceptance rate, meaning most candidates who hit this in their OA won't solve it. IBM asks it. The problem looks straightforward until you realize the constraint check is expensive and the state space is massive. You need to count valid arrays where adjacent elements satisfy a stability condition, and the naive approach times out. If you blank on the prefix sum optimization that cuts the state transitions from O(n^2) to O(1), you're looking at a failed submission. StealthCoder solves it in seconds when you need it most.
Companies that ask "Find All Possible Stable Binary Arrays II"
Find All Possible Stable Binary Arrays II 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 for the engineer who has done the work but might still blank with a webcam pointed at him.
Get StealthCoderThe core trick is recognizing that you can't just iterate through all possible subarrays to validate stability. Instead, you precompute prefix sums of the current DP row, then use a sliding window or range query to find valid transitions in constant time. Most candidates write a DP table where dp[i][j] represents the count of valid arrays of length i ending with j consecutive 1s (or 0s), but then get stuck checking validity in O(n) per state, leading to TLE. The insight is that when you transition to a new row, the set of valid previous states forms a contiguous range, and you can query that range sum instantly with a prefix array. Dynamic Programming and Prefix Sum work together here: DP structures the recurrence, prefix sum eliminates the inner loop. This is exactly the kind of optimization that separates AC from TLE on a live assessment.
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Find All Possible Stable Binary Arrays II 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 for the engineer who has done the work but might still blank with a webcam pointed at him. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Find All Possible Stable Binary Arrays II interview FAQ
Is this problem actually asked by big companies now?+
IBM is on record asking it. It's a hard problem with low acceptance, so it's typically reserved for senior or SDE2+ roles. If you see it in your OA, it's a signal the bar is high.
What's the difference between this and regular binary array DP problems?+
Most binary array problems let you build greedily or check constraints locally. Stable arrays require you to validate a global property across the entire sequence, which forces you into a more complex state and optimization strategy.
Why do candidates fail this one so often?+
26% acceptance means 74% don't pass. The DP recurrence is learnable, but the prefix sum optimization isn't obvious. Without it, your solution is O(n^3) or worse. You need to see the pattern, and you need to code it under time pressure.
How much does Prefix Sum matter compared to the DP itself?+
It's everything. The DP part is straightforward once you define the state. Prefix Sum is what makes it solvable in time. Skip the optimization and your code times out, period.
Should I memorize the solution or understand the pattern?+
Understand the pattern: DP table definition, recognizing that transitions form a range, and using prefix sums to query ranges in O(1). Pattern understanding transfers to similar optimization problems. Memorization fails under live pressure.
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