Warmup question, single linear scan, nothing to it.
Start by clarifying the problem constraints (e.g., array size, data types, whether the array can be empty) and then propose a simple linear scan solution. Discuss the time and space complexity, and consider edge cases such as empty arrays or arrays with a single element. If appropriate, mention alternative approaches like sorting or using built-in functions, but emphasize that linear scan is optimal for unsorted arrays.
Pro tip: Demonstrate awareness of production code by discussing how to handle edge cases gracefully (e.g., returning null or throwing an exception for empty arrays) and mentioning that in real-world scenarios, you might use a library function but understanding the underlying algorithm is crucial.
Ask about array size, data types, whether the array can be empty, and if there are any memory or time constraints. This shows you think before coding.
Explain that you will iterate through the array once, keeping track of the minimum value seen so far. Initialize the minimum with the first element or infinity, depending on handling of empty arrays.
State that the time complexity is O(n) and space complexity is O(1), which is optimal for an unsorted array since you must examine each element at least once.
Discuss how to handle empty arrays (e.g., return null, throw an exception, or return a sentinel value) and arrays with one element. Also consider negative numbers and duplicates.
Implement the function in your preferred language, then walk through a few test cases (e.g., empty array, single element, all negative, mixed) to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where the interview actually happened.
Start by clarifying constraints (array size, value range, memory limits) and then compare the three approaches: sorting (O(n log n) time, O(1) extra space), hash map (O(n) time, O(n) space), and counting array (O(n + k) time, O(k) space). For each, explain how to compute the mode, discuss tradeoffs, and recommend the best choice based on the scenario.
Pro tip: Mention that the hash map approach is generally preferred for unsorted arrays with arbitrary values, but if the value range is small and known, the counting array is optimal. Also, note that sorting modifies the input, which may be undesirable.
Ask about array size, value range, whether the array can be modified, and memory limitations. This determines which approach is most suitable.
Sort the array, then scan to find the longest run of equal elements. Time: O(n log n), Space: O(1) extra (or O(n) if sorting cannot be in-place).
Iterate through the array, count frequencies in a hash map, then find the key with the maximum count. Time: O(n), Space: O(n).
Create an array of size equal to the range, count occurrences, then find the index with the maximum count. Time: O(n + k), Space: O(k), where k is the range size.
Discuss when each approach is best: sorting for low memory, hash map for general case, counting array for small known range. Mention edge cases like ties or empty array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by contrasting the classic in-memory mode algorithm (e.g., Boyer-Moore majority vote for a single element or hash map for exact mode) with the streaming/memory-constrained setting. Then present a spectrum of solutions: exact algorithms with trade-offs (e.g., Misra-Gries, Count-Min Sketch) and approximate algorithms (e.g., reservoir sampling, space-saving), highlighting the balance between accuracy, memory, and update time. Finally, discuss how to choose based on requirements like exactness, frequency of queries, and data characteristics.
Pro tip: Mention that for strict memory constraints, you might need to accept approximation and discuss error bounds (e.g., Misra-Gries guarantees no overestimation and bounded underestimation). Also, note that if the stream is skewed, a simple heavy-hitters algorithm often suffices, but for uniform distributions, you may need more sophisticated sketches.
Ask about the definition of 'mode' (single element, all elements with max frequency, top-k), memory limits, whether exactness is required, and the nature of the stream (insertions only, deletions, sliding window).
Explain that exact mode in one pass with limited memory is impossible for arbitrary data (requires Ω(n) space). Mention that if memory is sufficient, a hash map works, but for strict constraints, exactness may be sacrificed.
Describe algorithms like Misra-Gries (frequent items), Count-Min Sketch (frequency estimation), or Space-Saving (top-k). Explain their memory-accuracy trade-offs and error guarantees.
Compare update time, query time, memory usage, and accuracy. Discuss how to handle deletions (e.g., using sketches with counters) and sliding windows (e.g., exponential histograms).
Based on the clarified requirements, suggest a suitable approach, such as using Misra-Gries for heavy hitters with bounded memory, or a combination of sketches for more complex scenarios.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.