I knew this problem but blanked on which data structure to lead with.
Start by clarifying the problem and constraints, then discuss both brute-force and optimized solutions. Focus on explaining a Fenwick tree or merge sort based approach that achieves O(n log n) time, and analyze trade-offs between time and space.
Pro tip: Mention that this is the classic 'count of smaller numbers after self' problem and that Google interviewers often expect you to derive the Fenwick tree solution from scratch, so practice explaining the intuition behind the data structure.
Ask about input size, range of integers, and whether duplicates count as smaller. Confirm that the output should be an array of the same length.
Explain a simple O(n^2) solution using nested loops to establish a baseline and show understanding of the problem.
Describe an O(n log n) approach using a Fenwick tree (BIT) or merge sort, explaining how to process elements from right to left and query counts efficiently.
Compare time and space complexity of different approaches, and discuss when a simpler solution might be acceptable based on constraints.
Write clean code for the chosen approach, handle edge cases, and walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.