← Plymouth Rock Assurance Corporation Interview Insights
Started with the naive recursive version because I always do that to show I understand the problem, then walked through memoization.
Start by clarifying the problem (zero-indexed, expected input range) and then present an iterative solution with O(n) time and O(1) space, which is optimal for a single query. Discuss trade-offs with other approaches (recursive, memoized, matrix exponentiation) and address large n by explaining integer overflow and possible mitigations like arbitrary-precision arithmetic or modular arithmetic.
Pro tip: For a data science role, emphasize that in practice you'd often use a closed-form or matrix exponentiation for very large n, but for typical n an iterative approach is simplest and most efficient. Also mention that Python's arbitrary-precision integers handle overflow automatically, but in fixed-width languages you'd need to consider overflow or use modular arithmetic.
Confirm zero-indexing, expected input range, and whether the result should be exact or modulo some number. Ask about potential large n to tailor the solution.
Write a simple iterative function that computes the nth Fibonacci number in O(n) time and O(1) space. Explain why this is efficient for a single query.
State that the iterative approach takes O(n) time and O(1) space. Compare with naive recursion (O(2^n) time, O(n) space) and memoization (O(n) time, O(n) space).
Explain that for very large n, O(n) time may be too slow; mention faster methods like matrix exponentiation (O(log n)) or fast doubling. Address integer overflow: in Python, integers are arbitrary precision, but in fixed-width languages, use modular arithmetic or big integers.
Conclude that for typical interview constraints, the iterative solution is best; for large n, consider advanced methods. Highlight awareness of trade-offs and practical considerations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.