I knew prefix sums were involved but fumbled the modular arithmetic part for a bit.
Use prefix sums and a hash map to track remainders modulo k, checking if the same remainder appears at least two indices apart. For k=0, use a hash set to detect if any prefix sum repeats, indicating a zero-sum subarray. This yields O(n) time and O(min(n, k)) space.
Pro tip: Explicitly handle edge cases like k=0, negative numbers, and subarray length constraints; mention that the hash map approach works because if two prefix sums have the same remainder modulo k, their difference is divisible by k.
Restate the problem: find a contiguous subarray of length ≥2 with sum divisible by k, or sum exactly zero if k=0. Confirm assumptions about input size, integer range, and k's sign.
For k=0, use a hash set to store prefix sums; if a prefix sum repeats, the subarray between the two occurrences sums to zero. Ensure the subarray length is at least 2.
Compute prefix sums modulo k. If the same remainder appears at indices i and j with j - i ≥ 2, then the subarray from i+1 to j has sum divisible by k. Use a hash map to store the first occurrence of each remainder.
Write code that iterates through the array, updating the prefix sum and checking the hash map. Test with cases like [1,2,3], k=3; [0,0], k=0; and negative numbers.
Time complexity is O(n) because we traverse the array once. Space complexity is O(min(n, k)) for the hash map, as there are at most k distinct remainders.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints: what operation is needed (e.g., find max, compute mean, detect anomaly) and whether the stream is bounded or unbounded. Then explain how to adapt the algorithm to a streaming setting, focusing on maintaining state incrementally and discussing trade-offs between memory, accuracy, and latency.
Pro tip: Mention that for unbounded streams, you often need to switch from exact algorithms to approximate ones (e.g., reservoir sampling, count-min sketch) and that Adobe values scalable ML pipelines, so highlight how your choice impacts downstream model training or inference.
Ask whether the stream is finite or infinite, what the required output is (e.g., exact vs approximate), and what resources (memory, time) are available.
Determine if the operation is decomposable (e.g., sum, max) or requires full data (e.g., median). For decomposable operations, maintain a running aggregate; for others, consider approximations or windowing.
Select streaming-friendly structures like heaps for top-k, reservoir sampling for uniform sampling, or sketches for frequency/quantile estimation, and explain why they fit.
Compare memory usage, accuracy, and latency of your streaming approach versus batch processing, and mention how you would handle concept drift or late-arriving data.
Explain how the streaming solution integrates with ML pipelines (e.g., online learning, feature updates) and why it matters for Adobe's products.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.