Design a 3D Binary Matrix with Efficient Layer Tracking
A medium-tier problem at 66% community acceptance, tagged with Array, Hash Table, Design. Reported in interviews at Amdocs and 0 others.
You're asked to design a 3D binary matrix that tracks which cells are set to 1, with efficient layer-level operations. This problem combines array indexing, hash tables, and ordered set logic to solve what looks like a straightforward storage problem. With a 66% acceptance rate, it's medium-difficulty territory, but the trick isn't complexity, it's knowing when to use a heap or ordered set to avoid brute-force layer scans. Amdocs has reportedly asked this. If you hit this during a live assessment and freeze on the data structure choice, StealthCoder runs invisibly and surfaces a working solution in seconds.
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Design a 3D Binary Matrix with Efficient Layer Tracking 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. Built by an Amazon engineer who used it to pass JPMorgan's OA and system design loop.
Get StealthCoderThe trap here is thinking you need to store the entire 3D matrix. You don't. The insight is to track only the cells set to 1, then use a hash table keyed by layer to group them. When you need to find the earliest or latest layer with a 1, that's where a heap or ordered set earns its keep, it gives you O(log n) or O(1) answer without scanning all layers. The medium difficulty comes from integrating these data structures smoothly, not from the problem itself. Most candidates over-engineer the matrix storage and get bogged down in naive layer iteration. That's where the acceptance rate dips. StealthCoder is your safety net if you blank on structure choice or the ordered set syntax during the timed OA.
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Design a 3D Binary Matrix with Efficient Layer Tracking recycles across companies for a reason. It's medium-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. Built by an Amazon engineer who used it to pass JPMorgan's OA and system design loop. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Design a 3D Binary Matrix with Efficient Layer Tracking interview FAQ
What's the real trick to this problem?+
Don't store the matrix itself. Store only the set cells with a hash table grouped by layer, plus a heap or ordered set of active layers. This collapses O(d*r*c) space into O(k) where k is the count of cells set to 1. The problem is really about choosing the right auxiliary data structure.
Is this problem still asked by big tech?+
Amdocs has reportedly asked it. It's not as common as array-sort problems, but it appears in systems-design and backend-heavy interviews. The 66% acceptance rate suggests it's weeded down to mid-level and senior candidates who know heap and ordered set patterns.
Should I use a heap or an ordered set?+
A heap works if you only need min/max layer queries. An ordered set is more flexible if you need to iterate ranges or remove arbitrary layers. Both have trade-offs. In the live OA, the problem statement will hint at which operations are hot. StealthCoder shows both implementations so you can pick the one matching the ops.
How does this relate to matrix and hash table topics?+
Matrix is the conceptual frame; you're 3D, so index by [layer, row, col]. Hash table is the execution: store cells as a dict keyed by layer, with sets of (row, col) tuples per layer. This avoids dense matrix allocation and makes layer queries instant.
What causes failures on this problem?+
Candidates often allocate a full 3D array upfront, then scan all layers on queries. That's O(d*r*c) space and O(d) time per layer operation. Sparse representation cuts both drastically. The other failure is forgetting to clean up empty layers from the heap/set, leaving dead references.
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