The naive pass to find the max first and then collect all matching indices works fine, but I kept second-guessing whether they wanted a single-pass solution.
Start by clarifying the problem constraints (e.g., array size, data type, whether the array can be empty) and then propose a linear scan solution that tracks the maximum value and collects all indices where it occurs. After the scan, randomly select one index from the collected list to satisfy the random tie-breaking requirement. Discuss time and space complexity and consider edge cases.
Pro tip: Mention that you can achieve O(1) space by using reservoir sampling during the scan, which is a more elegant solution than storing all indices. This shows you think about optimization and can handle randomness without extra memory.
Ask about array size, data types, whether the array can be empty, and if the random selection needs to be uniformly distributed. Confirm that returning any maximum index is acceptable when there are duplicates.
Propose a two-pass or one-pass solution: first find the maximum value, then collect all indices with that value and randomly pick one. Alternatively, use reservoir sampling to do it in one pass with O(1) space.
State that the time complexity is O(n) and discuss space complexity: O(n) if storing all indices, O(1) with reservoir sampling. Explain the trade-off between simplicity and memory efficiency.
Discuss edge cases: empty array (return -1 or throw exception), single element, all elements equal. Explain how to ensure uniform random selection among maximum indices.
Implement the chosen approach in code, using clear variable names and comments. Walk through a few test cases, including duplicates, to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.