The compression part was fine, I'd seen RLE before.
Start by defining a run-length encoding (RLE) representation for integer vectors, then design an algorithm to compute the dot product directly on the compressed runs by iterating through both RLE sequences and handling overlapping segments. Analyze the time and space complexity, and discuss trade-offs such as compression ratio and edge cases.
Pro tip: Emphasize that the dot product can be computed in O(n + m) time where n and m are the number of runs, which is optimal, and mention that this approach is particularly beneficial for sparse or highly repetitive data common in ML embeddings.
Propose a data structure for RLE, e.g., a list of (value, count) pairs, and explain how it compresses consecutive repeated integers.
Outline an algorithm that traverses both RLE sequences simultaneously, maintaining pointers and remaining counts, and accumulates the product of overlapping values.
Discuss how to handle runs of different lengths, ensure correct alignment, and manage cases where one vector is longer or runs do not overlap.
Compute time and space complexity, compare with expanding vectors, and discuss scenarios where RLE is advantageous or not.
Mention potential optimizations like early termination, parallelization, or adapting to sparse vectors, and relate to ML applications.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use a stack to track active function calls, computing exclusive time by subtracting nested durations from the total elapsed time. When a function starts, push its ID and start time; when it ends, pop and add the exclusive time, then update the parent's start time to account for the child's duration.
Pro tip: Clarify that timestamps are inclusive and that the CPU is single-threaded, so no overlapping calls occur. Also, mention that you'll handle edge cases like multiple top-level calls and deeply nested calls.
Confirm that logs are well-formed, timestamps are integers, and the CPU is single-threaded. Discuss handling of nested calls and multiple top-level calls.
Use a stack to track active function calls and a dictionary or array to accumulate exclusive times per function ID.
Iterate through logs: on 'start', push (id, timestamp); on 'end', pop, compute exclusive time as (end - start + 1) minus time spent in nested calls, and update parent's start time.
When a function ends, its exclusive time is the total duration from its start to end minus the sum of exclusive times of all nested calls. Adjust the parent's start time to the current end time + 1 to avoid double-counting.
Time complexity is O(n) for n logs, space O(n) for stack and output. Walk through a simple example and a nested example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.