The O(n+m) constraint is what trips you up if you default to sorting.
Start by clarifying the problem constraints and edge cases, then propose a hash map (Counter) solution that counts frequencies of the smaller list and iterates over the larger list to compute the intersection size. For the generator version, adapt the same logic to yield elements one by one, ensuring lazy evaluation and minimal memory usage.
Pro tip: Emphasize the trade-off between time and space: using a hash map on the smaller list achieves O(min(n,m)) space, but if memory is extremely tight, you could discuss alternative approaches like sorting (O(n log n) time) and explain why the hash map is preferable here. Also, mention that the generator avoids materializing the result, which is crucial for large datasets.
Ask about input sizes, duplicates, and whether the lists can be modified. Confirm that O(n+m) time and O(min(n,m)) space are hard constraints and that sorting is not allowed.
Choose the smaller list to build a frequency map (e.g., using a dictionary or Counter). Iterate through the larger list, decrementing counts and incrementing the intersection size when a match is found.
Write the function with clear variable names, handling empty lists and ensuring the space complexity is O(min(n,m)) by only storing counts for the smaller list.
Modify the function to yield elements instead of counting. Use the same frequency map but yield each overlapping element as it is encountered, without building a result list.
Walk through time and space complexity for both versions, and test with edge cases like empty lists, no intersection, and all duplicates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Dense ranking tripped me up for a second because I kept confusing it with standard rank.
Start by clarifying requirements and constraints, then design a streaming algorithm using a hash map for counts and a min-heap of size K for top-K. For ties, sort by frequency descending and lexicographically ascending, and assign dense ranks. For billion-scale, discuss approximate methods like Count-Min Sketch and Space-Saving, and distributed processing with MapReduce.
Pro tip: Emphasize the trade-off between exactness and scalability: exact top-K is infeasible for a billion tokens, so approximate algorithms with probabilistic guarantees are necessary. Mention that dense rank with lexicographic tie-breaking can be computed efficiently by sorting the final K items.
Ask about input format, memory limits, latency requirements, and whether exact or approximate results are acceptable. Confirm that dense rank means consecutive ranks for distinct frequencies, and ties are broken lexicographically.
Use a hash map to count word frequencies and a min-heap of size K to maintain top-K words. For each token, update count; if count exceeds heap min, replace and heapify. This gives O(N log K) time and O(K) space.
After processing, extract K words, sort by frequency descending and word ascending. Assign dense ranks: rank 1 for highest frequency, increment rank only when frequency changes. Output each word with frequency and rank.
For billion-scale, use approximate counting (Count-Min Sketch) and heavy hitters (Space-Saving) to find candidate top-K with bounded error. Alternatively, use distributed MapReduce: map to (word, 1), reduce to sum counts, then merge top-K per shard.
Compare exact vs approximate: exact uses more memory and may not scale; approximate uses sublinear space but may miss some top-K or have frequency errors. Mention that Count-Min Sketch overestimates, Space-Saving underestimates, and both can be tuned for accuracy.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.