Started with the hash map solution which is the obvious answer, O(n) time and O(k) space where k is distinct values.
Start by clarifying the problem constraints (e.g., data type, memory limits, whether the array is sorted) and then present multiple approaches, from naive to optimized, discussing time and space complexity for each. Emphasize the tradeoffs between simplicity, performance, and memory usage, and conclude with a recommendation based on typical scenarios.
Pro tip: Mention that for small, bounded integer ranges, a direct-address array can be more efficient than a hash map, but for general elements, a hash map is usually the go-to. Also, note that if the array is sorted, a two-pointer or single-pass counting approach can achieve O(n) time with O(1) extra space.
Ask about the element type (integers, strings, etc.), array size, memory limits, and whether the array is sorted. This determines which approaches are feasible.
For each element, scan the entire array to count occurrences. This is O(n^2) time and O(1) space, but inefficient for large n.
Use a hash map to store counts. Iterate through the array once, updating counts. This is O(n) time and O(k) space, where k is the number of distinct elements.
Sort the array (O(n log n)) and then count consecutive equal elements in one pass. This uses O(1) extra space if sorting in-place, but modifies the input.
Compare time/space complexity, stability, and practical considerations (e.g., hash map overhead, sorting cost). Recommend the hash map for general unsorted data, or sorting if memory is tight and modification is allowed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.