Used a dict to track count and first index in one pass, then a separate list to preserve insertion order.
Use a single pass with a dictionary to track each element's count and first index, then filter for counts > 1 while preserving insertion order. Emphasize that Python 3.7+ dicts maintain insertion order, so the result naturally follows first appearance. Discuss time and space complexity, noting O(n) time and O(n) space.
Pro tip: Mention that if the list contains unhashable elements, you'd need a different approach, but for typical hashable data this is optimal. Also, clarify that 'first-occurrence index' refers to the index of the first time the element appears, not the first duplicate.
Confirm that the list contains hashable elements and that we need counts and first-occurrence indices for values appearing more than once. Ask about handling unhashable types or memory constraints.
Select a dictionary to map each element to a [count, first_index] pair. Explain that a single pass achieves O(n) time and O(n) space.
Iterate through the list with enumerate. For each element, if it's not in the dictionary, add it with count 1 and its index; otherwise, increment its count.
After the pass, iterate through the dictionary items (which preserve insertion order) and collect those with count > 1 into a list of tuples or dictionaries containing value, count, and first index.
State that time is O(n) and space is O(n). Discuss edge cases: empty list, no duplicates, all duplicates, and unhashable elements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The index-negation trick came to mind fast but I fumbled the negative numbers part for a second.
Explain the in-place marking technique: iterate through the array, and for each element, use its value as an index to mark the presence of that number by negating the value at that index. If the value at that index is already negative, it indicates a duplicate. For negative numbers, first check if any negatives exist; if so, use an offset or a different marking strategy such as adding n to the value at the index, then taking modulo n to recover the original value.
Pro tip: Mention that the marking technique modifies the array but can be restored if needed, and discuss the trade-off between time and space complexity. Also, clarify that the O(1) space is extra space, not counting the input array.
Confirm that the array contains integers in range 0 to n-1, and that we can modify the array in place. Ask if the output should be the list of duplicates or just a boolean indicating existence.
For each element, treat its value as an index. If the value at that index is positive, negate it to mark presence. If it's already negative, the current value is a duplicate. This uses O(n) time and O(1) extra space.
If negative numbers might appear, first check if any negative exists. If so, use an offset: add n to the value at the index (mod n) to mark, or shift all numbers by a constant to make them non-negative. Alternatively, use a separate boolean array if extra space is allowed, but that violates O(1).
Mention that the marking technique destroys the original array unless restored. Discuss edge cases: all unique, all duplicates, multiple duplicates, and the presence of zero. Also, note that if the range is not 0 to n-1, the technique fails.
Reiterate that the approach achieves O(n) time and O(1) extra space by using the array itself as a hash table. For negative numbers, an offset or modulo trick can be applied, but it may require additional passes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying constraints (memory, disk, time, exact vs approximate). Then present a disk-based external sort or hash partitioning approach for exact duplicate detection, followed by probabilistic methods like Bloom filters or HyperLogLog for approximate detection with error bounds. Compare trade-offs and recommend a hybrid if appropriate.
Pro tip: Quantify the error bounds and resource usage (e.g., false positive rate of Bloom filter, memory for HyperLogLog) to show you understand the practical implications. Mention that in production, a hybrid approach often balances accuracy and efficiency.
Ask about memory limits, disk space, time constraints, and whether exact or approximate duplicates are needed. This determines the approach.
Describe external sorting or hash partitioning: split the stream into chunks that fit in memory, sort each chunk, write to disk, then merge and detect duplicates. Alternatively, hash integers into partitions and process each partition separately.
Explain using a Bloom filter to track seen integers with a small false positive rate, or HyperLogLog to estimate cardinality and infer duplicates. Discuss error bounds and memory trade-offs.
Compare disk-based (exact, slower, more I/O) vs probabilistic (approximate, faster, less memory). Suggest a hybrid: use Bloom filter to filter likely duplicates, then verify with disk-based method.
For Bloom filter, false positive rate p = (1 - e^(-kn/m))^k; for HyperLogLog, standard error ~1.04/√m. Explain how to tune parameters for 100M integers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sort-based is O(n log n) but cache-friendly once sorted, hash maps are O(n) average but can degrade badly with collisions and have poor locality, bitmaps are great for dense integer domains but blow up in memory for sparse ones.
Start by defining the problem scope: large integer domains, duplicate detection, and the need to compare hash-based counting, sort-based methods, and bitmap approaches. For each method, describe the algorithm, then analyze worst-case time and space complexity, and discuss cache behavior (locality, misses). Conclude with practical recommendations based on domain size, memory constraints, and performance requirements.
Pro tip: Emphasize that bitmap is only feasible when the integer domain is dense and bounded; for sparse or unbounded domains, hash or sort-based methods are more practical. Mention that cache behavior often dominates performance in large-scale duplicate detection, so choose algorithms with good locality.
Clarify the integer domain size, density, memory limits, and whether duplicates are exact. This sets the context for comparing methods.
Explain hash-based counting (hash table with counts), sort-based (sort then scan), and bitmap (bit array indexed by integer). Keep it concise.
For each, state worst-case time (e.g., hash: O(n) average but O(n^2) worst-case with collisions; sort: O(n log n); bitmap: O(n) but space O(U)) and space (hash: O(k) distinct; sort: O(n) or O(1) extra; bitmap: O(U/8)).
Compare memory access patterns: hash tables have random access causing cache misses; sorting has sequential access but may incur multiple passes; bitmap has random access but compact size improves cache utilization.
Conclude which method suits which scenario: bitmap for dense small domains, hash for sparse and fast average-case, sort for external memory or when order matters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the function's contract and expected behavior, then systematically design test cases that cover normal operation, edge cases, and performance. Use a structured test suite with clear naming and assertions, and discuss how you would validate correctness and efficiency.
Pro tip: Mention that you would use property-based testing (e.g., Hypothesis) to automatically generate diverse inputs and catch unexpected edge cases, and that you would also test for time and space complexity to ensure scalability.
Clarify the function's signature, return type, and expected behavior for duplicates (e.g., return list of duplicates, count, or boolean). Confirm assumptions about input types and constraints.
List categories: empty input, all unique, all duplicates, mixed positive/negative, large inputs, and possibly single element, two elements, and inputs with multiple duplicates.
For each category, create concrete examples with expected outputs. Include boundary cases like maximum integer values and inputs with zero.
Write test functions using a framework like pytest or unittest, with descriptive names and assertions. Use parameterization to cover multiple cases efficiently.
Run tests, ensure they pass, and consider adding performance tests for large inputs. Discuss how you would handle failures and refine tests.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.