I jumped straight to sorting and counting, which works but I could tell they wanted me to talk through a hash map approach first.
Start by clarifying the definition of mode and tie-breaking rules, then propose an efficient solution using a hash map to count frequencies. After counting, determine the maximum frequency and collect all values with that frequency; if the maximum frequency is 1, return None, otherwise return the list of modes (or a single mode if unique).
Pro tip: Discuss the trade-offs between time and space complexity, and mention that for large datasets, a streaming approach or using a heap could be more memory-efficient. Also, clarify whether the function should return a single mode or a list when ties occur, as this affects the implementation.
Ask about the expected return type when multiple modes exist (e.g., list of modes or any one mode) and confirm that if all values are unique, return None.
Use a hash map (dictionary) to count frequencies of each integer, which allows O(n) time complexity. Alternatively, consider sorting the list if memory is a concern, but that increases time to O(n log n).
Iterate through the list, updating the count for each element in the hash map. Track the maximum frequency seen so far to avoid a second pass.
After counting, if the maximum frequency is 1, return None. Otherwise, collect all keys with frequency equal to the maximum and return them as a list (or a single mode if unique).
State that the time complexity is O(n) and space complexity is O(n) in the worst case. Mention that if the list is sorted, we could find modes in O(n) time with O(1) extra space, but sorting itself takes O(n log n).
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Felt more straightforward than the mode question.
Start by clarifying the problem constraints (e.g., array size, value range, duplicates) and then propose an efficient algorithm. Use the Sieve of Eratosthenes to precompute primes up to n, then iterate through the array to filter primes. Discuss time and space complexity and potential trade-offs.
Pro tip: Mention that for very large n, a segmented sieve can reduce memory usage, and for small arrays, trial division might be simpler. Also, highlight that Amazon values scalable solutions, so emphasize efficiency and handling edge cases.
Ask about array size, value range, duplicates, and whether the output should be sorted or preserve order. Confirm if n is the maximum value or the array length.
Decide between trial division (O(√n) per number) and Sieve of Eratosthenes (O(n log log n) for all numbers up to n). For large n, sieve is better; for small arrays, trial division may suffice.
If using sieve, create a boolean array of size n+1, mark non-primes, then iterate through the input array and collect numbers that are prime. If using trial division, check each number individually.
Discuss time and space complexity: Sieve uses O(n) space and O(n log log n) time; trial division uses O(1) extra space but O(k√n) time for k elements. Mention that sieve is preferable when n is large and many queries are expected.
Consider edge cases: n < 2 (no primes), duplicates (output unique primes or preserve duplicates?), and memory constraints. For very large n, suggest segmented sieve or caching primes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.