Start by clarifying the problem constraints and edge cases, then propose a single-pass solution that computes the ratio for each product and tracks the maximum. Emphasize O(n) time and O(1) space, and handle ties by only updating when a strictly greater ratio is found.
Pro tip: Mention that using floating-point division can introduce precision errors, so compare ratios using cross-multiplication (rating1 * price2 > rating2 * price1) to avoid floating-point issues, especially with large numbers.
Ask about input size, data types, whether prices can be zero, and if arrays are guaranteed non-empty. Confirm that ties should return the smallest index.
Briefly mention that a naive solution would compute all ratios and find the max, but this is O(n) time and O(n) space if storing ratios, which can be optimized.
Iterate through the arrays once, maintaining the best index and best ratio so far. For each product, compute the ratio and compare with the best; update only if strictly greater to handle ties.
Explain that to avoid floating-point precision issues, compare ratios using cross-multiplication: rating[i] * price[best] > rating[best] * price[i]. This also naturally handles ties by not updating on equality.
State that the solution runs in O(n) time and O(1) space. Walk through a small example, including a tie case, to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.