My first instinct was to just divide the total product by each element, which is the obvious wrong answer given the constraint.
Use two passes: first compute prefix products (product of all elements to the left of each index), then compute suffix products (product of all elements to the right) and multiply them together. This avoids division and achieves O(n) time and O(n) space (or O(1) extra space if output array is reused).
Pro tip: Clarify edge cases upfront, like arrays with zeros or negative numbers, and mention that the output array can be used to store intermediate results to optimize space. Also, discuss trade-offs between time and space complexity.
Restate the problem: for each index i, output[i] = product of all elements except nums[i]. Note constraints: no division, O(n) time. Ask clarifying questions about input size, zeros, and negative numbers.
Explain that you'll compute prefix products in one pass and suffix products in another, then combine. This avoids division and meets linear time.
Initialize an output array. For each index i from left to right, set output[i] to the product of all elements before i. Update a running prefix product.
Traverse from right to left, maintaining a running suffix product. Multiply output[i] by the suffix product to get the final result.
State time complexity O(n) and space complexity O(n) for output (or O(1) extra if output is reused). Discuss handling of zeros, empty array, and single-element array.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.