I jumped straight to hash-set because that's the reflex answer and it is fine, O(n) time, O(n) space.
Start by clarifying constraints (e.g., array size, value range, memory limits) and then present multiple approaches with increasing efficiency: brute force, sorting, hash set, and in-place marking. For each, analyze time and space complexity, and discuss trade-offs such as whether the input can be modified or if extra space is allowed.
Pro tip: Mention that if the array values are within a known range (e.g., 1 to n), you can use the array itself as a hash table by marking visited indices, achieving O(n) time and O(1) extra space. This demonstrates deep understanding of space-time trade-offs and often impresses interviewers.
Ask about the input size, value range, whether the array can be modified, and memory constraints. This determines which approaches are feasible.
Describe the naive O(n^2) comparison and the O(n log n) sorting method, noting their simplicity but inefficiency for large inputs.
Explain using a hash set to track seen elements, achieving O(n) time but O(n) extra space. Discuss when this is acceptable.
If values are in range 1 to n, use index marking (e.g., negate values or add n) to find duplicates in O(n) time and O(1) extra space, noting it modifies the array.
Compare time/space complexities, modification of input, and practical considerations. Recommend the best approach based on constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I started sweating a little.
First, clarify the problem context: what operation is needed (e.g., find duplicates, missing numbers, frequency count) and constraints (time, space, mutability). Then compare bitmask, counting array, and in-place index marking in terms of time/space complexity, implementation simplicity, and trade-offs, highlighting when each is optimal given the bounded range 1–200.
Pro tip: Mention that with a small fixed bound like 200, a bitmask of 4 64-bit words is extremely space-efficient and cache-friendly, but if you need frequencies, a counting array is simpler; in-place marking is best when memory is tight and mutation is allowed.
Ask what operation is required (e.g., detect duplicates, find missing numbers, count frequencies) and note constraints like time, space, and whether the input can be modified.
Explain that a bitmask uses one bit per possible value (1–200), requiring only 200 bits (~25 bytes). It supports O(1) set/test operations and is ideal for presence/absence queries, but not for counting frequencies.
Describe using an array of size 201 (or 200) to store frequencies. It uses O(n) extra space but allows O(1) increment and lookup, and is straightforward to implement.
Explain that if the input array can be mutated, you can use the array itself as a hash table by marking visited indices (e.g., negating values or adding n). This achieves O(1) extra space but modifies input and requires careful handling.
Summarize trade-offs: bitmask for minimal space and fast presence checks; counting array for frequency counts and simplicity; in-place marking for O(1) space when mutation is allowed. Choose based on the specific problem requirements.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.